Research Reports of the International Centre for Numerical Methods in Engineering (CIMNE) : Scipedia

A finite point method for elasticity problems
E. Oñate, F. Perazzo, J. Canet

(2001). Research Report, Nº PI202

Abstract
The basis of the finite point method (FPM) for the fully meshless solution of elasticity problems in structural mechanics is described. A stabilization technique based on a finite calculus procedure is used to improve the quality of the numerical solution. The efficiency and accuracy of the stabilized FPM in the meshless analysis of simple linear elastic structural problems is shown in some examples of applications.
Abstract
The basis of the finite point method (FPM) for the fully meshless solution of elasticity problems in structural mechanics is described. A stabilization [...]
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Finite element analysis of membrane structures
R. Taylor

(2001). Research Report, Nº PI203

Abstract
This report summarizes the formulation for a large displacement formulation of a membrance composed of three-node triangular elements. A formulation in terms of the deformation gradient is first constructed in terms of nodal variables. In particular, the use of the right Caunchy-Green deformation tensor is shown to lead to a particulary simple representation in terms of nodal quantities. This may then be used to construct general models for use in static and transient analyses.
Abstract
This report summarizes the formulation for a large displacement formulation of a membrance composed of three-node triangular elements. A formulation in terms of the deformation [...]
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On discontinuous Galerkin methods
O. Zienkiewicz, R. Taylor

(2001). Research Report, Nº PI204

Abstract
Discontinuous Galerkin methods have received considerable attention in recent years for applications to many problems in which convection and diffusion terms are present. Several alternatives for treating the diffusion flux effects have been introduced, as well as, for treatment of the convective flux terms. This report summarizes some of the treatments that have been proposed. It also considers how elementary finite volume methods may be considered as the most primative form of a discontinuous Galerkin method as well as how it may be formed as a finite element method. Several numerical examples are included in the report which summarize results for discontinuous Galerkin solutions of one-dimensional problems with a scalar variable. Results are presented for diffusion-reaction problems, convection-diffusion problems, and a special problem with a turning point. We identify aspects which relate to accuracy as well as stability of the method.
Abstract
Discontinuous Galerkin methods have received considerable attention in recent years for applications to many problems in which convection and diffusion terms are present. [...]
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Possibilities of finite calculus in computational mechanics
E. Oñate

(2001). Research Report, Nº PI205

Abstract
The expression ‘finite calculus’ refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a space–time domain of finite size. The governing equations resulting from this approach are different from those of infinitesimal calculus theory and they incorporate new terms which depend on the dimensions of the balance domain. The new governing equations allow the derivation of naturally stabilized numerical schemes using any discretization procedure. The paper discusses the possibilities of the finite calculus method for the finite element solution of convection–diffusion problems with sharp gradients, incompressible fluid flow and incompressible solid mechanics problems and strain localization situations.
Abstract
The expression ‘finite calculus’ refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a [...]
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A finite element methodology for local global damage evaluation in civil engineering structures
A. Hanganu, E. Oñate, A. Barbat

(2001). Research Report, Nº PI206

Abstract
The paper introduces a new global damage evaluation method, thus obtaining a meaningful global damage index (GDI). A numerical procedure for predicting a local and global damage in civil engineering structures using the finite element method and a continuum damage model is presented. The method is adequate for computing the limit load in reinforced concrete structures and for predicting the failure mechanisms. Details of the damage model used a given together with a description of the finite element implementation and the procedure for computing the global damage parameters. Examples of applications to the non-linear analysis of a range of reinforced concrete structures presented.
Abstract
The paper introduces a new global damage evaluation method, thus obtaining a meaningful global damage index (GDI). A numerical procedure for predicting a local and global [...]
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Posibilidades de los métodos numéricos en el mundo industrial
E. Oñate

(2001). Research Report, Nº PI207

Abstract
Se presentan en el artículo las ideas básicas de qué son los métodos numéricos, cuáles son los métodos numéricos más populares, cómo se aplican para resolver ecuaciones diferenciales de interés práctico en ingeniería y qué posibilidades y limitaciones tienen para ayudarnos a entender mejor el mundo que nos rodea. El contenido del artículo se completa con diversas aplicaciones prácticas del método de elementos finitos a diversos problemas de ingeniería.
Abstract
Se presentan en el artículo las ideas básicas de qué son los métodos numéricos, cuáles son los métodos numéricos más [...]
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A finite element method for fluid-structure interaction with surface waves using finite calculus formulation
E. Oñate, J. García-Espinosa

(2001). Research Report, Nº PI208

Abstract
A stabilized semi-implicit fractional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus procedure. A mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described. Examples of the efficiency of the stabilized semi-implicit algorithm for the analysis of fluid-structure interaction problems in totally or partially submerged bodies is presented.
Abstract
A stabilized semi-implicit fractional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized [...]
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Recovering lower bounds of the error postprocessing implicit residual a posteriori error estimates
P. Díez, N. Parés, A. Huerta

(2001). Research Report, Nº PI209

Abstract
Classical Residual type error estimators approximate the error flux around the elements and yield upper bounds of the exact (or references) error. Lower bounds of the error are also needed in goal oriented adaptivity and for bounds on functional outputs. This work introduces a simple and cheap strategy to recover a lower bound estimate from standard upper bound estimates. This lower bound mat be also to assess the effectivity of the former estimate and to improve it.
Abstract
Classical Residual type error estimators approximate the error flux around the elements and yield upper bounds of the exact (or references) error. Lower bounds of the error [...]
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A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation
E. Oñate, J. García-Espinosa

(2000). Research Report, Nº PI180

Abstract
A stabilized semi-implicit step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized governing equations for the viscous fluid and the free surface are derived at a differential level via finite increment calculus procedure. A mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described. Examples of the efficiency of the stabilized semi-implicit algorithm for the analysis of fluid-structure interaction problems in totally or partially submerged bodies is presented.
Abstract
A stabilized semi-implicit step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized governing [...]
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Stabilization techniques for finite element analysis of convection-diffusion problems
E. Oñate, M. Manzan

(2000). Research Report, Nº PI183

Abstract
The accurate solution of convection type problems on practical grids has been ever a challenging issue, and invariably some sort of stabilization is needed in order to get a physical solution. This has pushed researchers to develop various stabilization algorithms used in every day practice by numerical analysts. In this chapter some methods are presented along with a new finite increment calculus approach to obtain the different algorithms using higher order conservation equations.
Abstract
The accurate solution of convection type problems on practical grids has been ever a challenging issue, and invariably some sort of stabilization is needed in order to get [...]
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The Monte Carlo method. Application to the stochastic analysis of sheet stamping processes
J. Hurtado, F. Zárate, E. Oñate

(2000). Research Report, Nº PI184

Abstract
Stochastic Mechanics is a rapidly growing area of research, whose importance is being recognized not only in academic circles but also in industrial practice. This is no doubt due to the fact that most structural properties and loads are either random or uncertain. The first term refers to a natural chaotic variation of the parameter, while the second is associated to the human lack of knowledge about it. Both kinds of unpredictability work together in rendering doubtful the results of a (usually single) deterministic mechanical analysis. When thinking about the randomness and uncertainty linked to all physical parameters and phenomena a big question mark closes the large list of numbers produced by a finite element calculation. In Stochastic Mechanics there are several techniques to analyse the natural scatter of strains and stresses caused by the dispersion in the given loads and/or the structural parameters. The most general one is the Monte Carlo method. However, it must be recognized that is as well the most costly in computational terms. Nevertheless, this cost has becoming feasible with the advance in Computer Science, specially with the advent of parallel computing, due to the fact that a Monte Carlo calculation is intrinsically a task that can be performed in parallel. The present report is intended to provide the reader an introduction to the Monte Carlo method in the context of Computational Mechanics. The technique is applied to the analysis of the uncertainty spread in a stamping process. The first chapter summarises the Monte Carlo method and its theoretical backgrounds. The second chapter is devoted to the case study, namely, the stochastic analysis of a square cup deep drawing problem. Finally, the basic equations governing the mechanical modelling of the stamping process are summarized in the appendix.
Abstract
Stochastic Mechanics is a rapidly growing area of research, whose importance is being recognized not only in academic circles but also in industrial practice. This is no doubt [...]
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Stabilized finite element approximation of transient incompressible flows using orthogonal subscales
R. Codina

(2000). Research Report, Nº PI185

Abstract
In this paper we present a stabilized finite element formulation to solve the Oseen equations as a model problem involving both convection effects and the incompressibility restriction. The need for stabilization techniques to solve this problem arises because of the restriction in the possible choices for the velocity and pressure spaces dictated by the inf-sup condition, as well as the instabilities encountered when convection is dominant. Both can be overcome by resorting from the standard Galerkin method to a stabilized formulation. The one presented here is based on the subgrid scale concept, in which unresolvable scales of the continuous solution are approximately accounted for. In particular, the approach developed herein is based on the assumption that unresolved subscales are orthogonal to the finite element space. The motivation of the method is fully described. It is also shown that this formulation is table and optimally convergent for an adequate choice of the algorithmic on which the method depends.
Abstract
In this paper we present a stabilized finite element formulation to solve the Oseen equations as a model problem involving both convection effects and the incompressibility [...]
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Pressure stability in fractional step finite element methods for incompressible flows
R. Codina

(2000). Research Report, Nº PI186

Abstract
The objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows. For the classical first order projection method, it is shown that there is a pressure control which depends on the time step size, and therefore there is a lower bound for this time step for stability reasons. The situation is much worse for a second order scheme in which part of the extremely weak. To overcome these shortcomings, a stabilized fractional step finite element method is also considered, and its stability is analyzed. Some simple numerical examples are presented to support the theoretical results.
Abstract
The objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows. For the classical first order projection [...]
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Implementation of a stabilized finite element formulation for the incompressible Navier-Stokes equations based on a pressure gradient projection
R. Codina, J. Blasco, G. Buscaglia, A. Huerta

(2000). Research Report, Nº PI187

Abstract
We discuss in this paper some implementation aspects of a finite element formulation for the incompressible Navier-Stokes which allows the use of equal order velocity-pressure interpolations. The method consists in introducing the project of the pressure gradient and adding the difference between the pressure Laplacian and divergence of this new field to the incompressibility equations, both multiplied by suitable algorithmic parameters. The main purpose of this paper is to discuss how to deal with the new variable in the implementation of the algorithm. Obviously, it could be treated as one extra unknown, either explicitly or as a condensed variable. However, we take for granted that the only way or another. Here we discuss some iterative schemes to perform this uncoupling of the pressure gradient projection (PGP) from the calculation of the velocity and the pressure, both for stationary and the transient of the linearization loop and the iterative segregation of the PGP, whereas in the second the main dilemma concerns the explicit or implicit treatment of the PGP.
Abstract
We discuss in this paper some implementation aspects of a finite element formulation for the incompressible Navier-Stokes which allows the use of equal order velocity-pressure [...]
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Prediction of damage and failure in civil engineering structures using a finite element model.
E. Oñate, A. Hanganu, J. Canet

(2000). Research Report, Nº PI188

Abstract
The paper describes a finite element damage model for non linear analysis of concrete or reinforced structures. It is show how can be effectively used to predict local and global damage up to structural failure. Examples of applications of the model to the analysis of different structures such as a nuclear containment shell, a housing building and the domes of St. Mark Basilica are presented.
Abstract
The paper describes a finite element damage model for non linear analysis of concrete or reinforced structures. It is show how can be effectively used to predict local and [...]
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Rigid-flexible body analysis without rotation parameters
R. Taylor

(2000). Research Report, Nº PI189

Abstract
This paper addresses the coupled flexible and rigid body response of solids undergoing large motions and deformations. The formulation is presented in a form which is free of rotation parameters and thus avoids the need of finding compatible integration formulae for translations and rotations. The motion of each rigid body is represented in terms of the nodal parameters of a simplex element subject to constraints which ensure rigid motions. Flexible structural members for rods and shells are then expressed in terms of displacement and relative displacement parameters leading to total system of equations involving only translation degrees of freedom. The motions are integrated using classical energy and momentum conserving schemes, thus leading to systems which are unconditionally stable for Hamiltonian (elastic-rigid) systems. The only requirement for absolute stability is that the non-linear algebraic equations representing the solution at each time step must converge. The formulation is illustrated in two dimensions by representative numerical problems which involve both rigid and flexible parts or multi-rigid body situations. In all cases the conservation properties are observed.
Abstract
This paper addresses the coupled flexible and rigid body response of solids undergoing large motions and deformations. The formulation is presented in a form which is free [...]
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Locking in the incompressible limit for the element free galerkin method
A. Huerta, S. Fernández-Méndez

(2000). Research Report, Nº PI190

Abstract
Volumetric locking (locking in the incompressible limit) for linear elastic isotropic materials is studied in the context of the Element Free Galerkin method. The modal analysis developed here shows here shows that the number of non-physical locking modes is independent of the dilation parameter (support of the interpolation functions). Thus increasing the dilation parameter does not suppress locking. Nevertheless, an increase in the dilation parameter does reduce the energy associated to the non-physical locking behavior. Although more locking modes are present in the Element Free Galerkin method with quadratic consistency than with the standard biquadratic finite element method. Finally, numerical examples are shown.
Abstract
Volumetric locking (locking in the incompressible limit) for linear elastic isotropic materials is studied in the context of the Element Free Galerkin method. The modal analysis [...]
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Límites de los métodos numéricos
E. Oñate

(2000). Research Report, Nº PI191

Abstract
Se plantean en el artículo los límites de los métodos numéricos para resolver cualquier problema que afecte a la vida del hombre. Se discute la capacidad de la razón para expresar todos los problemas del universo en forma matemática, y la posibilidad de encontrar su solución en forma numérica. Finalmente, se especula sobre el alcance y posibilidad de los métodos numéricos en el amplio campo de las ciencias sociales
Abstract
Se plantean en el artículo los límites de los métodos numéricos para resolver cualquier problema que afecte a la vida del hombre. Se discute la [...]
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El bucle de los números
E. Oñate

(2000). Research Report, Nº PI192

Abstract
El artículo presenta una sucinta panorámica sobre la evolución de los métodos numéricos dese la antigua Babilonia hasta nuestros días. Se destaca como la máxima Pitagórica de que “todo es número”, adquiere plena actualidad en nuestros días, en que, con la ayuda de los ordenadores, podemos dar respuestas numéricas a prácticamente cualquier problema que afecte a la vida del hombre. Recorriendo ese bucle de los números se relata brevemente en el artículo como la humanidad ha evolucionado paralelamente en su aspiración de cuantificar los fenómenos de la naturaleza, y como el paso de los pueblos ha ido de la mano de los avances en expresar numéricamente la solución de sus problemas más cotidianos.
Abstract
El artículo presenta una sucinta panorámica sobre la evolución de los métodos numéricos dese la antigua Babilonia hasta nuestros días. [...]
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Simulación por ordenador del comportamiento resistente de estructuras: El laboratorio virtual de estructuras
E. Oñate, A. Hanganu, J. Miquel, B. Suárez

(2000). Research Report, Nº PI193

Abstract
Se presenta el concepto de Laboratorio Virtual de Estructuras (LAVE) para evaluar por ordenador la capacidad resistente de estructuras de hormigón y el coeficiente de seguridad al colapso utilizando modelos de cálculo no lineal basados en la teoría del daño y el método de elementos finitos. Se describen diversos ejemplos de aplicación del LAVE al análisis de la resistencia última de estructuras de hormigón en masa y armado.
Abstract
Se presenta el concepto de Laboratorio Virtual de Estructuras (LAVE) para evaluar por ordenador la capacidad resistente de estructuras de hormigón y el coeficiente [...]
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Del ábaco de fichas a Internet
E. Oñate

(2000). Research Report, Nº PI194
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The braid of numbers
E. Oñate

(2000). Research Report, Nº PI195
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Meshless analysis of incompressible flows using the Finite Point Method
E. Oñate, C. Sacco, S. Idelsohn

(2000). Research Report, Nº PI196

Abstract
A stabilized finite point method (FPM) for meshless analysis of incompressible fluid flows is presented. The stabilization approach is based in the finite calculus (FIC) procedure. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the PFM is described. Examples of application of the stabilized FPM to the solution of incompressible flows problems are presented.
Abstract
A stabilized finite point method (FPM) for meshless analysis of incompressible fluid flows is presented. The stabilization approach is based in the finite calculus (FIC) procedure. [...]
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Stabilized finite element approximation of transient incompressible flows using orthogonal subscales
R. Codina

(2000). Research Report, Nº PI197

Abstract
In this paper we present a stabilized finite element method to solve the transient Navier-Stokes equations based on the decomposition of the unknowns into resolvable and sub grid scales. The latter are approximately accounted for, so as to end up with a stable finite element problem which, in particular, allows to deal with convection-dominated flows and the use of equal velocity-pressure interpolations. Three main issues are addressed. The first is a method to estimate the behavior of the stabilization parameters based on a Fourier analysis of the problem for the subscales. Secondly, the way to deal with transient problems discretized using a finite difference scheme is discussed. Finally, the treatment of the nonlinear term is also analyzed. A very important feature of this work is that the sub grid scales are taken as orthogonal to the finite element space. In the transient case, this simplifies considerably the numerical scheme.
Abstract
In this paper we present a stabilized finite element method to solve the transient Navier-Stokes equations based on the decomposition of the unknowns into resolvable and sub [...]
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On isotropic scalar damage models for the numerical analysis of concrete structures
R. Faria, J. Oliver, M. Cervera

(2000). Research Report, Nº PI198

Abstract
Within the framework of Continuum Damage Mechanics some isotropic scalar damage models for concrete are revisited, with emphasis on a recent one proposed by the authors. This scalar damage model is based on the assumption that a stress split is required to capture unilateral behaviour exhibited by concrete when passing from tension to compression. Similar assumptions are pursued on many scalar damage models, yet with many differences being encountered on the strategies adopted for the implementation of such split, which sometimes is performed over the strain tensor. In this paper a discussion on the implications of those splits is conducted, as well as on the norms that define the elastic domain in the stress space. For the proposed damage model a strain-driven formalism is adopted, but the stress split is performed on the effective elastic stress tensor, which is shown to correspond to a split of the Cauchy stress tensor. This strategy improves the algorithmic efficiency as much as required for the seismic analysis of large-scale problems, and circumvents many of the drawbacks present in similar damage models. Besides, two scalar damage variable are introduced as internal variables, as well as an inelastic strain tensor. Efficiency of the proposed constitutive model is illustrated through numerical applications. Algorithmic implementation is also detailed.
Abstract
Within the framework of Continuum Damage Mechanics some isotropic scalar damage models for concrete are revisited, with emphasis on a recent one proposed by the authors. This [...]
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Interface GiD-SAP90 elemento ASOLID
J. Maristany, F. Salinas, A. Mestre

(2000). Research Report, Nº PI199
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Desarrollos y aplicaciones de modelos de fractura en la escuela de ingenieros de caminos de Barcelona
E. Oñate

(2000). Research Report, Nº PI201

Abstract
El artículo es una panorámica de los aspectos teóricos y algunas aplicaciones prácticas de los modelos de fractura desarrollados por diversos grupos en la Escuela de Ingenieros de Caminos de Barcelona (EICB) durante los últimos quince para el análisis no lineal de estructuras. La motivación fundamental para el desarrollo de estos modelos se centra en el análisis de la seguridad de estructuras de hormigón en masa y armado. La mayor parte de los modelos se basan en la teoría de daño continuo y utilizan el método de los elementos finitos para la solución numérica. Los modelos de daño se han extendido y aplicado también con éxito el análisis de diversas estructuras de edificios históricos. Los desarrollos más recientes de estos modelos en la EICB incluyen la predicción de fenómenos de localización en estructuras de hormigón y el análisis del comportamiento no lineal de estructuras con materiales compuestos. De todos estos modelos se presentan en el artículo unas breves pinceladas, las aplicaciones más relevantes y las referencias donde pueden encontrarse los detalles de cada caso.
Abstract
El artículo es una panorámica de los aspectos teóricos y algunas aplicaciones prácticas de los modelos de fractura desarrollados por diversos grupos [...]
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Métodos avanzados para el cálculo de la resistencia de la última de estructuras de hormigón
E. Oñate, A. Hanganu

(1999). Research Report, Nº PI176

Abstract
Se presenta en el trabajo una panorámica de los modelos más recientes para evaluar la resistencia última de estructuras de hormigón en masa y armado. Se presta especial atención al modelo de daño, descubriéndose varios ejemplos de aplicación de este modelo.
Abstract
Se presenta en el trabajo una panorámica de los modelos más recientes para evaluar la resistencia última de estructuras de hormigón en masa y armado. [...]
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Thermo‐mechanical analysis of industrial solidification processes
M. Cervera, C. Agelet de Saracibar, M. Chiumenti

(1999). Research Report, Nº PI153

Abstract
The paper presents an up‐to‐date finite element numerical model for fully coupled thermo‐mechanical problems, focussing in the simulation of solidification processes of industrial metal parts. The proposed constitutive model is defined by a thermo‐visco‐elasto‐(visco)plastic free energy function which includes a contribution for thermal multiphase changes. Mechanical and thermal properties are assumed to be temperature‐dependent, and viscous‐like strains are introduced to account for the variation of the elastic moduli during the cooling process. The continuous transition between the initial fluid‐like and the final solid‐like behaviour of the part is modelled by considering separate viscous and elasto‐plastic responses as a function of the solid fraction. Thermo‐mechanical contact conditions between the mould and the part are specifically considered, assuming that the heat flux is a function of the normal pressure and the thermal and mechanical gaps. A fractional step method arising from an operator split of the governing equations is used to solve the non‐linear coupled system of equations, leading to a staggered product formula solution algorithm suitable for large‐scale computations. Representative simulations of industrial solidification processes are shown, and comparison of computed results using the proposed model with available experimental data is given.
Abstract
The paper presents an up‐to‐date finite element numerical model for fully coupled thermo‐mechanical problems, focussing in the simulation of solidification processes [...]
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A stabilized finite element method for generalized stationary incompressible flows
R. Codina

(1999). Research Report, Nº PI148

Abstract
In this paper we describe a finite element formulation for the numerical solution of the stationary Navier-Stokes equations including Coriolis forces and the permeability of the medium. The stabilized method is based on the algebraic version of the sub-grid scale approach. We first describe this technique for general systems of convection-diffusion-reaction equations and then we apply it to linearized flow equations. The important point is the design of the matrix of stabilization parameters that the method has. This design is based on the identification of the stability problems of the Galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix. This, together with the convergence analysis of the linearized problem, leads to a simple expression for the stabilization parameters in the general situation considered in the paper. The numerical analysis of the linearized problem also shows that the method has optimal convergence properties.
Abstract
In this paper we describe a finite element formulation for the numerical solution of the stationary Navier-Stokes equations including Coriolis forces and the permeability [...]
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Rotation‐free triangular plate and shell elements
E. Oñate, F. Zárate

(1999). Research Report, Nº PI149

Abstract
The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with translational degrees of freedom as the only nodal variables. The simplest elements of the two families based on combining a linear interpolation of displacements with cell centred and cell vertex finite volume schemes are presented in detail. Examples of the good performance of the new rotation‐free plate and shell triangles are given.
Abstract
The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with [...]
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A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation
E. Oñate

(1999). Research Report, Nº PI150

Abstract
A stabilized finite element formulation for incompressible viscous flows is derived. The starting point are the modified Navier-Stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus (FIC) procedure. Application of the standard finite element Galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields. The FIC method also provides a natural explanation for the stabilization terms appearing in all equations for both the Navier-Stokes and the simpler Stokes equations. Transient solution schemes with enhanced stabilization properties are also proposed. Finally a procedure for computing the stabilization parameters is presented.
Abstract
A stabilized finite element formulation for incompressible viscous flows is derived. The starting point are the modified Navier-Stokes equations incorporating naturally the [...]
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Numerical differentiation for Non-Trivial consistent tangent matrices: An application to the MRS-Lade model
A. Pérez-Foguet, A. Rodríguez-Ferran, A. Huerta

(1999). Research Report, Nº PI151

Abstract
In Reference the authors have shown that numerical differentiation is a competitive alternative to analytical derivatives for the computation of consistent tangent matrices. Relatively simple models were treated in that reference. The approach is extended here to a complex model: the MRS-Lade model. This plastic model has a cone-cap yield surface and exhibits strong coupling between the flow vector and the hardening moduli. Because of this, derivating these quantities with respect to stresses and internal variables –crucial step in obtaining consistent tangent matrices- is rather involved. Numerical differentiation is used here to approximate these derivatives. The approximated derivatives are then used 1) to compute consistent tangent matrices (global problem) and 2) to integrate the constitutive equation at each Gauss point (local problem) with the Newton-Raphson method. The choice of the stepsize (i.e. the perturbation in the approximation schemes), based on the concept of relative stepsize, poses no difficulties. In contrast to previous approaches the global problems. The computational efficiency (CPU time) and robustness of the proposed approach is illustrated by means of several numerical examples, where the major relevant topics are discussed in details.
Abstract
In Reference the authors have shown that numerical differentiation is a competitive alternative to analytical derivatives for the computation of consistent tangent matrices. [...]
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New degrees of freedom in computational mechanics: mesh free finite point method, rotation free shell triangles and moving free meshes
E. Oñate

(1999). Research Report, Nº PI154

Abstract
The paper presents an overview of some recent developments in computational mechanics introducing new degrees of “freedom” allowing the solution of more challenging problems. First advances in the finite point method for fully mesh free solution in fluid and solid mechanics are described. Next, new rotation free shell triangles incorporating membrane and bending effects are presented. Finally, a simple method allowing free movement of meshes is described. Examples of application of all the “free” methods are given.
Abstract
The paper presents an overview of some recent developments in computational mechanics introducing new degrees of “freedom” allowing the solution of more challenging [...]
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Transferencia de calor por conducción. Verificación del programa ED-Poiss
S. Robles, F. Zárate

(1999). Research Report, Nº PI161
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A nodal-based implementation of a stabilized Finite Element Method for Incompressible Flow Problems
R. Codina

(1999). Research Report, Nº PI156

Abstract
The objective of this paper is twofold. First, a stabilized finite element method for the incompressible Navier-Stokes is presented, and several numerical experiments are conducted to check its performance. This method is able to deal with all the instabilities that the standard Galerkin method presents, namely, the pressure instability, the instability arising in convection dominated situations and also the less popular instabilities found when the Navier-Stokes equations have a dominant Coriolis force, or there is a dominant absorption term arising from the small permeability of the medium where the flow takes place. The second objective is to describe a nodal-based implementation of the finite element formulation introduced. This implementation is based on an a priori calculation of the integrals appearing in the formulation and then the construction of the matrix approximations, this matrix and this vector can be constructed directly for each nodal point, without the need to loop over element and thus making the calculations much faster. In order to be able to do this, all the variables have to be defined at the nodes of the finite element mesh, not on the elements. This is also so for the stabilization parameters of the formulation. However, doing this given rise to questions regarding the consistency and the conservation properties of the final scheme that are addressed in this paper.
Abstract
The objective of this paper is twofold. First, a stabilized finite element method for the incompressible Navier-Stokes is presented, and several numerical experiments are [...]
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Simulation of Construction of RCC Dams. I: Temperature and Aging
M. Cervera, J. Oliver, T. Prato

(1999). Research Report, Nº PI157

Abstract
In this work a numerical procedure for the simulation of the construction process of Roller Compacted Concrete (RCC) dams is described. The basis of the work is a coupled thermos-chemo-mechanical model for the behaviour of concrete at early ages that allows to simulate the observed phenomena of hydration, aging, creep and damage. In this first part only the thermochemical aspects of the simulation of the construction process are presented. The proposed procedure can accurately predict the evolution in time of the hydration degree and the hydration heat production. This allows to obtain the temperature field inside the dam at any time during the construction and the following years. The evolution of the compressive and tensile strengths and elastic moduli can also be predicted in terms of the evolutions of the hydration degree and the temperature conditions. Results from 2d and simplified vertical 1D models are compared and several parametric studies are carried out. The simulation and discussion of the mechanical aspects of the construction process are relegated to a companion paper that follows.
Abstract
In this work a numerical procedure for the simulation of the construction process of Roller Compacted Concrete (RCC) dams is described. The basis of the work is a coupled [...]
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BLAY3D: 3D boundary layer code. User's guide.
M. Storti

(1999). Research Report, Nº PI158

Abstract
This is the user’s guide for the BLAY3D code (version 2.2 of December 28, 1998). BLAY3D is a fluid mechanics code for solving the incompressible Boundary Layer Equations (BLE), based on a spectral approximation in the transversal direction and a mesh-less approximation on the surface of the body. It contains a basic description of what are the BLE, the governing equations involved, how they are solved, which is the data and how is it entered in order to be processed by BLAY3D, what kind of result BLAY3D generates, and finally several examples are shown.
Abstract
This is the user’s guide for the BLAY3D code (version 2.2 of December 28, 1998). BLAY3D is a fluid mechanics code for solving the incompressible Boundary Layer Equations [...]
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Stabilization of incompressibility and convection through orthogonal sub-scale in finite element methods
R. Codina

(1999). Research Report, Nº PI162

Abstract
Two apparently different forms of dealing with the numerical instability due to the incompressibility constraint of the stokes problem are analyzed in this paper. The first of them is the stabilization thought the pressure gradient projection, which consists of adding a certain least-squares form of the difference between the pressure gradient and its L² projection onto the discrete velocity space in the variational equations of the problem. The second is a sub-grid scale method, whose stabilization effect is very similar to that of the Galerkin/least-squares method for the Stokes problem. It is shown here that the first method can also be recast in the framework of sub-grid scale method with a particular choice for the space of sub-scales. This leads to a new stabilization procedure, whose applicability to stabilize convection is also studied in this paper.
Abstract
Two apparently different forms of dealing with the numerical instability due to the incompressibility constraint of the stokes problem are analyzed in this paper. The first [...]
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On the constitutive modeling of coupled thermomechanical phase-change problems
C. Agelet de Saracibar, M. Cervera, M. Chiumenti

(1999). Research Report, Nº PI163

Abstract
This paper deals with a thermodynamically consistent numerical formulation for coupled thermoplastic problems including phase-change phenomena and frictional contact. The final goal is to get an accurate, efficient and robust numerical model, able for the numerical simulation of industrial solidification processes. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. All the material properties have been considered to be temperature dependent. The constitutive behavior has been defined by a thermoviscous/elastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. The constitutive model proposed accounts for a continuous transition between the initial liquid state, the intermediate mushy state and the final solid state taking place in a solidification process. In particular, a pure viscous deviatoric model has been used at the initial fluid-like state. A thermomecanical contact model, including a frictional hardening and temperature dependent coupled potential, is derived within a fully consistent thermodinamical theory. The numerical model has been implemented into the computational finite element code COMET developed by the authors. Numerical simulations of solidification processes show the good performance of the computational model developed.
Abstract
This paper deals with a thermodynamically consistent numerical formulation for coupled thermoplastic problems including phase-change phenomena and frictional contact. The [...]
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Advances in the stabilized finite point method for structural mechanics
E. Oñate, F. Perazzo, J. Canet

(1999). Research Report, Nº PI164

Abstract
The basis of the finite point method for the fully meshless solution of structure mechanics problems is described. A new stabilization technique based on a finite increment calculus procedure is used. The efficiency and accuracy of the stabilized finite point method in the meshless analysis of simple structural problems is shown in two examples of applications.
Abstract
The basis of the finite point method for the fully meshless solution of structure mechanics problems is described. A new stabilization technique based on a finite increment [...]
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A methodology for analysis of fluid structure interaction accouting for free surface waves
E. Oñate, J. García-Espinosa

(1999). Research Report, Nº PI166

Abstract
A stabilized semi-implicit frictional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized equations are derived at a differential level via a finite element calculus procedure. A new mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described. One example of the efficiency of the stabilized semi-implicit algorithm for the coupled solution of fluid-structure interaction problems is presented.
Abstract
A stabilized semi-implicit frictional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized [...]
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A finite point method for incompressible flow problems
E. Oñate, C. Sacco, S. Idelsohn

(1999). Research Report, Nº PI167

Abstract
A stabilized finite point method (FPM) for meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment calculus (FIC) procedure developed by Oñate. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the FPM is described. Examples of application of the stabilized FPM to the solution of two incompressible flow problems are presented.
Abstract
A stabilized finite point method (FPM) for meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment [...]
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New rotation free shell triangle for crash-worthiness analysis in parallel PC networks
E. Oñate, F. Zárate, X. Plana, L. Neamtu

(1999). Research Report, Nº PI168

Abstract
A new three node shell triangular element with translational degree of freedom as the only modal variables is presented. The element formulation is based on combining a standard linear finite element interpolation with a cell centered finite volume scheme. Details of the implementation of the element in an explicit dynamic code operating in parallel on networks of PC’s are presented. The efficiency and applicability of the new rotation free shell triangle is shown in the solution of some contact/impact and crash-worthiness problem.
Abstract
A new three node shell triangular element with translational degree of freedom as the only modal variables is presented. The element formulation is based on combining a standard [...]
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Formulación de elementos finitos estabilizada para problemas de transporte convectivo y flujo incompresible mediante técnicas de cálculo finitesimal
E. Oñate

(1999). Research Report, Nº PI169

Abstract
El trabajo muestra que los términos de estabilización para la solución por el MEF de problemas de transporte convectivo y de flujo incompresible, pueden obtenerse de manera natural utilizando aproximaciones de mayor orden en las ecuaciones de balance en un dominio finito. Este procedimiento de cálculo finitesimal permite reinterpretar muchos algoritmos de elementos finitos estabilizados utilizando en la práctica y proporciona también una expresión para calcular los parámetros de estabilización.
Abstract
El trabajo muestra que los términos de estabilización para la solución por el MEF de problemas de transporte convectivo y de flujo incompresible, pueden [...]
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Macroscopic modelling of concrete aging regarding hydration and temperature effects
M. Cervera, R. Faria, J. Oliver, T. Prato

(1999). Research Report, Nº PI170

Abstract
A macroscopic model to account for the hydration and aging phenomena that occur during the early ages of concrete is proposed in this work. Assuming the percolation of water through the hydrates already formed as the dominant mechanism of cement hydration, a normalized variable called hydration degree is adopted in the model, which has an evolution law that can be easily calibrated through an adiabatic calorimetric test. This methodology allows an accurate prediction of the evolution of the hydration degree and the hydration heat production. The evolution of the compressive strength is related to the aging degree, a novel concept which accounts for the effect of the hydration degree and the influence of the curing temperature on the final mechanical properties of concrete, a feature not attended with classic maturity concepts. A wide set of experimental tests validates the proposed model for ordinary and high performance concretes. Fly ash admixture concretes with a large spectrum of cement substitutions can be also modelled with the proposed approach.
Abstract
A macroscopic model to account for the hydration and aging phenomena that occur during the early ages of concrete is proposed in this work. Assuming the percolation of water [...]
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Enrichment and coupling of the finite element and meshless methods
A. Huerta, S. Fernández-Méndez

(1999). Research Report, Nº PI171

Abstract
A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements or meshless methods are used to interpolate: continuity and consistency is preserved. The second one enriches a finite element mesh with processes. In both cases the same formulation is used, convergence is studied and examples are shown.
Abstract
A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements [...]
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Efficient unstructured quadrilateral meshes preserving the prescribed element size
J. Sarrate, A. Huerta

(1999). Research Report, Nº PI172

Abstract
This work devoted to the description of an algorithm for automatic quadrilateral mesh generation. The technique is based on a recursive decomposition of the domain into quadrilateral over complex geometries (there is not need for a previous step where triangles are generated). A background mesh with the desired element sizes allows to obtain the preferred sizes anywhere in the domain. The final mesh can be viewed as the optimal one given the objective function defined. The recursive algorithm induces an efficient data structure which optimizes the computer cost. Several examples are presents to show the efficiency of this algorithm
Abstract
This work devoted to the description of an algorithm for automatic quadrilateral mesh generation. The technique is based on a recursive decomposition of the domain into quadrilateral [...]
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An improved algorithm to smooth graded quadrilateral meshes preserving the prescribed element size
J. Sarrate, A. Huerta

(1999). Research Report, Nº PI173

Abstract
In the generation of quadrilateral unstructured meshes, special attention is focused to the shape of the elements. This is because it is well known that the distortion of the elements and the accuracy of the analysis are closely related. However, in adaptive schemes it is also essential that the new generated mesh meets the prescribed element sizes in order to obtain a solution with the desired precision. In 1982 Giuliani developed a robust rezoning algorithm based on geometrical criteria. It gives proven results is a smooth element size distribution, but elements do not verify the prescribed element size when sharp distributions appear. This paper presents a modification of the Giuliani method that generates non-distorted elements while preserving the element size. Similar to the original method, this modification can be extended to three-dimensional cases
Abstract
In the generation of quadrilateral unstructured meshes, special attention is focused to the shape of the elements. This is because it is well known that the distortion of [...]
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Probabilistic analysis of an a posteriori error estimator for Finite Elements
P. Díez, J. Egozcue

(1999). Research Report, Nº PI175
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EMANT: Programa de análisis de problemas electrotécnicos mediante el método de los elementos finitos
J. Mora, J. Canet, E. Oñate, C. Sacco, L. Martínez

(1999). Research Report, Nº PI177

Abstract
La sencillez conceptual de la electrostática esconde todo un abanico de aplicaciones industriales que precisa de herramientas de cálculo numérico para su optimización. En particular, el diseño de aisladores para sistemas de alta tensión o de las cámaras de tratamiento de alimentos implica una cuidadosa elección de la geometría del sistema y materiales empleados. A la ayuda que supone el conocimiento de la distribución de los campos eléctricos asociados a cada prototipo desde el punto de vista de prestaciones del equipo (homogeneidad de campo, minimización de puntos triples), se añade la interesante posibilidad de contribuir a la comprensión del fenómeno físico (cómo se alteran los alimentos al aplicar un campo eléctrico intenso). Se recoge en las siguientes líneas la formulación desarrollada para escribir un código de resolución de problemas electrostáticos mediante el método de los elementos finitos, no tanto como nuevo problema sino como transición desde otras disciplinas como son la mecánica o transferencia de calor.
Abstract
La sencillez conceptual de la electrostática esconde todo un abanico de aplicaciones industriales que precisa de herramientas de cálculo numérico para [...]
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An anisotropic elastoplastic constitutive model for large deformation analysis of fibre reinforced composites
E. Car, S. Oller, E. Oñate

(1999). Research Report, Nº PI178

Abstract
In this work a generalized anisotropic elastoplastic constitutive model in large deformation is presented. It is used for the analysis of fiber-reinforced composite materials in the frame of the finite element method. Mixing theory is applied to simulate the behavior of the composite material. The elastic anisotropic behavior is simulated with classical elasticity theory, while that of a non-proportional anisotropic solid is simulated by means of the proposed generalized anisotropic elastoplastic model. The approach assumes the existence of a real anisotropic space and of a fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order tensor incorporating complete information on the real anisotropic material. Details of the numerical implementations of the model into a non-linear, large deformations finite element solution scheme are provided. Examples of application showing the performance of the model for the analysis of fiber-reinforced composite materials are given.
Abstract
In this work a generalized anisotropic elastoplastic constitutive model in large deformation is presented. It is used for the analysis of fiber-reinforced composite [...]
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Numerical aerodynamic analysis of large buildings using a finite element model with application to a telescope building
R. Codina, C. Morton, E. Oñate, O. Soto

(1999). Research Report, Nº PI181

Abstract
Presents a numerical strategy for the aerodynamic analysis of large buildings, with an application to the simulation of the air flow within a telescope building. The finite element formulation is presented first, and then the methodology followed to obtain significant data from the calculations is described. The quality of the ventilation of the building is defined by the average residence times, and the feasibility of this ventilation by the actions created on the instruments and the general flow pattern.
Abstract
Presents a numerical strategy for the aerodynamic analysis of large buildings, with an application to the simulation of the air flow within a telescope building. The finite [...]
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Análisis termo-mecánico del proceso de fabricación de un tablero del viaducto de Öresund
T. Prato, R. Faria, M. Cervera, J. Oliver

(1999). Research Report, Nº PI165

Abstract
El objetivo de este trabajo es presentar una metodología para el estudio del riesgo de fisuración de una estructura de hormigón en primeras edades. Para ello, se presenta un modelo termo-quimio-mecánico y se estudia el comportamiento estructural del tablero de uno de los viaductos de acceso al puente de Öresund (Dinamarca) durante el proceso de construcción y los 10 primeros días de vida. Esta obra se encuentra en proceso de construcción en el Yard que la constructora DRAGADOS posee en el Puerto Real (Cádiz). Primeramente, en el Capítulo 2, se describe los fundamentos básicos del modelo numérico que se propone. A continuación, en el Capítulo 3, se presenta un análisis del tablero del viaducto mencionado anteriormente, que consiste en evaluar el riesgo de fisuración provocado por el calentamiento asociado a la liberación del calor de hidratación y su proceso de construcción y los materiales utilizados para la construcción del viaducto. Seguidamente, en el Capítulo 4, se presenta el análisis térmico correspondiente a la simulación del proceso de hidratación del hormigón del tablero. Se incluyen algunos estudios sobre las posibles consecuencias de la modificación del proceso de calentamiento debido al cambio de las condiciones ambientales y de curado. En el Capítulo 5 se presenta el análisis termo-mecánico del proceso de construcción de uno de los tramos del viaducto. Se presentan también estudios alternativos sobre la evolución del riesgo de fisuración bajo diferentes escenarios de ejecución. Para ello se estudia el comportamiento estructural en condiciones de invierno y verano.
Abstract
El objetivo de este trabajo es presentar una metodología para el estudio del riesgo de fisuración de una estructura de hormigón en primeras edades. Para [...]
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El proyecto "BAJEL". Una herramienta de diseño hidrodinámico de buques de pasaje
J. García-Espinosa, L. Rojas, J. Cabezas, J. Alonso

(1998). Research Report, Nº PI140

Abstract
The BAJEL project consists on the validation and final development of a comprehensive computer system to support the hydrodynamic design of ships. It aims at contributing to the optimal design of the new generations of ships, specially passenger vessels, improving their navigation conditions. This project is developed as a result of the joint work of a center specialized in Computational Analysis (CIMNE) and two Hydrodynamic Research Centers (ETSIN and Canal de El Pardo) within the framework of the industrial reality represented by the company BAZAN. This work presents the objectives of the project, describing the computer tools that have served as the basis and starting point for it. It also presents the achievements that in this field have achieved in recent years the member of the research teams. Finally, different results of studies carried out on real geometries of ships with special dedication to high-speed passenger ships are included.
Abstract
The BAJEL project consists on the validation and final development of a comprehensive computer system to support the hydrodynamic design of ships. It aims at contributing to [...]
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Error estimation including pollution assesment for nonlinear finite element analysis
A. Huerta, P. Díez

(1998). Research Report, Nº PI132

Abstract
The present paper proposes a new technique for the definition of the shape design variables in 2D and 3D optimisation problems. It can be applied to the discrete model of the analysed structure or to the original geometry without any previous knowledge of the analytical expression of the CAD defining surfaces. The proposed technique allows the surface continuity to be preserved during the geometry modification process to be defined a priori. This capability allows for the definition of shape variables suitable for every kind of discipline involved in the optimisation process (structural analysis, fluid-dynamic analysis, crash analysis, aerodynamic analysis, etc.).
Abstract
The present paper proposes a new technique for the definition of the shape design variables in 2D and 3D optimisation problems. It can be applied to the discrete model of [...]
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High-order accuarte time-stepping schemes for convection-diffusion problems
J. Donea, B. Roig, A. Huerta

(1998). Research Report, Nº PI135

Abstract
A major objective of the study described in the present paper is to achieve a high accuracy in the time integration of transient convection-diffusion problems and to eventually combine this with new methods for space discretization, such as meshless methods. In this way, a uniformly high-order accurate methodology could be made available for the numerical solution of convection-diffusion problems. Both Padé approximations of the exponential function and Runge-Kutta methods are considered for deriving multi-stage schemes involving first time derivatives only, thus easier to implement than standard Taylor-Galerkin schemes which incorporate second and third time derivatives. After a brief discussion of the stability and accuracy properties of the stability and accuracy properties of the multi-stage schemes and the presentation of illustrative examples, the paper closes with some considerations on the coupling of high-order accurate temporal schemes and meshless methods for the spatial representation.
Abstract
A major objective of the study described in the present paper is to achieve a high accuracy in the time integration of transient convection-diffusion problems and to eventually [...]
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Adaptive finite element strategies based on error assessment
A. Huerta, A. Rodríguez-Ferran, P. Diez

(1998). Research Report, Nº PI136

Abstract
Two main ingredients are needed for adaptive finite element computations. First, the error of a given solution must be assessed, by means of either error estimators or errors indicators. After that, a new spatial discretization must be defined via h, p or r-adaptivity. In principle, any of the approaches for error assessment may be combined with any of the procedures for adapting the discretization. However, some combinations are elearly preferable. The advantages and limitations of the various alternatives are discussed. The most adequate strategies are illustrated by means of several applications in solid mechanics.
Abstract
Two main ingredients are needed for adaptive finite element computations. First, the error of a given solution must be assessed, by means of either error estimators or errors [...]
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Arbitrary Lagrangian-Eulerian formulation for fluid-rigid body interaction
J. Sarrate, A. Huerta, J. Donea

(1998). Research Report, Nº PI137

Abstract
A new formulation for two-dimensional fluid-rigid body interaction problems is developed. In particular, vortex-induced oscillations of a rigid boy in viscous incompressible flow are studied. The incompressible Naiver-Stokes equations are used to describe the motion of the fluid, while it is assumed that the rigid body is mounted on a system consisting of a spring and a dashpot. An arbitrary Lagrangian-Eulerian formulation (ALE) is used in order to account for large boundary motion. A general formulation for coupled problem is obtained by uncoupling the translation motion of the body from its rotational motion and developing a specific algorithm to efficiently handle the nonlinear dependence of the rotations. This general formulation ca be easily applied to multi-body problems. Two numerical examples involving either translations and rotations are presented as an illustration of the proposed methodologies for fluid-rigid body interaction.
Abstract
A new formulation for two-dimensional fluid-rigid body interaction problems is developed. In particular, vortex-induced oscillations of a rigid boy in viscous incompressible [...]
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Modelo constitutivo elastoplástico anisótropo en deformaciones finitas para análisis de materiales compuestos reforzados con fibras
E. Car, S. Oller, E. Oñate

(1998). Research Report, Nº PI139

Abstract
En este trabajo se presenta un modelo constitutivo elastoplástico anisótropo generalizado en deformaciones finitas para el análisis de materiales compuestos multifase utilizando el método de los elementos finitos. En la modelización del material compuesto se utiliza la teoría de mezclas en la cual se inserta el modelo constitutivo elastoplástico propuesto. El comportamiento elástico de un sólido anisótropo se simula con la teoría de la elasticidad clásica, mientras que el comportamiento no proporcional de un sólido anisótropo se simula mediante un modelo elastroplástico anisótropo en régimen de grandes deformaciones basado en una formulación isótropa equivalente. Este modelo asume la existencia de un espacio real anisótropo y de un espacio ficticio isótropo, en el cual se resuelve un problema ficticio. Ambos espacios están relacionados a través de una transformación lineal utilizando un tensor de cuarto orden que contiene la información del material real. Por último se presenta los detalles de la implementación numérica del modelo propuesto en un código de elementos finitos y ejemplos de aplicación del modelo al análisis del comportamiento lineal y no-lineal de materiales compuestos.
Abstract
En este trabajo se presenta un modelo constitutivo elastoplástico anisótropo generalizado en deformaciones finitas para el análisis de materiales compuestos [...]
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Estudio comparativo de métodos numéricos para resolver ecuaciones en derivadas parciales lineales
D. Vives

(1998). Research Report, Nº PI141

Abstract
La principal ventaja del método de los elementos finitos y del método de los volúmenes finitos es la capacidad que tienen de tratar con dominios ciertamente complejos de manera simple dándole un carácter local a la aproximación. Estos métodos dividen el dominio en un número finito de subdominios, que cumplen unas condiciones geométricas regulares. Para el caso 2-dimensional, ambos métodos no presentan grandes dificultades para la generación de una malla, mientras que en el caso 3-dimensional ello resulta bastante complicado y es uno de los problemas que actualmente se están estudiando con mayor profundidad, ya que, en la mayoría de los casos, la creación de una malla resulta computacionalmente más caro que la resolución numérica del problema. Principalmente por este motivo, se empezaron a estudiar los denominados métodos sin malla. Los primeros métodos se basaron es un intento de generalizar el método de las diferencias finitas a mallas irregulares. Otro de los primeros métodos estudiados son los denominados Smooth Particle Hydrodynamics (SPH). Estos métodos trabajan la ausencia de contornos, aunque no son tan precisos, como los métodos de elementos finitos regulares. Esta clase de métodos suele utilizarse frecuentemente para modelar fenómenos astrofísicos que no posean contornos. Recientemente, se han estudiado una clase de métodos, donde no es necesaria la creación de una malla. Los principios métodos son el método de los elementos difusos (DE), cuyo principal precursor fue Nayroles y el método Element-Free Galerkin (EFG). Ambos se basan en que las funciones interpolatorias son polinomios que tratan de aproximar la función en los nodos por un método de aproximación por mínimos cuadrados. En los dos casos no basta para formular las ecuaciones de Galerkin con una colección de nodos y una descripción del contorno. La diferencia entre ambos métodos radica es que en los métodos de los elementos difusos no se consideran necesarios. Los dos métodos son consistentes y bastante estables, aunque sustancialmente más caros que los métodos SPH. Gracias a un estudio de Duarte y Oden y a otro de Babuska y Melenk se han comprendido con mayor profundidad, y dicen que son métodos basados en la partición de la unidad. Estos personajes junto con Liu fueron los primeros en probar la convergencia de estos dos métodos. Finalmente, para concluir, hay que destacar la presencia de otra clase de métodos denominados Reproducing Kernel Particle (RKP), cuyo principal precursor fue Liu. En la sección 2, veremos una introducción teórica a algunos métodos como son elementos finitos, el método de los elementos difusos, el método EFG, los métodos SPH y finalmente el método de las diferencias finitas para el caso bidimensional. En la sección 3, abordaremos algunos aspectos sobre la programación de ellos, que ha sido efectuada, en el caso 1-dimensional, donde se han programada todos los anteriormente citados, salvo los SPH. La sección 4, contendrá breves remarcar sobre la programación de los métodos en el caso 2-dimensional, donde se han implementado los mismos métodos que en el caso 1-dimensional, con la excepción única de reemplazar el método de los elementos finitos por el de las diferencias finitas. La sección 5 y 6 se comentarán los resultados obtenidos para el caso 1-dimensional y 2-dimensional respectivamente. La seccón 7 contendrá algunas conclusiones y comentarios sobre el estudio.
Abstract
La principal ventaja del método de los elementos finitos y del método de los volúmenes finitos es la capacidad que tienen de tratar con dominios ciertamente [...]
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A viscoplastic model including non-linear isotropic and kinematic hardening
M. Chiumenti, C. Agelet de Saracibar, M. Cervera

(1998). Research Report, Nº PI143

Abstract
In this work the formulation of a general elasto-viscoplastic constitutive model is consistently derived within a thermodynamic framework. The constitutive behavior has been by a elasto-plastic free energy function. Plastic response has been modeled considering a J2 viscoplastic constitutive model, including non-linear isotropic and kinematic hardening. Time integration and linearization of the constitutive model is also introduced. Finally, a number of numerical tests will show the mechanical response of a specimen submitted to a loading-unloading cycle.
Abstract
In this work the formulation of a general elasto-viscoplastic constitutive model is consistently derived within a thermodynamic framework. The constitutive behavior has been [...]
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Numerical differentiation for local and global tangent operators in computational plasticity
G. Chiandussi, G. Bugeda, E. Oñate

(1998). Research Report, Nº PI144

Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed. The method considers the mesh as a fictitious elastic body subjected to prescribed displacements at selected boundary points. The mechanical properties of each mesh element are appropriately selected in order to minimize the deformation and the distortion of the mesh elements. Different selection strategies have been used and compared in their application to simple examples. The method avoids the use of remeshing in the solution of shape optimization problems and reduces the number of remeshing steps in the solution of coupled fluid–structure interaction problems.
Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed. The method considers the mesh as a fictitious elastic body subjected to [...]
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Thermo-chemo-mechanical model for concrete. I: Hydration and aging
M. Cervera, J. Oliver, T. Prato

(1998). Research Report, Nº PI146

Abstract
In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. The model allows simulation of the observed phenomena of hydration, aging, damage, and creep. It is formulated within an appropriate thermodynamic framework, from which the state equations are derived. In this first part, the formulation and assessment of the thermochemical aspects of the model are presented. It is based on the reactive porous media theory, and it can accurately predict the evolution in time of the hydration degree and the hydration heat production. The evolution of the compressive and tensile strengths and elastic moduli is related to the aging degree, a concept introduced to account for the effect of the curing temperature in the evolution of the mechanical properties. The short- and long-term mechanical behavior is modeled by means of a viscoelastic damage model that accounts for the aging effects. The formulation and assessment of the mechanical part of the model are relegated to a companion paper.
Abstract
In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. The model allows simulation of the observed phenomena of hydration, [...]
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A simple method for automatic update of finite element meshes
G. Chiandussi, G. Bugeda, E. Oñate

(1998). Research Report, Nº PI147

Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed. The method considers the mesh as a fictitious elastic body subjected to prescribed displacements at selected boundary points. The mechanical properties of each mesh element are appropriately selected in order to minimize the deformation and the distortion of the mesh elements. Different selection strategies have been used and compared in their application to simple examples. The method avoids the use of remeshing in the solution of shape optimization problems and reduces the number of remeshing steps in the solution of coupled fluid–structure interaction problems
Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed. The method considers the mesh as a fictitious elastic body subjected to [...]
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A fractional step method for the solution of the compressible Navier-Stokes equations
R. Codina, M. Vázquez, O. Zienkiewicz

(1997). Research Report, Nº PI118

Abstract
In this paper we present a summary of the splitting technique for both compressible and incompressible flows previously proposed in [22, 23, 7]. Also, we extend it to the case of a fully implicit treatment of the viscous and convective terms of the momentum equations. For incompressible flows, this scheme for a non-standard treatment of the boundary conditions. For compressible flows the continuity equation involves two variables which must be related through the equation of state. Convective terms of the conservation equations to be solved are stabilized by means of a Characteristic – Galerkin scheme. Also, in the presence of shocks some additional dissipation is needed. Both numerical techniques are explained here taking the transport of a scalar quantity as a model problem.
Abstract
In this paper we present a summary of the splitting technique for both compressible and incompressible flows previously proposed in [22, 23, 7]. Also, we extend it to the [...]
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On stabilized finite element methods for linear systems of convection-diffusion-reaction equations
R. Codina

(1997). Research Report, Nº PI126

Abstract
A stabilized finite element method for solving systems of convection-diffusion-reaction equations is studied in this paper. The method is based on the subgrid scale approach and an algebraic approximation to the subscales. After presenting the formulation of the method, it is analyzed how it behaves under changes of variables, showing that it relies on the law of change of the matrix of stabilization parameters associated to the method. An expression for this matrix is proposed for the case of general coupled systems of equations that is an extension of the expression proposed for a 1D model problem. Applications of the stabilization technique to the Stokes problem with convection and to the bending of Reissner-Mindlin plates are discussed next. The design of the matrix of stabilization parameters is based on the identification of the stability deficiencies of the standard Galerkin method applied to these two problems.
Abstract
A stabilized finite element method for solving systems of convection-diffusion-reaction equations is studied in this paper. The method is based on the subgrid scale approach [...]
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On the stabilization of numerical solution for advective-diffusive transport and fluid flow problems
E. Oñate

(1996). Research Report, Nº PI81

Abstract
The concept of the so called “artificial or balancing diffusion” used to stabilize the numerical solution of advective diffusive transport and fluid flow problems is revised in this paper. It is shown that the standard forms of the balancing diffusion terms, usually chosen in a heuristic manner, can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation (or equilibrium) principles. This allows us to reinterprete many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter.
Abstract
The concept of the so called “artificial or balancing diffusion” used to stabilize the numerical solution of advective diffusive transport and fluid flow [...]
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Comparing two algorithms to add large strains to a small strain finite element code
A. Rodríguez-Ferran, A. Huerta

(1996). Research Report, Nº PI91

Abstract
Two algorithms for the stress update (i.e., time-integration of the constitutive equation) in large strain solid mechanics are discussed, with particular emphasis on two issues: the incremental objectivity and the implementation aspects. It is shown that both algorithms are incrementally objective (i.e., they treat rigid rotations properly) and that they can be employed to add large strain capabilities to a small large deformation paths (rigid rotation, simple shear, extension, extension and compression, dilatation, extension and rotation), have been used to test and compare the two algorithms, both for elastic and plastic analysis. These test evidence different time integration accuracy for each algorithm. However, it is demonstrated that the, in general, less accurate algorithm gives exact results for shear-free deformation paths.
Abstract
Two algorithms for the stress update (i.e., time-integration of the constitutive equation) in large strain solid mechanics are discussed, with particular emphasis on two issues: [...]
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Comparison of some finite element methods for solving the diffusion-convection-reaction equation
R. Codina

(1996). Research Report, Nº PI101

Abstract
In this paper we describe several finite element methods for solving the diffusion-convection-reaction equation. None of them is new, although the presentation is non-standard in an effort to emphasize the similarities and differences between them. In particular, it is shown that the classical SUPG method is very similar to an explicit version of the Characteristic-Galerkin method, whereas the Taylor-Galerkin method has a stabilization effect similar to a sub-grid scale model, which is un turn related to the introduction of bubbles functions.
Abstract
In this paper we describe several finite element methods for solving the diffusion-convection-reaction equation. None of them is new, although the presentation is non-standard [...]
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Adaptive finite element computations of hypersonic inviscid flows around a double ellipsoid.
T. Fischer, E. Oñate

(1995). Research Report, Nº PI60

Abstract
This report documents the potential capabilities of adaptive inviscid flow calculations on unstructured meshes in three dimensions using the finite element method. The finite element formulation of the compressible Euler and Navier-Stokes equations is based on a two-step explicit Taylor-Galerkin scheme. Adaptive remeshing is applied to enhance the numerical solution in the vicinity the shocks. Particular emphasis is put on the generation of unstructured tetrahedral meshes as well as in the discussion of estimating the error in the numerical solution. Finally, an application to a well-known 3D high speed flow problem is shown where adaptive remeshing techniques become essential to keep the computational cost within reasonable limits. Its results are compared to some seemingly best reference solutions using other algorithms.
Abstract
This report documents the potential capabilities of adaptive inviscid flow calculations on unstructured meshes in three dimensions using the finite element method. The finite [...]
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PARAMESH. Two dimensional unstructured parallel mesh generation program
J. Mestres, E. Oñate, G. Bugeda

(1995). Research Report, Nº PI61
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A fractional-step method for the incompressible navier-stokes equations related to a predictor-multicorrector algorithm
J. Blasco, R. Codina, A. Huerta

(1995). Research Report, Nº PI63

Abstract
An implicit fractional-step method for the numerical solution of the time-dependent incompressible Naiver-Stokes equations in primitive variables is developed and studied in this paper. The method, which is first order accurate in the time-step, is shown to convergence to an exact solution of the equations. By adequately splitting the viscous term, it allows to enforce full Dirichlet boundary conditions on the velocity in all substeps of the scheme, while needing no boundary condition at all for the pressure. It is also shown to be related to an iterative predictor-multicorrector algorithm for evolution equations, when this is applied to the incompressible Naiver-Stokes system. A new derivation of the algorithm in a general setting is provided. Two different finite element interpolations are considered for the implementation of the algorithm; numerical results obtained with them for standard benchmark cases are presented.
Abstract
An implicit fractional-step method for the numerical solution of the time-dependent incompressible Naiver-Stokes equations in primitive variables is developed and studied [...]
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A finite element formulation for Stokes proble allowing equal velocity-pressure interpolation
R. Codina, J. Blasco

(1995). Research Report, Nº PI66

Abstract
In this paper we study a variational formulation of the Stokes problem that accommodates the use of equal velocity-pressure finite element interpolations. The motivation of this method relies on the analysis of a class of fractional-step methods for the Navier-Stokes equations for which it is known that equal interpolations yield good numerical results. The reason for this turns out to be the difference between two discrete Laplacian operators computed in a different manner. The formulation of the Stokes problem considered here aims to reproduce this effect. From the analysis of the finite element approximation of the problem we obtain stability and optimal error estimates using velocity-pressure interpolations satisfying of the standard formulation. In particular, this condition is fulfilled by the most common equal order interpolations.
Abstract
In this paper we study a variational formulation of the Stokes problem that accommodates the use of equal velocity-pressure finite element interpolations. The motivation of [...]
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Finite point methods in computational mechanics
E. Oñate, S. Idelsohn, O. Zienkiewicz

(1995). Research Report, Nº PI67
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Numerical simulation of wear phenomena
M. Chiumenti, C. Agelet de Saracibar

(1995). Research Report, Nº PI68

Abstract
Over the last few years a remarkable progress has been achieved in the field of computational contact mechanics. The formulation by means of variational inequalities, as well as the use of return mapping algorithms and tools of mathematical programming have provided efficient frameworks for the numerical treatment of such problems. The objective is the numerical simulation of the frictional behavior of steel sheets subjected to large sliding distances and variables normal pressures. A simple phenomenological model for frictional contact accounting for wear effects is proposed with a view to its prediction and consequent minimization. Within the context of thermodynamics with internal variables, the coefficient of friction is assumed to be a function of the density of frictional work resulting in a theory analogous to classical work hardening elastoplasticity. The finite element simulation of a series of sliding test is carried out and the results are compared with experiment. The calculation presented in the following in the following have been performed at the Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE) in Barcelona, Spain with the program for finite element analysis FEAP.
Abstract
Over the last few years a remarkable progress has been achieved in the field of computational contact mechanics. The formulation by means of variational inequalities, as [...]
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A new frictional time integration algorithm for large slip multi-body frictional contact problems
C. Agelet de Saracibar

(1995). Research Report, Nº PI69

Abstract
In this paper a new frictional time integration algorithm suitable for large slip multibody frictional contact problems is presented. The algorithm is introduced within the simple context of a model problem: the sliding motion of a particle onto a rough surface. Time integration of frictional traction is performed introducing a new slip path parametrization, which is defined independently traction is performed introducing element parametrization used in the spatial triangularization. The key point of the algorithm is that now, in presence of large slips, problems associated with slip motions such that a full incremental slip path is not within a single surface element, are completed bypassed. Remarkably, the algorithm is defined on the solely basis of the unit outward normal field to the surface without any appeal to the underlying local surface finite element triangularization. Geometrically, the assumed slip path can be viewed as an approximation to the geodesic passing throughout the initial and final points of each incremental slip path. The algorithm is amenable to exact linearization and asymptotic quadratic rate of convergence can be achieved within a Newton-Raphson iterative solution scheme. The algorithm can easily be extended to large slip multi-body frictional contact problems, involving finite strains.
Abstract
In this paper a new frictional time integration algorithm suitable for large slip multibody frictional contact problems is presented. The algorithm is introduced within the [...]
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Numerical analysis of frictional wear contact problems computational model and applications
C. Agelet de Saracibar, M. Chiumenti

(1995). Research Report, Nº PI70

Abstract
In this paper a numerical model for the analysis of multi-body frictional wear contact problems at finite deformations is presented. Wear phenomena are analysed and the main wear mechanics are identified. Archard’s wear law provides an estimate of the amount of wear volume produced during forming operations. Wear phenomena are incorporated into the Coulomb frictional model by considering a friction coefficient as function of an internal variable to be defined as the frictional dissipation or the slip amount. Within the context of a displacement-driven formulation of frictional contact problems, i.e. penalty or augmented Lagrangian methods, and exploiting the computational framework developed for plasticity, two methods are considered for the time integration of the constrained frictional evolution problems: the lowest Backward Difference (BD) method, Backward Euler (BE) algorithm, and an Implicit Runge-Kutta (IRK) method, the generalized Projected Mid-Point (PMP) algorithm. The constrained frictional algebraic problem arising from the application of these time integration algorithms to the constrained frictional evolution problem, is amenable to exact linearization leading to an asymptotic quadratic rate of convergence when used within a Newton-Raphson solution scheme. The numerical model has been implemented into an enhanced version of the computational finite element program FEAP. Numerical examples and simulation of industrial metal forming processes show the performance of the numerical model in the analysis of frictional wear contact problems.
Abstract
In this paper a numerical model for the analysis of multi-body frictional wear contact problems at finite deformations is presented. Wear phenomena are analysed and the main [...]
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Simulación del choque de vehículos por el método de los elementos finitos. Programa "SIMPACT"
J. Rojek, E. Oñate, J. Canet

(1995). Research Report, Nº PI71

Abstract
En este trabajo se presentan las principales características del programa de ordenador “SIMPACT” desarrollado en el Centro Internacional de Métodos Numéricos en Ingeniería de Barcelona para la simulación numérica de problemas de impacto y choque de vehículos. El programa se basa en una formulación de elementos finitos de lámina no lineal incorporando también elementos de sólido y de viga para modelar correctamente todos los componentes resistente típicos de estructuras de vehículos. El programa permite la utilización de algoritmos de integración en el tiempo explícitos incluyendo además modelos constitutivos para materiales compuestos. Los ejemplos que se presentan muestran la aplicación del programa a la deformación de una puerta sometida a un ensayo penetración lateral, el choque frontal de un prototipo de vehículo industrial, y el vuelco de una cabina de autobús.
Abstract
En este trabajo se presentan las principales características del programa de ordenador “SIMPACT” desarrollado en el Centro Internacional de Métodos [...]
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Análisis de procesos de conformado de metales por el método de los elementos finitos. Posibilidades y perspectivas.
E. Oñate

(1995). Research Report, Nº PI72
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Structural analysis and durability assessment of historical construction using a finite element damage model
E. Oñate, A. Hanganu, A. Barbat, S. Oller, R. Vitaliani, A. Saetta, R. Scotta

(1995). Research Report, Nº PI73
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Moving least square approximations for solution of differential equations
R. Taylor, O. Zienkiewicz, E. Oñate

(1995). Research Report, Nº PI74
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A rate-dependent isotropic damage model for the seismic analysis of concrete dams
M. Cervera, J. Oliver, O. Manzoli

(1995). Research Report, Nº PI76

Abstract
In this paper a rate‐dependent isotropic damage model developed for the numerical analysis of concrete dams subjected to seismic excitation is presented. The model is shown to incorporate two features essential for seismic analysis: stiffness degradation and stiffness recovery upon load reversals and strain‐rate sensitivity. The issue of mesh objectivity is addressed using the concept of the ‘characteristic length’ of the fracture zone, to show that both the softening modulus and the fluidity parameter must depend on it to provide consistent results as the computational mesh is refined. Some aspects of the numerical implementation of the model are also treated, to show that the model can be easily incorporated in any standard non‐linear finite element code. The application of the proposed model to the seismic analysis of a large gravity concrete dam shows that the structural response may vary significantly in terms of the development of damage. The inclusion of rate sensitivity is able to reproduce the experimental observation that the tensile peak strength of concrete can be increased up to 50 percent for the range of strain rates that appear in a structural safety analysis of a dam subjected to severe seismic actions.
Abstract
In this paper a rate‐dependent isotropic damage model developed for the numerical analysis of concrete dams subjected to seismic excitation is presented. The model is shown [...]
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Viscous damage model for Timoshenko beam structures
A. Barbat, S. Oller, E. Oñate, A. Hanganu

(1995). Research Report, Nº PI77

Abstract
A local damage constitutive model based on Kachanov’s theory is used within a finite element frame and applied to the case of 2D and 3D Timoshenko beam elements. The model takes into account viscous effects, thus allowing damping to be considered in a rigorous way. A damage index based on potential energy criteria, useful in evaluating the behaviour of structures or of parts of structures, is proposed. The procedure is applied to estimate the damage produced by seismic actions in reinforced concrete building structures, whose response is computed by using a non-linear Newmark-type incremental time integration scheme. Three numerical examples are included; one of them compares results obtained by using the proposed model with results of a laboratory test.
Abstract
A local damage constitutive model based on Kachanov’s theory is used within a finite element frame and applied to the case of 2D and 3D Timoshenko beam elements. The [...]
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Alguns aspectos da simulação numérica pelo método dos elementos finitos da estampagem de chapas finas
E. Casas

(1995). Research Report, Nº PI78
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The energy input spectrum scaling laws and synthetic compatible records
J. Hurtado, A. Barbat

(1995). Research Report, Nº PI79

Abstract
A method for predicting the seismic energy input spectrum is presented. The method is based on the analytical relationship linking this spectrum and other measures of earthquake energy such as power spectrum and Arias intensity, and the results of the statistical analysis made on 120 strong motion records. Upon the same relationships, a method for simulating artificial accelerograms compatible with a prescribed energy input spectrum is also developed. This procedure is used for the calculation of damage indexes for reinforced concrete single-degree-of freedom-systems, corresponding to types of energy input spectra and different ground motion durations.
Abstract
A method for predicting the seismic energy input spectrum is presented. The method is based on the analytical relationship linking this spectrum and other measures of earthquake [...]
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Adaptive control of uncertain coupled mechanical systems: application to base-isolated structures
J. Rodellar, E. Ryan, A. Barbat

(1994). Research Report, Nº PI45

Abstract
A problem of feedback stabilization is addressed for a class of uncertain nonlinear mechanical systems with n degrees of freedom and nc < n control inputs. Each system of the class has the structure of two coupled subsystems with nc and nr degrees of freedom, respectively, a prototype being an uncertain base isolated building structure with n degrees of freedom actively controlled via actuators applying forces to specific degrees of freedom of the base movement, nc < n in number. A nonlinear adaptive feedback strategy is described, which, under appropriate assumptions on the system uncertainties, guarantees a form of practical stability of the zero state. Numerical simulations are also presented to illustrate the application of the control strategy to a base isolated building.
Abstract
A problem of feedback stabilization is addressed for a class of uncertain nonlinear mechanical systems with n degrees of freedom and nc < n control inputs. Each system [...]
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Hybrid control of buildings with nonlinear base isolation
A. Barbat, J. Rodellar, .. Ryan, N. Molinares

(1994). Research Report, Nº PI46

Abstract
A hybrid seismic control system for buildings structures is considered, which combines a class of passive nonlinear base isolator with an active control system. The active control forces are applied to the structural base with the objective of reducing its displacements. An adaptive control law is formulated to compute the control forces in order to assure a form of stable behaviour of the system under seismic excitation and in the presence of uncertainties in the characteristics of the building of the hybrid control system. The global behavoiur of the structure-base isolator system is such that the absolute base displacement is significantly reduced, the price paid being a slight increase of the response of the structure.
Abstract
A hybrid seismic control system for buildings structures is considered, which combines a class of passive nonlinear base isolator with an active control system. The active [...]
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SLAP: Programa para modelado numérico de procesos de esterolitografía utilizando el método de los elementos finitos.
G. Lombera, G. Bugeda, M. Cervera, E. Oñate

(1994). Research Report, Nº PI47

Abstract
Dentro de todos los procesos denominados “Rapid Prototyping”, se presenta en esta publicación el denominado estereolitografía. Estos procesos cuyo origen se remontan a fines de la década de los ochenta, poseen un gran interés por parte de las industrias, dado que posibilitan a la fabricación de piezas en tiempos muy inferiores a los obtenidos por los métodos tradicionales y una gran versatilidad en cuanto a materiales y formas utilizadas. Las máquinas actualmente existentes en el mercado generan de forma automática la pieza a partir de su representación geométrica en un ordenador. El modelado numérico del proceso se justifica por la necesidad de poder predecir la geometría final de la pieza con el objeto de realimentar el proceso variando los parámetros de control, con el fin de obtener la pieza deseada con la mayor precisión posible. En esta publicación se presenta un resumen de las posibilidades del programa “SLAP” desarrollado en el CIMNE (Centro Internacional de Métodos Numéricos en Ingeniería) para simular mediante el método de los Elementos Finitos procesos de fabricación de prototipos por estereolitografía. Asimismo, se presentan las instrucciones para la utilización práctica del programa y algunos ejemplos de aplicación.
Abstract
Dentro de todos los procesos denominados “Rapid Prototyping”, se presenta en esta publicación el denominado estereolitografía. Estos procesos cuyo [...]
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Derivation of the secant stiffness matrix for non linear finite element analysis of solids and trusses
E. Oñate

(1994). Research Report, Nº PI49

Abstract
In this paper the general non symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids using the finite element method is derived. A convenient symmetric expression for a particular value of the parameters is obtained. The geometrically nonlinear formulation is based on a Generalized Lagrangian approach. Detailed expressions of all the relevant matrices involved in the analysis 3D solids are obtained. The possibilities of application of the secant stiffness matrix for nonlinear structural problems including stability, bifurcation and limit load analysis are also discussed. Examples of application are given for the nonlinear analysis of pin joined frames.
Abstract
In this paper the general non symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids using the finite element method is derived. [...]
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3D finite element computations for viscous aerodynamic flows around automobiles
T. Fischer, J. Canet, O. Fruitos, E. Oñate

(1994). Research Report, Nº PI50
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A review of some finite element families for thick and thin plate and shell analysis
E. Oñate

(1994). Research Report, Nº PI53

Abstract
This paper describes a number of triangular and quadrilateral plate and Shell elements derived via Reissner-Mindlin plate theory and mixed interpolation. It shown how by introducing the adequate constrains the original thick plate element evolve into DK forms adequate for this situations only. This evolution process allows to revisite some classical elements like the Morley triangle and also to derive simple plate and shell triangles and quadrilates with only translational degrees of freedom as nodal variables.
Abstract
This paper describes a number of triangular and quadrilateral plate and Shell elements derived via Reissner-Mindlin plate theory and mixed interpolation. It shown how by introducing [...]
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Petrov-Galerkin methods for the transient advective-diffusive equation with sharp gradients
S. Idelsohn, J. Heinrich, E. Oñate

(1994). Research Report, Nº PI51

Abstract
A Petrov–Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally exhibited by the numerical solution of the transient advective–diffusive equation in the vicinity of sharp gradients produced by transient loads and boundary layers. The formulation may be written as a generalization of the Galerkin Least‐Square method.
Abstract
A Petrov–Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally [...]
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Block iterative scheme of the seismic response of base isolated buildings
A. Barbat, N. Molinares, R. Codina

(1994). Research Report, Nº PI52

Abstract
Base insolation systems partially uncoupled a structure from the seismic ground motion by means of specially designed, replaceable, devices inserted between the structure and its foundation. These devices are capable of absorbing part of the energy induced by earthquake [1-4] and drastically reduce the seismic action transmitted to the structure. A numerical simulation of their effect on the seismic response of structures requires algorithms capable of analyzing structures with both elastomeric (hysteric) bearing and sliding (frictional) bearings [5,6]. Different numerical schemes for solving the equations of motion have been proposed. The most often used numerical procedures are monolithic step-by-step integration schemes, that is, schemes that lead to algebraic systems of equations involving both the degrees of freedom corresponding to the structure and the foundation. On the other hand, there is the possibility of coupling these two sets of unknowns interactively, rather than by solving the full algebraic system. These iterative methods, when combined with the proper linearization of the nonlinear terms, yield block iterative schemes as those considered in this paper. Their capability for solving other problems, such as the dam-fluid interaction or the motion of thermally driven flows, is described in reference [7]. In this paper, the application of schemes of this type in computing the seismic response of building structures with base isolation is considered, being this a problem of two systems coupled across their boundary conditions. The corresponding equations of motion are first written and details concerning the possibilities of numerical computation of the seismic response are given. Different manners of formulating block iterative schemes are described in a generic form and are then applied to the studied case. Their effectiveness in then explored on the basis of a complete numerical example.
Abstract
Base insolation systems partially uncoupled a structure from the seismic ground motion by means of specially designed, replaceable, devices inserted between the structure [...]
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Seismic evaluation of concrete dams via continuum damage models
M. Cervera, J. Oliver, M. Galindo

(1994). Research Report, Nº PI54

Abstract
In this paper a general methodology for the analysis of large concrete dams subjected to seismic excitation is outlined. It is valid both for gravity dams (2D representation) and arch dams (3D representation). The method allows for non‐linear material behaviour of the dam, ‘transparent fictitious boundaries’ for dealing properly with in‐coming and out‐going seismic waves, and an efficient procedure to deal with dam‐soil‐fluid interaction. The mechanical behaviour of concrete is modelled using an isotropic damage model which allows for tension and compression damage, and exhibits stiffness recovery upon load reversals. Emphasis is placed in the treatment of fluid‐structure interaction, regarding both formulation and efficiency aspects. A gravity dam and an arch dam are analysed subjected to artificially generated earthquakes of different intensities, and the results are used to study the degree of (un)safety of the dams.
Abstract
In this paper a general methodology for the analysis of large concrete dams subjected to seismic excitation is outlined. It is valid both for gravity dams (2D representation) [...]
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Random vibration of systems subjected to support motion
A. Barbat

(1994). Research Report, Nº PI55
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Arbitrary Lagrangian-Eulerian finite element analysis of strain localization in transient problems
G. Pijaudier-Cabot, L. Bodé, A. Huerta

(1994). Research Report, Nº PI56

Abstract
Nonlocal models guaranty that finite element computations on strain materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality prevents strain localization with zero global dissipation of energy, and consequently finite element calculations converge upon mesh refinements. One of the major drawbacks of these models is that the element size needed in order to capture the localization zone, must be smaller than the internal length. Hence, the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity. This paper deals with the application of the arbitrary Lagrangian-Eulerian (ALE) formulation, well known in hydrodynamics and fluid-structure interaction problems, to transient strain localization in a nonlocal damageable material. It is shown that the ALE formulation which is employed in large boundary motion problems, can also be well suited for nonlinear transient analysis of softening materials where localization bands appear. The remeshing strategy is based on the equi-distribution of an indicator that quantifies the interelement jump of a selected state variable. Two well-known one-dimensional examples illustrate the capabilities of this technique: the first one deals with localization due to a propagating wave in a bar, and the second one studies the wave propagation in a hollow sphere.
Abstract
Nonlocal models guaranty that finite element computations on strain materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality prevents [...]
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Reliability and cost-efficiency of finite methods for non-linear structural analysis
R. Codina, O. Soto

(1994). Research Report, Nº PI58

Abstract
The objective of this paper is to present a finite element formulation to solve the Stokes problem with Coriolis force. This force results in a skew-symmetric term in the weak formulation of the problem that deteriorates the stability of the standard Galerkin finite element method when the viscosity is small. We show that the stability is worsened due to the presence of the pressure gradient to enforce the incompressibility of the flow. The relevance of this effect depends on the relative importance of the viscous force and the Coriolis force, which measured by the Ekman number. When it is small, oscillations occur using the Galerkin approach. To overcome them, we propose two different methods based on a consistent modification of the basic Galerkin formulation. Both methods eliminate oscillations, keeping the accuracy of the formulation and enhancing its numerical stability.
Abstract
The objective of this paper is to present a finite element formulation to solve the Stokes problem with Coriolis force. This force results in a skew-symmetric term in the [...]
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A generalized theory of plasticity
A. Crescenzo, A. Fusco

(1993). Research Report, Nº PI36

Abstract
The classical incremental theory of plasticity is not able to predict plastic strain accumulation during cycling loading. This because plastic deformation may occur only during loading conditions and when the stress point lies on the yield surface F. on the other hand, F remains fixed in the stress space durinf unloading conditions, so thar successice loading does not produce any plastic deformation until the stress point does not reach again F. this work presents a feneralizarion of the classical theory, which allows to describe plastic strain accumulation during cyclic loading. This obtained postulatinf that F follows always the stress point. Moreover, it is assumed the existence of a surface F, which bounds always F and of an elastic surface F, which bounds the stress states at which only elastic strain mat occur. In the limit case F=F the presented generalized theory recovers the classical one.
Abstract
The classical incremental theory of plasticity is not able to predict plastic strain accumulation during cycling loading. This because plastic deformation may occur only during [...]
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An anisotropic elastoplastic model based on an isotropic formulation
S. Oller, S. Botello, J. Canet, E. Oñate

(1993). Research Report, Nº PI41

Abstract
This paper shows a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials. This approach assumes the existence of a real anisotropic space, and other fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order transformation tensor that contains all the information concerning the real anisotropic material. The paper describes the basis of the spaces transformation proposed and the expressions of the resulting secant and tangent constitutive equations. Also details of the numerical integration of the constitutive equation are provided. Examples of application showing the good performance of the model for analysis of orthotropic materials and fibre‐reinforced composites are given.
Abstract
This paper shows a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials. This approach assumes the existence of [...]
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Caltep programa para el cálculo transitorio de la ecacuación de Poisson
F. Zarate, E. Oñate

(1993). Research Report, Nº PI27

Abstract
Esta publicación explica la utilización de un programa de elementos finitos que permita resolver la ecuación de Poisson transitoria, que rige una gran cantidad de problemas físicos como son la transición del calor a través de diversos medios, el flujo de un líquido a través de un medio permeable, problemas de magnetismo, etc. En la publicación describe las etapas que intervienen en un programa de elementos finitos para cálculo de la ecuación de Poisson transitoria incidiendo principalmente en la metodología general de la programación de las diferentes subrutinas, así como en su aplicación a varios problemas. En la última parte de esta publicación se presentan diversos ejemplos de aplicación del programa, así como un listado completo del mismo, una descripción de sus variables más significativas y las instrucciones para la entrada de datos.
Abstract
Esta publicación explica la utilización de un programa de elementos finitos que permita resolver la ecuación de Poisson transitoria, que rige una gran [...]
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A temperature‐based formulation for finite element analysis of generalized phase‐change problems
D. Celentano, E. Oñate, S. Oller

(1993). Research Report, Nº PI28

Abstract
A finite element formulation for solving multidimensional phase-change problems is presented. The formulation considers the temperature as the unique state variable, it is conservative in the weak form sense and it preserves the moving interface condition. In this work, a consistent Jacobian matrix that ensures numerical convergence and stability is derived. Also, a comparative analysis with other different phase-change finite element techniques is performed. Finally, two numerical examples are analyzed in order to show the performance of the proposed methodology.
Abstract
A finite element formulation for solving multidimensional phase-change problems is presented. The formulation considers the temperature as the unique state variable, it is [...]
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Aerodynamic shape optimization using automatic adaptive remeshing
G. Bugeda, E. Oñate, D. Joannas

(1993). Research Report, Nº PI29

Abstract
This work presents a new methodology base on the use adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element Method. A suitable and very general technique for the parametrization of the optimization problem using B-splines to define the boundary is first presented. Then, mesh generation using the advancing front method, the estimation of error and the mesh refinement criterion are studied in the context of shape optimization problems. In particular, the sensitivities of the different ingredients ruling the problem (B-splines, finite element mesh, flow behavior, and error estimator) are studied in detail. The sensitivities of the finite element mesh and the error estimator allow their projection from one design to the next, thus leading to an “a priori knowledge” of the error distribution on the new design without the need of any additional analysis. This information allows to build up a finite element mesh for the new design with a specified and controlled level error. The robustness and reliability of the proposed methodology is checked out with some 2D application examples.
Abstract
This work presents a new methodology base on the use adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element [...]
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A methodology for adaptive mesh refinement in optimum shape design problems
G. Bugeda, E. Oñate

(1993). Research Report, Nº PI31

Abstract
This work presents a methodology based on the use of adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element Method (FEM). A suitable and very general technique for the parametrization of the optimization problem using B-splines to define the boundary is first presented. Then, mesh generation using the advancing front method, the error estimation and the mesh refinement criteria are dealt with in the context of a shape optimization problems. In particular, the sensitivities of the different ingredients ruling the problem (B-splines, finite element mesh, design behaviour, and error estimator) are studied in detail. The sensitivities of the finite element mesh coordinates and the error estimator allow their projection from one design to the next, giving an “a priori knowledge” of the error distribution on the new design. This allows to build up a finite element mesh for the new design with a specified and controlled level of error. The robustness and reliability of the proposed methodology is checked out with some 2D examples.
Abstract
This work presents a methodology based on the use of adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element [...]
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A general procedure ofr deriving thin plate bending elements with one degree of freedom per node
E. Oñate, M. Cervera

(1993). Research Report, Nº PI32

Abstract
A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C₀ finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of the deflection gradient along the sides using a finite volume-like approach. The formulation is particularized for the simplest element of the family, i.e. the three node triangle with three degrees of freedom. The potential of the new element is shown through different examples of application.
Abstract
A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard [...]
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A simple triangular element for thick and thin plate and shell analysis
E. Oñate, F. Zárate, F. Flores

(1993). Research Report, Nº PI33

Abstract
A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field expressed in terms of the mid‐side rotations. Locking is avoided by introducing an assumed linear shear strain field based on the tangential shear strains at the mid‐sides. The element is free of spurious modes, satisfies the patch test and behaves correctly for thick and thin plate and shell situations. The element degenerates in an explicit manner to a simple discrete Kirchhoff form.
Abstract
A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field [...]
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Utilisation de maillages adaptatifs dans un processus d'optimisation de formes en aérodynamique
G. Bugeda, D. Joannas, E. Oñate

(1993). Research Report, Nº PI34

Abstract
L’objet de ce rapport est de presenter l’approche choise par le CIMNE afin d’optimiser des forms, dans le cadre des équations du potentiel incompressible portant. Plus précisément, nous nous intéresserons ici à étudier l’influence de la partie “maillage adaptatif” sur la convergence globale d’un problème d’optimisation de formes. Les formes à optimiser sont des profils d’ailes d’avions (dimension 2). L’approche retenue utilice paramétrisation des formes considérées par des B-splines. Chaque domaine de calcul est alors discrétisé à l’aide d’un algorithme de maillage classique appelé méthode frontale avancée. Afin de definir à l’avance la taille des éléments de la d’erreur pour la solution des équations du potentiel incompressible (c’est l’influence de la précision requise pour cet estimateur, sur la convergence globale du processus, que nous étudierons). Enfin, on écrit le problème de reconstruction sous la forme d’un problème de minimisation, résolu par une méthode de quasi-Newton où le gradient de la fonctionnelle à minimiser est calculé exactement.
Abstract
L’objet de ce rapport est de presenter l’approche choise par le CIMNE afin d’optimiser des forms, dans le cadre des équations du potentiel incompressible [...]
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A new class of constitutive models for soils
A. Crescenzo, A. Fusco

(1993). Research Report, Nº PI35

Abstract
This work presents the theoretical framework of a new class of constitutive models, which allows to respect five simple physical hypotheses on the mechanical behavior of soils. The most significant of them is that the (effective) stress and the specific volume are the state variables of soils. The well-known Cam-Clay model may be seen as a particular case of the presented class of models. However, in its generality, this class of models allows to describe the progressive accumulation of plastic deformation under cyclic loading.
Abstract
This work presents the theoretical framework of a new class of constitutive models, which allows to respect five simple physical hypotheses on the mechanical behavior of soils. [...]
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Evaluación de diferentes elementos finitos basados en la teoría de láminas de Simó
F. Flores, E. Oñate

(1993). Research Report, Nº PI38

Abstract
En este trabajo se presenta la evaluación de varios elementos basados en la teoría de láminas desarrollada por Simó y colaboradores [1-5]. Se ha implementado una versión simplificada del elemento de cuatro nodos y varios elementos triangulares. Los estudios se refieren principalmente al comportamiento no lineal geométrico dentro de una formulación lagrangeana total. Se presentan también algunos ejemplos con comportamiento no lineal material.
Abstract
En este trabajo se presenta la evaluación de varios elementos basados en la teoría de láminas desarrollada por Simó y colaboradores [1-5]. Se ha [...]
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Análisis dinámico de estructura de láminas y vigas
F. Flores, E. Oñate

(1993). Research Report, Nº PI39

Abstract
En este trabajo se realiza inicialmente un resumen teórico de las teorías de láminas y vigas desarrolladas por Simo y colaboradores [2-6,12-15]. Luego se presentan un elemento cuadrilátero y 4 elementos triangulares adecuados para el análisis no lineal geométrico y material en régimen dinámico. Se presentan también un elemento de viga y se propone un criterio de fluencia en esfuerzos generalizados. Se muestran algunos ejemplos del comportamiento de los elementos y la teoría subyacente, incluyendo problemas de contacto entre cuerpos deformables. Finalmente se presentan una metodología para la compatibilización de desplazamientos entre elementos de láminas, vigas y sólidos que permita el análisis de estructuras compuestas sin necesidad de elementos transición entre diferentes elementos y maneje rigidizadores excéntricos.
Abstract
En este trabajo se realiza inicialmente un resumen teórico de las teorías de láminas y vigas desarrolladas por Simo y colaboradores [2-6,12-15]. Luego [...]
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Finite element analysis of hot rolling processes
O. Soto, E. Oñate, R. Codina

(1993). Research Report, Nº PI40

Abstract
The numerical simulation of hot rolling forming processes is very important for the metallurgic industry. This is an efficient and economic tool to simulate the rolling process and to predict the evolution of some parameters like the velocity field, temperatures, strains, stresses and rolling forces. In this way, computer simulations are becoming a necessary tool in the design and optimization of hot rolling processes [2,3,4,5,21,25,26,27]. In this publication an incompressible flow based formulation to simulate hot rolling processes is presented. First, some theorical aspects about the process are shown as well as numerical solution using the finite element method. Finally, some numerical examples are presented.
Abstract
The numerical simulation of hot rolling forming processes is very important for the metallurgic industry. This is an efficient and economic tool to simulate the rolling process [...]
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The small-gap equation in rotary lip seals
J. Heinrich, C. Vionnet

(1993). Research Report, Nº PI42

Abstract
The study of a thin, incompressible Newtonian fluid layer trapped between two almost parallel, sliding surfaces has been actively pursued in the last decades. This subject includes lubrication applications such as slider bearing or the sealing of non-pressurized fluids with rubber rotary shaft seals. In the present work we analyze the flow of lubricant fluid through the micro-gap of rotary lip seals. This study is carried out assuming that a “small-gap” parameter δ attains an extreme value in the Navier-Stokes equations. In particular, the effect of surface roughness, excentricity and centrifugal forces is analyzed using the technique. The precise meaning of small gap is achieved by the particular limit δ=0 which, within the bounds of the hypotheses, predicts transport of lubricant through the sealed area by centrifugal instabilities. Numerical results obtained with the finite element method are presented.
Abstract
The study of a thin, incompressible Newtonian fluid layer trapped between two almost parallel, sliding surfaces has been actively pursued in the last decades. This subject [...]
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On the Computational efficiency and implementation of block-iterative algorithms for nonlienar coupled problems
M. Cervera, R. Codina, J. Galindo

(1993). Research Report, Nº PI43

Abstract
In this paper we outline a general methodology for the solution of the system of algebraic equations arising from the discretization of the field equations governing coupled problems. In our examples, we shall consider that this discrete problem is obtained from the finite element discretization in space and the finite difference discretization in time. Our motivation is to preserve software modularity, to be able to use existing single field codes to solve more complex problems, and to exploit computer resources optimally, emulating parallel processing. To this end we deal with two well-known coupled problems of computational mechanics – the fluid-structure interaction problem and thermally driven flows of incompressible fluids. The possibility of coupling the block-iterative loop with the nonlinearity of the problems is demonstrated through numerical experiments, which suggest that even a mild nonlinearity drives the convergence rate of the complete iterative scheme, at least for the two problems considered here. The paper discusses the implementation of this alternative to the direct coupled solution, stating advantages and disadvantages. The need for on-line synchronized communication between the different codes used is also explained, together with the description of the master code who will control overall algorithm.
Abstract
In this paper we outline a general methodology for the solution of the system of algebraic equations arising from the discretization of the field equations governing coupled [...]
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Search for general fluid mechanics algortihm
O. Zienkiewicz, R. Codina

(1993). Research Report, Nº PI44

Abstract
The paper outlines the formulation of a novel algorithm which can be used for the solution of both compressible and incompressible Navier-Stokes or Euler equations. Full incompressibility can be dealt with if the algorithm is used in tis semi-explicit form and its structure permits arbitrary interpolation functions to be used avoiding the Babuska-Brezzi restriction. In a fully explicit version it introduces a rational form balancing dissipation avoiding the use of arbitrary parameters and forms for this.
Abstract
The paper outlines the formulation of a novel algorithm which can be used for the solution of both compressible and incompressible Navier-Stokes or Euler equations. Full incompressibility [...]
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CALSEF: Programa para cálculo estático lineal de sólidos y estructuras para el método de elementos finitos
E. Oñate, S. Botello

(1992). Research Report, Nº PI18
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A general methodology for structural shape optimization problems using automatic adaptive remeshing
G. Bugeda, J. Oliver

(1992). Research Report, Nº PI19

Abstract
The proposed methodology lies on the use of the adaptive mesh remeshing (AMR) technique in the context of 2D shape optimization problems analyzed by the Finite Element Method. A suitable and very general technique for the parametrization of the optimization problem, that uses B-splines to define the boundary, is first presented. Then, mesh generation, using the advancing frontal method, the error estimator and the remeshing criteria are studied in the context of shape optimization problems. Particularly, the analytical sensitivity analysis of the different items ruling the problem (B-splines, Finite Element Mesh, structural behaviour, and error estimator) is studied in detail. The sensitivities of the Finite Element Mesh and error estimator permit their projection from one design to the next one leading to an “a priori knowledge” of the finite element error distribution on the new design without the necessity of any additional structural analysis. With this information the remeshing criteria permits to build up a finite element mesh on the new design with aa specified and controlled level of error. The robustness and reliability of the proposed methodology is checked through several examples.
Abstract
The proposed methodology lies on the use of the adaptive mesh remeshing (AMR) technique in the context of 2D shape optimization problems analyzed by the Finite Element Method. [...]
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Equivalent FE and BE forms of a substructure oriented boundary solutions approach
J. Jirousek

(1992). Research Report, Nº PI20
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A perspective of recent developments in the finite element simulation of metal forming processes
E. Oñate

(1992). Research Report, Nº PI21

Abstract
This paper presents an overview of different computational procedures for finite element analysis of metal forming problems. Both the displacement and flow approaches are discussed together with other aspects like the treatment of temperature coupling, the techniques for geometry updating, the treatment of contact and friction, the use of quasi-static versus explicit dynamic methods and other topics of interest. Examples of applications of some of the methods proposed to extrusion, rolling, mould filling and sheet metal forming problems are presented.
Abstract
This paper presents an overview of different computational procedures for finite element analysis of metal forming problems. Both the displacement and flow approaches are [...]
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Una panorámica de las posibilidades del MEF para análisis de procesos de conformado de metales.
E. Oñate

(1992). Research Report, Nº PI23

Abstract
Se presenta en este trabajo una breve panorámica de diferentes procedimientos para análisis de procesos de conformado de metales por el método de elementos finitos (MEF). Se describen las formulaciones de flujo y de sólido junto a diversos temas como el acoplamiento térmico, las técnicas para actualización de geometría, el tratamiento de contacto y rozamiento, el uso de métodos cuasi-estáticos frente a dinámicos explícitos y otros temas de interés. Asimismo, se presentan ejemplos de aplicación de algunos de los métodos propuestos a problemas de extrusión, laminado, llenado de moldes y embutición de chapa.
Abstract
Se presenta en este trabajo una breve panorámica de diferentes procedimientos para análisis de procesos de conformado de metales por el método de elementos [...]
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Petrov-Galerkin finite element model for compressible flows using adaptive refinement of nonstructured grids
F. Brueckner

(1990). Research Report, Nº PI10

Abstract
This report outlines the formulation and implementation of the Petrov-Galerkin finite element model under development at The Universe of Arizona into the adaptive computational mesh algorithms of the International Center for Numerical Methods in Engineering, Barcelona, Spain. This work included the formulation of linear triangular elements, their use on the unstructured grids generated by the mesh generator of the ICNME, and the subsequent numerical error estimation of the results and remeshing. The implementation yielded good results for the Petrov-Galerkin weighting of the convective terms. Additional algorithmic modifications were made in order to investigate the effects of alternate weighting schemes, higher order spatial and temporal integration schemes, more consistent treatment of the mass matrices, and a formulation based on the use of the internal energy. In general, oscillatory results were obtained for schemes in which all terms were weighted with the Petrov-Galerkin functions, but additional work in this area and an investigation of the use of the other modifications are needed. The computer codes generated or modified for use in this study are described herein. A copy of the flow solvers themselves is also included.
Abstract
This report outlines the formulation and implementation of the Petrov-Galerkin finite element model under development at The Universe of Arizona into the adaptive computational [...]
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A finite element method for the solution of potencial flow in two dimensions
T. Hughes, E. Oñate, J. Canet

(1991). Research Report, Nº PI11

Abstract
This report presents a method for the solution of two dimensional, potential flow around an aerofoil base on a Finite Element Method for the solution of Laplace’s equation. Solutions to approximate the “real” flow are constructed from the observation that potential flow solutions are linear and thus, many potential flows may be superimposed to yield the desired flow. Indeed, in this way, one of the effects of viscosity, that of fixing the rear stagnation point to the trailing edge for up to moderate angle of attack cases, is modelled by the imposition of a potential flow due to a point vortex (located at the ¼ chord point) sufficient to fix the rear stagnation point at the trailing edge (Kutta condition). It must be remembered however, that potential flow solutions are inviscid and as such do not model correctly the flow separation point and further, the absence of viscosity falsely causes the model to predict zero drag caused by the aerofoil. However, the predictions made for the lift (derived from the calculated circulation to fix the Kutta condition via the Kutta-Joukowski theorem) are shown to be good for low Mach number cases at moderate angles of attack.
Abstract
This report presents a method for the solution of two dimensional, potential flow around an aerofoil base on a Finite Element Method for the solution of Laplace’s equation. [...]
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A penalty finite element method for non‐Newtonian creeping flows
R. Codina, M. Cervera, E. Oñate

(1991). Research Report, Nº PI13

Abstract
In this paper we present an iterative penalty finite element method for viscous non‐Newtonian creeping flows. The basic idea is solving the equations for the difference between the exact solution and the solution obtained in the last iteration by the penalty method. For the case of Newtonian flows, one can show that for sufficiently small penalty parameters the iterates converge to the incompressible solution. The objective of the present work is to show that the iterative penalization can be coupled with the iterative scheme used to deal with the non‐linearity arising from the constitutive law of non‐Newtonian fluids. Some numerical experiments are conducted in order to assess the performance of the approach for fluids whose viscosity obeys the power law.
Abstract
In this paper we present an iterative penalty finite element method for viscous non‐Newtonian creeping flows. The basic idea is solving the equations for the difference [...]
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Finite element procedures for incompressible and compressible flows
E. Oñate, F. Quintana, R. Codina, J. Canet

(1991). Research Report, Nº PI14
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Simulación numérica del choque de vehículos por el método de los elementos finitos
E. Oñate, S. Botello

(1991). Research Report, Nº PI17

Abstract
En este trabajo se presentan las principales características del programa de ordenador “IMPACT 3D” actualmente en desarrollo en el Centro Internacional de Métodos Numéricos en Ingeniería de Barcelona para la simulación numérica de problemas de impacto y choque de vehículos. El programa se basa en una formulación de elementos finitos de lámina no lineal incorporando también elementos de sólidos y de viga para modelar correctamente todos los componentes resistente típico de estructuras de vehículos. El programa permite la utilización de algoritmos de integración en el tiempo explícitos e implícitos incluyendo además modelos constitutivos para materiales compuestos. Los ejemplos que se presentan muestran la aplicación del programa a la deformación de una puerta sometida a un ensayo penetración lateral y el choque frontal de un prototipo de vehículo industrial.
Abstract
En este trabajo se presentan las principales características del programa de ordenador “IMPACT 3D” actualmente en desarrollo en el Centro Internacional [...]
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Generació de malles estructurades a partir d'equacions el·líptiques
R. Codina

(1990). Research Report, Nº PI7

Abstract
En aquest treball es descriu un mètode de generació de malles estructurades d'elements finits basat en imposar que les línies coordenades satisfacin una equació el·líptica, analitzant l'efecte de diferents termes amb les incògnites sense derivar d'aquesta equció sobre la malla resultant. Les equacions que cal resoldre es descrititzen en diferències finites, adaptant-hi les tècniques anomenades d'upwind pròpies del mètode dels elements finits. Es presenta també una tècnica de resolució del sistema algebraic d'equacions resultant.
Abstract
En aquest treball es descriu un mètode de generació de malles estructurades d'elements finits basat en imposar que les línies coordenades satisfacin [...]
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A general methodology for deriving shear constrained Reissner-Mindlin plate elements
E. Oñate, O. Zienkiewicz, B. Suarez

(1990). Research Report, Nº PI5

Abstract
In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re‐interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re‐formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are given.
Abstract
In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re‐interpreted [...]
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Finite volume VS finite element. Is there really a choice
O. Zienkiewicz, E. Oñate

(1990). Research Report, Nº PI8

Abstract
The finite volume method appears to be a particular case of finite elements with a non Galerkin weighting. It is course less accurate for self adjoint problems but has some computationally useful features for first order equations involving only surface integrals. For certain problems this is a substational economy and leads to computationally useful approximations.
Abstract
The finite volume method appears to be a particular case of finite elements with a non Galerkin weighting. It is course less accurate for self adjoint problems but has some [...]
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Nuevos materiales estructurales: "Cerámicos en ingeniería"
S. Oller

(1989). Research Report, Nº PI2

Abstract
El presente trabajo tiene por objetivo hacer una revisión introductoria sobre el estado actual de los pulvimateriales y en particular sobre los nuevos cerámicos ingenieriles. Sería interminable escribir una relación profunda sobre las distintas tipologías de cerámicos que existen en la actualidad; sin embargo, es posible presentar conceptos que puedan delinear en forma general una respuesta a la pregunta: ¿qué son los nuevos cerámicos en ingeniería? Responder a esta pregunta es precisamente parte del trabajo que se presenta. Al final, en el capítulo 4, se desarrolla una idea para tratar en forma global el comportamiento mecánico térmico de los pulvimateriales. Es decir, desde su fabricación a la puesta en servicio. Es conveniente resaltar que esta primera presentación del tema solamente pretende introducir al lector en el conocimiento sobre el comportamiento mecánico de los pulvimateriales. Por lo tanto, es mi esperanza que sirva de utilidad para aclarar las dudas básicas y permita iniciar estudios más profundos. Previo a iniciar el tema del trabajo, quisiera resaltar la razón más importante que ha conducido a su desarrollo: “la inquietud e invalorable apoyo que he recibido iniciar la investigación en este nuevo tema”. Además, quiero agradecer la colaboración de Carlos García Garino, Jean Bapstiste Dalin y Alfredo Balmaceda.
Abstract
El presente trabajo tiene por objetivo hacer una revisión introductoria sobre el estado actual de los pulvimateriales y en particular sobre los nuevos cerámicos [...]
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Una formulación arbitrariamente Lagrangiana-Euleriana para grandes desplazamientos del contorno
A. Huerta

(1988). Research Report, Nº PI1

Abstract
En este estudio se desarrolla una técnica de elementos finitos basada en una formulación de Petrov-Galerkin y una descripción Arbitrariamente Lagrangiana-Euleriana (ALE) para el análisis de fluidos viscosos no lineares con granes movimientos del contorno. Se pasa revista a las ecuaciones fundamentales y a las ecuaciones cinemáticas contempladas desde una referencia arbitraria. Puesto que los algoritmos de remallado son el principal reto de la descripción ALE, se desarrollan varios métodos, incluyendo una nueva formulación mixta, para actualizar la malla de una manera racional. Además, se ha implementado, en las ecuaciones de remallado, la formulación de Petrov-Galerkin pondera a contracorriente, dado que permite analizar con exactitud flujos curos movimientos en un estudio de interacción fluido estructura, tsunamis, el problema de la rotura de una presa –donde se alcanzan número de Reynolds tan elevados como 3000– y un análisis de chapoteo de gran amplitud.
Abstract
En este estudio se desarrolla una técnica de elementos finitos basada en una formulación de Petrov-Galerkin y una descripción Arbitrariamente Lagrangiana-Euleriana [...]
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A large strain plasticity model for anisotropic composite materials
E. Car, S. Oller, E. Oñate

(1999). Research Report, Nº PI179
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Higher-order simulations: Strategic investment under model-induced market structures
G. Peffer, B. Llacay

(2004). Research Report, Nº PI261

Abstract
The trading and investment decision processes in financial markets becomes ever more dependent on the use of valuation and risk models. In certain, cases such as risk management, modelling practice has become so homogeneous that one is led to ask about the effect this has on the price formation process. Furthermore, should stable price patterns emerge from this, can sophisticated investors who have private information about the use and characteristics of these models make superior gains? The aim of this article is to test this hypothesis in a stylised market environment, where a strategic trader who trades on information about the valuation and risk management models used by competitors. Results show that for our particular market setting, such a strategy has an advantage over those that do not use this information.
Abstract
The trading and investment decision processes in financial markets becomes ever more dependent on the use of valuation and risk models. In certain, cases such as risk management, [...]
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Smeared crack approach: Back to the original track
M. Cervera, M. Chiumenti

(2006). Research Report, Nº PI295

Abstract
This paper reviews briefly the formulations used over the last 40 years for the solution of problems involving tensile cracking, both with the discrete and smeared crack approaches. The paper focuses in the smeared approach, identifying as its main drawbacks the observed mesh-size and mesh-bias spurious dependence when the method is applied “straightly”. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and strong discontinuity (discrete cracks) approaches are analyzed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure uniqueness of the solution, attaining the necessary stability and convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is well posed, stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious meshsize or mesh-bias dependence, comparing very favorably with those obtained with other fracture and continuum mechanics approaches.
Abstract
This paper reviews briefly the formulations used over the last 40 years for the solution of problems involving tensile cracking, both with the discrete and smeared crack [...]
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The CIMNE model for generating knowledge on computational engineering and its transfer to society
E. Oñate

(2017). Research Report, Nº PI417
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Analysis of time dependent problems using exponential basis functions
B. Movahedian, B. Boroomand

(2011). Research Report, Nº PI364

Abstract
In this research we present a method based on using Exponential Basis Functions (EBFs) to solve a class of time dependent engineering problems. The solution is first approximated by a summation of EBFs satisfying the differential equation and then completed by satisfying the time dependent boundary conditions as well as the initial conditions through a collocation method. This can be performed by considering two approaches. In the first one the solution is split into three parts, i.e. a homogeneous solution obtained by homogeneous boundary conditions, a homogeneous solution obtained by non-homogeneous solution and finally a particular solution induced by source terms. In the second approach the solution is split into two parts, i.e. a homogeneous solution and a particular solution induced by source terms. The two approaches are then employed to construct a time marching algorithm for the solution of problems over a long period of time. We shall present the details of the application of the two approaches introduced to some mathematical and engineering problems. The details of the time marching algorithm proposed are explained. Several problems are solved to show the capabilities of the approaches used. Some benchmark problems are also devised and solved for further studies. It is shown that the one of the introduced approaches is capable of solving a class of problems with moving boundaries.
Abstract
In this research we present a method based on using Exponential Basis Functions (EBFs) to solve a class of time dependent engineering problems. The solution is first approximated [...]
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Exponential basis functions in solution of incompressible fluid problems with moving free surfaces
S. Zandi, B. Boroomand, S. Soghrati

(2011). Research Report, Nº PI363

Abstract
In this report, a new simple meshless method is presented for the solution of incompressible inviscid fluid flow problems with moving boundaries. A Lagrangian formulation established on pressure, as a potential equation, is employed. In this method, the approximate solution is expressed by a linear combination of exponential basis functions (EBFs), with complex-valued exponents, satisfying the governing equation. Constant coefficients of the solution series are evaluated through point collocation on the domain boundaries via a complex discrete transformation technique. The numerical solution is performed in a time marching approach using an implicit algorithm. In each time step, the governing equation is solved at the beginning and the end of the step, with the aid of an intermediate geometry. The use of EBFs helps to find boundary velocities with high accuracy leading to a precise geometry updating. The developed Lagrangian meshless algorithm is applied to variety of linear and nonlinear benchmark problems. Non-linear sloshing fluids in rigid rectangular two-dimensional basins are particularly addressed.
Abstract
In this report, a new simple meshless method is presented for the solution of incompressible inviscid fluid flow problems with moving boundaries. A Lagrangian formulation [...]
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Paralelización del código Stampack v7.10
W. Castelló, F. Flores

(2011). Research Report, Nº PI362

Abstract
El objetivo principal del presente informe es mostrar las mejoras en la performance del código Stampack, cuando se lo emplea en conjunto con OpenMP en máquinas del tipo multi-núcleo (ej.: Intel Core2 Duo, Intel Core2 Quad, etc) o multi-thread (ej.: Intel Core i3, i5, i7, etc). Esta última tecnología en los procesadores (multi-thread) permite aumentar de manera importante la potencia de cálculo, dado que además de contar con más de un procesador, permite aumentar los hilos (threads) de tareas simultaneas de cada núcleo. Por ejemplo un procesador Intel Core i3, puede tener dos procesadores y realizar dos tareas simultaneas por cada procesador, lo cual es equivalente a tener una máquina con cuatro procesadores. En el caso del procesador Intel Core i7 empleado en este trabajo cuenta con cuatro núcleos y la posibilidad de realizar dos tareas simultaneas por núcleo, lo cual equivale a tener ocho procesadores. La paralelización del software Stampack se ha realizado siguiendo la idea básica de modificar o intervenir mínimamente los archivos fuente originales de la versión serial. Bajo estas condiciones, se ha realizado un análisis de tiempos para detectar zonas del código que representen un importante porcentaje del tiempo total de cálculo. Para finalizar se debe destacar que el software paralelizado debe funcionar también de manera correcta cuando es ejecutado en ordenadores con un solo procesador, de manera que la versión paralela debe ser compatible en su totalidad con la versión serial original del código Stampack.
Abstract
El objetivo principal del presente informe es mostrar las mejoras en la performance del código Stampack, cuando se lo emplea en conjunto con OpenMP en máquinas [...]
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Simplificación de mallas de triángulos
M. Pasenau, C. Andújar

(2011). Research Report, Nº PI361

Abstract
El objetivo principal del proyecto de fin de carrera es el análisis, diseño, implementación y prueba de un algoritmo que permita simplificar rápidamente una malla de triángulos muy densa, tratando de minimizar tanto el error geométrico como el error de atributos definidos en la superficie, para que el usuario pueda interaccionar con ella en plataformas modestas.
Abstract
El objetivo principal del proyecto de fin de carrera es el análisis, diseño, implementación y prueba de un algoritmo que permita simplificar rápidamente [...]
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Possibilities of the particle finite element method for fluid-soil-structure interaction problems
E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, B. Suarez

(2011). Research Report, Nº PI357

Abstract
We present some developments in the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the later including soil/rock and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The stabilization for dealing with an incompressibility continuum is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid-solid and solid-solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of a river bed adjacent to a bridge foundation, the stability of breakwaters and constructions sea waves and the study of landslides.
Abstract
We present some developments in the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure interaction [...]
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El ciclo de las ideas en la I+D+I
E. Oñate

(2011). Research Report, Nº PI354

Abstract
Cuando se habla de la investigación, el desarrollo tecnológico y la innovación (I+D+I en siglas, que yo escribo todas en mayúsculas [1]) es frecuente confundir fines, medios y responsabilidades. La última moda parece que es exigir que los grupos que investigan en Universidades y Centros de I+D, sean "rentables". Es decir, se pretende que su investigación se financie con créditos públicos, que los resultados de la misma se implementen en el mercado rápidamente y que los beneficios de su comercialización sirvan para devolver los créditos y para refinanciar esos grupos. También parece que se echa de menos que las empresas investiguen más, es decir, que inviertan recursos en descubrir nuevos conocimientos. El límite caricaturesco de esas aspiraciones sería pretender que las empresas produjeran premios Nobel y que un grupo universitario estuviera entre los 10 primeros puestos en el ranking de la actividad económica de un país. Ciertamente, esto no es imposible, pero es altamente improbable. Lo contrario desgraciadamente es más frecuente. Es decir, que los investigadores universitarios en su afán por la supervivencia económica de sus grupos, descuiden sus tareas investigadoras y que las empresas, confundiendo lo que es un Departamento Técnico o de Proyectos, con un Departamento de Innovación, se consideren autosuficientes y menosprecien u obvien el contacto con el mundo de la I+D real.
Abstract
Cuando se habla de la investigación, el desarrollo tecnológico y la innovación (I+D+I en siglas, que yo escribo todas en mayúsculas [1]) es frecuente [...]
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On the use of exponential basis functions in the analysis of shear deformable laminated plates
M. Shahbazi, B. Boroomand, S. Soghrati

(2011). Research Report, Nº PI353

Abstract
In this report, we introduce a meshfree approach for static analysis of isotropic/orthotropic crossply laminated plates with symmetric/non-symmetric layers. Classical, first and third order shear deformation plate theories are employed to perform the analyses. In this method, the solution is first split into homogenous and particular parts and then the homogenous part is approximated by the summation of an appropriately selected set of exponential basis functions (EBFs) with unknown coefficients. In the homogenous solution the EBFs are restricted to satisfy the governing differential equation. The particular solution is derived using a similar approach and another series of EBFs. The imposition of the boundary conditions and determination of the unknown coefficients are performed by a collocation method through a discrete transformation technique. The solution method allows us to obtain semi-analytical solution of plate problems with various shapes and boundary conditions. The solutions of several benchmark plate problems with various geometries are presented to validate the results.
Abstract
In this report, we introduce a meshfree approach for static analysis of isotropic/orthotropic crossply laminated plates with symmetric/non-symmetric layers. Classical, first [...]
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Methodologies for tracking of load extremes and error estimation using probabilistic techniques
R. Flores, E. Ortega, R. López

(2012). Research Report, Nº PI375

Abstract
This work, conducted at CIMNE under ALEF project task 1.2.3, presents an investigation about the potential capabilities of neural networks to assist simulation campaigns. The discrete gust response of an aircraft has been chosen as a typical problem in which the determination of the critical loads requires exploring a large parameter space. A very simple model has been used to compute the aerodynamic loads. This allows creating a large database while at the same time retaining some of the fundamental properties of the problem. Using this comprehensive dataset the effects of network structure, training method and sampling strategy on the level of approximation over the complete domain have been investigated. The capabilities of the neural network to predict the peak load as well as the critical values of the design parameters have also been assessed. The applicability of neural networks to the combination of multi-fidelity results is also explored.
Abstract
This work, conducted at CIMNE under ALEF project task 1.2.3, presents an investigation about the potential capabilities of neural networks to assist simulation campaigns. [...]
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A four-noded quadrilateral element for composite laminated plates/shell using the refined zigzag theory
A. Eijo, E. Oñate, S. Oller

(2012). Research Report, Nº PI378

Abstract
A new bilinear 4-noded quadrilateral element (called QLRZ) for the analysis of composite laminated and sandwich plates/shells based on the refined zigzag theory (RZT) proposed by Tessler et al. [1] is presented. The element has seven kinematic variables per node. Shear locking is avoided by introducing an assumed linear shear strain field. The performance of the element is studied in several examples where the reference solution is the 3D finite element analysis using 20-noded hexahedral elements. Finally, the capability for capturing delamination effects is analyzed.
Abstract
A new bilinear 4-noded quadrilateral element (called QLRZ) for the analysis of composite laminated and sandwich plates/shells based on the refined zigzag theory (RZT) proposed [...]
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Puente Tensairity para pasarela peatonal en el PMT-UPC de Castelldefels (737-PRO-CA-5385)
C. Estruch, B. Suárez, J. Marcipar

(2012). Research Report, Nº PI380

Abstract
Actualmente el espacio formado por el “Parc Mediterrani de la Tecnologia” y el Campus Universitario de la Universitat Politècnica de Catalunya (PMT-UPC) de Castelldefels está en expansión. Es por ello que se está pensando en la construcción de dos pasarelas peatonales para cruzar la laguna de laminación de la “Olla del Rei”, conectando de esta forma el PMT-UPC con el paseo del Pitort. Dado que el PMT-UPC pretende ser un referente ambiental y tecnológico, se plantea como alternativa óptima la construcción de una pasarela peatonal ligera diseñada mediante una novedosa tecnología neumática conocida y patentada con el nombre de Tensairity®. Las estructuras ligeras son un reto para el ingeniero estructural y un importante avance hacia una arquitectura sostenible. Tensairity® es un concepto que hace referencia a estructuras neumáticas ligeras basadas en una sutil interacción entre cables, elementos de compresión, membranas y aire a baja presión. En Tensairity®, compresión y tracción están físicamente separados por una membrana de tejido hinchada a baja presión, el fin de la cual es, por un lado pretensar el elemento de tracción, y por el otro estabilizar el elemento de compresión frente al pandeo. Esto permite llevar al material hasta su límite plástico, tanto para tracción como para compresión, dando como resultado vigas que pueden ser varios órdenes de magnitud más ligeras que las vigas metálicas convencionales, manteniendo siempre su misma capacidad de carga. Aplicaciones ideales para esta tecnología son cerchas, estructuras con grandes luces, estructuras temporales, pasarelas peatonales o incluso estructuras de despliegue rápido para casos de emergencia, entre otras. La pasarela peatonal objeto de este proyecto está compuesta por dos partes bien diferenciadas, una pasarela Tensairity® que cruza la laguna de laminación y dos estructuras de madera a modo de embarcaderos, una a cada lado de la pasarela y donde ésta se apoya hasta alcanzar los caminos que bordean el trazado de la laguna. La pasarela Tensairity® está formada por dos vigas Tensairity® compuestas cada una de ellas por un tubo hinchable de PVC en cuya parte superior se apoya una viga de madera a modo de elemento de compresión y en su parte inferior una cinta de carga a modo de elemento de tracción. Sobre estas dos vigas se sustenta la superestructura de la pasarela formada por vigas transversales de madera sobre las que se apoya el tablero y las barandillas, también de madera. Las estructuras de apoyo se construyen igualmente en madera, con una tipología estructural similar al de la pasarela y mediante el uso de pilotes que recuerda en cierta manera los embarcaderos presentes en los ríos, de forma que la estructura completa esté integrada en el entorno.
Abstract
Actualmente el espacio formado por el “Parc Mediterrani de la Tecnologia” y el Campus Universitario de la Universitat Politècnica de Catalunya (PMT-UPC) [...]
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Continuum modelling using the discrete element method. theory and implementation in an object-oriented software platform
M. Santasusana, E. Oñate

(2012). Research Report, Nº PI381

Abstract
The Discrete Element Method is a relatively new technique that has nowadays and intense research in the field of numerical methods. In its first conception, the method was designed for simulations of dynamic system of particles where each element is considered to be an independent and non-deformable entity that interacts with other particles by the laws of the contact mechanics and moves following the second Newton’s law. This first approach for the DEM has obtained excellent results for granular media simulations or another discontinuouslike case. The existing challenge nowadays for the DEM is to be able to simulate the behaviour on a continuous media discretized by a mesh of particles ruled by the equations of the DEM. Although there exist more adequate methods to solve the continuous problem as they are the different variants of the Finite Element Method, the DEM is expected to have a better behaviour when the failure of the media occurs; in terms of tracking the evolution of the fracture locally between the elements of the discretization and also the post-fractural behaviour of the material. Nowadays, there are several DEM codes that try to solve this problem although there is no one which can assure an accurate solution applicable universally to any case. The objective of the present work is to develop calculation software for the Discrete Element Method included in the platform for numerical methods KRATOS, which is developed in CIMNE. One of the goals of the so-called DEM-Application is to be able to reproduce a wide set of engineering problems; not only the discrete ones such as the excavation or agroalimentary applications but also to reproduce the continuous media, simulating compression test for concrete or asphalt samples for instance. In addition it is desired that the application permits the coupling with another methods, particularly the Finite Element Method. In order to do this, the present work includes the study of all the advances and ideas that, globally in the numerical method field and particularly in CIMNE, have been discussed to give other approaches and to keep improving and developing the to the Discrete Element Method.
Abstract
The Discrete Element Method is a relatively new technique that has nowadays and intense research in the field of numerical methods. In its first conception, the method was [...]
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Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: Application to harbor agitation
D. Modesto, S. Zlotnik, A. Huerta

(2013). Research Report, Nº PI401

Abstract
Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular nature of the Helmholtz operator and the sensibility of the solution to small variations of the data. Here a reduced order model is used to determine the scattered solution everywhere in the domain for any incoming wave direction and frequency. Moreover, this is applied to a real engineering problem: water agitation inside real harbors for low to mid-high frequencies. The Proper Generalized Decomposition (PGD) model reduction approach is used to obtain a separable representation of the solution at any point and for any incoming wave direction and frequency. Here, its applicability to such a problem is discussed and demonstrated. More precisely, the separability of the operator is addressed taking into account both the non-constant coe
Abstract
Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular [...]
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Desarrollo y aplicación de un modelo de elementos finitos para cálculo de vigas con materiales compuestos laminados basado en la teoría de Timoshenko
A. Llanos, E. Oñate, F. Zárate

(2013). Research Report, Nº PI398

Abstract
Actualmente existen programas de MAT-fem para calcular vigas de material homogéneo, según la teoría de Euler-Bernoulli o de Timoshenko. El objetivo de la presente tesina es conseguir un nuevo programa capaz de calcular vigas de materiales compuestos con la teoría de Timoshenko. En el capítulo 1, se introducen los materiales compuestos describiendo las ventajas y aplicaciones que tienen hoy en día en el ámbito de la Ingeniería Cívil. En el capítulo 2 y 3 se expone la teoría de las vigas planas laminadas y, en particular, de las vigas compuestas de Timoshenko. El capítulo 4 explica cómo se ha llevado a cabo la implementación numérica y da paso al capítulo 5, en el que se exponen varios ejemplos. Por último, en el capítulo 6, se exponen las conclusiones que se extraen del trabajo realizado y de los resultados obtenidos. Finalmente se presentan los anejos. Primero, en el anejo 1, se muestra un ejemplo real de refuerzo de viga mediante materiales compuestos. En el segundo anejo se presentan más ejemplos de los expuestos en el quinto capítulo y, por último, se termina la tesina con el anejo 3, que presenta los distintos archivos de programación utilizados para el cálculo de vigas compuestas de Timoshenko.
Abstract
Actualmente existen programas de MAT-fem para calcular vigas de material homogéneo, según la teoría de Euler-Bernoulli o de Timoshenko. El objetivo de [...]
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Numerically stable formulas for a material point based explicit exponential integrator
P. Nadukandi

(2014). Research Report, Nº PI408

Abstract
We present numerically stable formulas for the analytical solution in the closed form of the so-called X-IVAS scheme in 3D. The X-IVAS scheme is a material point based explicit exponential integrator. An intermediate step in the X-IVAS scheme is the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes. This is what we refer to as particle tracing of streamlines and independent formulas for the same can be easily distilled from the ones presented for the X-IVAS scheme. The formulas involve functions of matrices which are defined using the corresponding Newton interpolating polynomial. The evaluation of these formulas is stable, i.e. a certain number of significant digits in the computed values are guaranteed to be exact. Using the double-precision floating-point arithmetic specified by the IEEE 754 standard, we obtain at least 10 significant decimal digits in the worst case scenarios. These scenarios involve fourth-order divided differences of the exponential function. Additionally, an optimal series approximation of divided differences is presented which is an essential part of the exposition.
Abstract
We present numerically stable formulas for the analytical solution in the closed form of the so-called X-IVAS scheme in 3D. The X-IVAS scheme is a material point based [...]
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PARACHUTES: A computer program for calculating ram-air parachutes. Theory document
E. Ortega, R. Flores

(2016). Research Report, Nº PI415

Abstract
PARACHUTES is a computer program developed at the International Center for Numerical Methods in Engineering (CIMNE) for the simulation of ram-air (gliding) parachute systems. The solution methodology in PARACHUTES is based on two unsteady calculation modules which work in a coupled manner. The aerodynamics of the gliding parachute is solved by a low-order panel method and a finite-element technique is used for the structure. The latter allows modelling the suspension lines, textile fabric and suspended payloads of a typical parachute system by means of cable, membrane and solid linear elements. For specified flight conditions, the simulation program solves the fluid-structural problem governing the behavior of arbitrary parachute-payload configurations and also allows analyzing user-defined maneuvers. This document describes the theoretical formulation and the numerical procedures adopted in PARACHUTES.
Abstract
PARACHUTES is a computer program developed at the International Center for Numerical Methods in Engineering (CIMNE) for the simulation of ram-air (gliding) parachute systems. The [...]
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Reflexiones sobre el tránsito de la idea al producto en el entorno de la Escuela de Ingenieros de Caminos de Barcelona
E. Oñate

(2011). Research Report, Nº PI359

Abstract
Se presentan unas reflexiones sobre el ciclo que las ideas recorren desde que surgen en un entorno universitario hasta que se transforman en un producto industrial. Se concretan estas reflexiones en el contexto de la Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos de la Universitat Politècnica de Catalunya y se presentan algunos ejemplos de éxitos en la implantación del denominado Círculo de las Ideas.
Abstract
Se presentan unas reflexiones sobre el ciclo que las ideas recorren desde que surgen en un entorno universitario hasta que se transforman en un producto industrial. Se concretan [...]
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On using linear elements in incompressible plane strain problems. A simple edge based approach for triangles
B. Boroomand, B. Khalilian

(2004). Research Report, Nº PI248

Abstract
In this paper a simple iterative method is presented for finite element solution of incompressible plane strain problems using linear elements. Instead of using a mixed formulation approach, we use an equivalent displacement/velocity approach in an iterative manner. Control volumes are taken for regions where are to exhibit incompressible behavior. For triangular elements the control volume is chosen as the area built on the parts of each pair of elements at the sides of an edge. In this case, elements are let to exchange volume. It is shown that the proposed edge based approach removes the deficiency of the linear triangular elements i.e. locking effect.Similar edge based approach is applied to the linear quadrilateral elements. However, if the control volume is chosen as the element volume the formulation gives similar results as the discontinuous mixed formulation using one pressure point without exhibiting instability behavior. The formulation is based on decomposition of the displacement/velocity field into deviatoric and volumetric parts. The volumetric part is iteratively eliminated without confronting locking or instability phenomenon. The iterative procedure is very cheap and simple to be implemented in any FEM code. Several examples are given to demonstrate the performance of the procedure.
Abstract
In this paper a simple iterative method is presented for finite element solution of incompressible plane strain problems using linear elements. Instead of using a mixed formulation [...]
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On application of two superconvergent recovery procedures to plate problems
B. Boroomand, M. Ghaffarian, O. Zienkiewicz

(2004). Research Report, Nº PI247

Abstract
In this paper a study is performed on application of two recovery methods, i.e. Superconvergent Patch Recovery (SPR) and the Recovery by Equilibrium of Patches (REP), to plate problems. The two recovery methods have been recognized to give similar results in adaptive solutions of two dimensional stress problems. While the former applies a least square fit over a set of values at the so called superconvergent points, the latter does not need any knowledge of such points and thus has a wider application especially in non-linear problems. The formulation of REP is extended to Reissner-Mindlin plate problems. The convergence rates of the recovered fields of the gradients obtained from application of the two methods are compared using series of regular triangular and rectangular meshes for thick and thin plate solution cases. Assumed strain formulation based elements, i.e. the elements formulated by Mixed Interpolation of Tensorial Components, as well as conventional from of elements based on selective integration schemes are employed for the study. In order to investigate the possibility of any improvement in the results by adding equilibrium constraints to SPR, as some authors suggest for simple two-dimensional problems, some weighted forms of such conditions are designed and added to the formulation. Comprehensive study has been given first by varying the weight terms to obtain the best enhanced results and then using the optimal values to investigate the effects of the constraints on the rate of convergence. It is observed that despite of the cost of this approach, due to the coupling of the gradient terms, no significant improvement is achieved.
Abstract
In this paper a study is performed on application of two recovery methods, i.e. Superconvergent Patch Recovery (SPR) and the Recovery by Equilibrium of Patches (REP), to plate [...]
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Sistemas de ayuda a la decisión en ingeniería civil. posibilidades y perspectivas
E. Oñate, J. Marcipar, J. Piazzese

(2003). Research Report, Nº PI238

Abstract
La eclosión de las Tecnologías de la Información y las Comunicaciones (TIC), y en particular de Internet, ha facilitado el desarrollo de sistemas que, apoyados por bases de datos y potentes programas de simulación, transforman la información que existe en relación con un problema concreto, en conocimiento que permite tomar decisiones para su solución. Los denominados Sistemas de Ayuda a la Decisión (SAD) son ya una realidad en múltiples áreas de la ingeniería. En este trabajo se analizan las posibilidades y perspectivas de los SAD en ingeniería civil y se presentan tres ejemplos concretos de su aplicación a la prevención del riesgo de inundaciones y a la gestión de las emergencias correspondientes, al diseño de instalaciones en proyectos urbanísticos y a la gestión energética en municipios.
Abstract
La eclosión de las Tecnologías de la Información y las Comunicaciones (TIC), y en particular de Internet, ha facilitado el desarrollo de sistemas que, [...]
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On the arc length method: combining ideas and implementations aspects
N. Lafontaine, X. Wang, K. Huang, M. Yuan, E. Oñate

(2013). Research Report, Nº PI399

Abstract
In this work we introduced and implemented the AL method in NOLM program. Basically the actual implementation in NOLM is based in the work proposed by Lam and Morley (1992) and was coded with take into account the sign for no tracking back the solution. An ecient method was included for avoid complex roots and if the problem persist, two method is available to get the convergence. In case of no convergence is reached, we introduce a user factor, for reducing the arc-length, that should be taken betweens (0:5 - 0:75) per cent of the actual arc length. A linear truss-element, together to the isotropic smeared crack model was introduced for testing and benchmarking the AL method . During the work, we found several diculties to converge in the standard constitutive law implemented in NOLM when a softening parameter was introduced. It is caused by the no mechanical dissipation in the model. However, for a perfect plastic an hardening they get the corresponding results. All meshing process and post-processing was made with Gid[4], proving that it is possible to connect the developed owner software and this Pre-and post processing program.
Abstract
In this work we introduced and implemented the AL method in NOLM program. Basically the actual implementation in NOLM is based in the work proposed by Lam and Morley (1992) [...]
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Advances in the DEM and coupled DEM and FEM techniques in non linear solid mechanics
E. Oñate, F. Zarate, M. Celigueta, J. Gonzalez, J. Miquel, J. Carbonell, F. Garcia, S. Latorre, M. Santasusana

(2017). Research Report, Nº PI416

Abstract
In this chapter we present recent advances in the Discrete Element Method (DEM) and in the coupling of the DEM with the Finite Element Method (FEM) for solving a variety of problems in non linear solid mechanics involving damage, plasticity and multifracture situations.
Abstract
In this chapter we present recent advances in the Discrete Element Method (DEM) and in the coupling of the DEM with the Finite Element Method (FEM) for solving a variety of [...]
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The CIMNE model for generating knowledge on computational engineering and its transfer to society
E. Oñate

(2017). Research Report, Nº PI417

Abstract
We present an overview of the model implemented by the International Centre for Numerical Methods in Engineering (CIMNE, www.cimne.com ) for the generation of scientific and technical knowledge on computational engineering, understood in the broad sense, the subsequent generation of product resulting from the research activities and the transfer of these products to society for their exploitation in the industrial sector. We present examples of application of the CIMNE model to a number of academic, scientific and industry activities of CIMNE.
Abstract
We present an overview of the model implemented by the International Centre for Numerical Methods in Engineering (CIMNE, www.cimne.com ) for the generation of scientific [...]
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Analysis of the melting, burning and flame spread of polymers with the Particle Finite Element Method
E. Oñate, J. Marti, P. Ryzhakov, R. Rossi, S. Idelsohn

(2013). Research Report, Nº PI395

Abstract
A computational procedure for analysis of the melting, burning and flame spread of polymers under fire conditions is presented. The method, termed Particle Finite Element Method (PFEM), combines concepts from particle-based techniques with those of the standard finite element method (FEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in the thermoplastic material. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of melting and dripping of polymer particles. A mesh connects the nodes defining the discretized domain where the governing equations are solved using the FEM. An incremental iterative scheme for the solution of the nonlinear transient coupled thermal-flow problem, including radiation, loss of mass by gasification and combustion is used. Examples of the possibilities of the PFEM for the modelling and simulation of the melting, burning and flame spread of polymers under different fire conditions are described.
Abstract
A computational procedure for analysis of the melting, burning and flame spread of polymers under fire conditions is presented. The method, termed Particle Finite Element [...]
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Improving an input of material model in the D-DEMPack package programme in the Kratos application for granular non-cohesive materials
H. Koszur

(2015). Research Report, Nº PI412

Abstract
The main objective of this document is to present an idea of calibration tests used to improve an input material model in the DEM simulations in the D-DEMPack package programme in the Kratos application, which is developed in CIMNE. Presented method lets increase the precision and validity of discrete element modeling work. The calibration tests presented in this protocol may be used for granular non-cohesive materials ( for loose, dry granular material). They concern only the sphere shape of particles. The tests were conducted on couple different sizes of particles, in this work are presented results for average diameter of grains equal to 5cm (normal distribution with standard deviation equal to 0,05). The results of research may provide a basis for proper computing project data for preparing material model for loose, dry granular material. Tested by the author methods have been developed based on an article [1].
Abstract
The main objective of this document is to present an idea of calibration tests used to improve an input material model in the DEM simulations in the D-DEMPack package programme [...]
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Lagrangian analysis of multiscale particulate flows with the particle finite element method
E. Oñate, M. Celigueta, S. Latorre, G. Casas, R. Rossi, J. Rojek

(2014). Research Report, Nº PI405

Abstract
We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the Particle Finite Element Method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.
Abstract
We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the Particle [...]
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A particle finite element method for analysis of industrial forming processes
E. Oñate, A. Franci, J. Carbonell

(2014). Research Report, Nº PI406

Abstract
We present a generalized Lagrangian formulation for analysis of industrial forming processes involving thermally coupled interactions between deformable continua. The governing equations for the deformable bodies are written in a unified manner that holds both for fluids and solids. The success of the formulation lays on a residual-based expression of the mass conservation equation obtained using the Finite Calculus (FIC) method that provides the necessary stability for quasi/fully incompressible situations. The governing equations are discretized with the FEM via a mixed formulation using simplicial elements with equal linear interpolation for the velocities, the pressure and the temperature. The merits of the formulation are demonstrated in the solution of 2D and 3D thermally-coupled forming processes using the Particle Finite Element Method (PFEM).
Abstract
We present a generalized Lagrangian formulation for analysis of industrial forming processes involving thermally coupled interactions between deformable continua. The governing [...]
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A Particle Finite Element Method (PFEM) for coupled thermal analysis of quasi and fully incompressible flows and fluid-structure interaction
E. Oñate, A. Franci, J. Carbonell

(2014). Research Report, Nº PI403

Abstract
We present a Lagrangian formulation for coupled thermal analysis of quasi and fully incompressible flows and fluid-structure interaction (FSI) problems that has excellent mass preservation features. The success of the formulation lays on a residual-based stabilized expression of the mass balance equation obtained using the Finite Calculus (FIC) method. The governing equations are discretized with the FEM using simplicial elements with equal linear interpolation for the velocities, the pressure and the temperature. The merits of the formulation in terms of reduced mass loss and overall accuracy are verified in the solution of 2D and 3D adiabatic and thermally-coupled quasi-incompressible free-surface flow problems using the Particle Finite Element Method (PFEM). Examples include the sloshing of water in a tank and the falling of a water sphere and a cylinder into a tank containing water.
Abstract
We present a Lagrangian formulation for coupled thermal analysis of quasi and fully incompressible flows and fluid-structure interaction (FSI) problems that has excellent [...]
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Unified updated Lagrangian formulation for the analysis of quasi and fully incompressible fluids and solids and their interaction via a partitioned scheme and the PFEM
A. Franci, E. Oñate, J. Carbonell

(2014). Research Report, Nº PI407

Abstract
In this work, a unified updated Lagrangian formulation for solving fluid-structure interaction (FSI) problems is derived. The mixed velocity-pressure formulation for hypoelastic solids and quasi and fully incompressible Newtonian fluids is obtained as an extension of the velocity formulation derived for a general continuum. The space discretization for the fluid domain is performed via the Particle Finite Element Method (PFEM), where for the solid domain a standard FEM is used. Linear interpolation is used for both the velocity and the pressure fields. The global FSI problem is solved using a Gauss-Seidel iterative scheme. The required stabilization for dealing with incompressible situations is given by an enhanced formulation of the Finite Calculus (FIC) technique [Oñate et al.]. The efficiency of the proposed strategy is tested by solving benchmark FSI problems.
Abstract
In this work, a unified updated Lagrangian formulation for solving fluid-structure interaction (FSI) problems is derived. The mixed velocity-pressure formulation for hypoelastic [...]
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Updated Lagrangian mixed finite element formulation for quasi and fully incompressible fluids
E. Oñate, J. Carbonell

(2013). Research Report, Nº PI393

Abstract
We present a mixed velocity-pressure finite element formulation for solving the updated Lagrangian equations for quasi and fully incompressible fluids. Details of the governing equations for the conservation of momentum and mass are given in both differential and variational form. The finite element interpolation uses an equal order approximation for the velocity and pressure unknowns. The procedure for obtaining stabilized FEM solutions is outlined. The solution in time of the discretized governing conservation equations using an incremental iterative segregated scheme is described. The linearization of these equations and the derivation of the corresponding tangent stiffness matrices is detailed. Other iterative schemes for the direct computation of the nodal velocities and pressures at the updated configuration are presented. The advantages and disadvantages of choosing the current or the updated configuration as the reference configuration in the Lagrangian formulation are discussed.
Abstract
We present a mixed velocity-pressure finite element formulation for solving the updated Lagrangian equations for quasi and fully incompressible fluids. Details of the governing [...]
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El papel de los modelos numéricos en la investigación y el diseño de aliviaderos de presas
F. Salazar, J. Mauro, J. Irazábal, A. Larese, . R. Rossi, E. Oñate, R. Morán, M. Toledo

(2013). Research Report, Nº PI396

Abstract
El Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE) es un centro de investigación dependiente del Gobierno de Cataluña y de la Universidad Politécnica de Cataluña creado en 1987. Su principal actividad es el desarrollo y aplicación de métodos numéricos innovadores para resolver problemas prácticos en diversos campos de la ingeniería, y se desarrolla fundamentalmente en el marco de proyectos de investigación nacionales e internacionales. En los últimos años el centro ha participado en diversos proyectos relacionados con la seguridad de presas, fundamentalmente hidráulica, pero también estructural, en cooperación con diversas empresas y organismos públicos de investigación como el CEDEX y la UPM. La presente comunicación describe brevemente los objetivos principales de los mencionados proyectos, haciendo hincapié en cómo la modelación numérica ha contribuido a alcanzarlos.
Abstract
El Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE) es un centro de investigación dependiente del Gobierno de Cataluña y [...]
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The International Center for Numerical Methods in Engineering (CIMNE). A partner for education, research and technology transfer in computational engineering and applied sciences.
E. Oñate

(2012). Research Report, Nº PI379
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Analysis of fluid-soil-structure interaction problems with the Particle Finite Element Method (PFEM)
E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, A. Larese, R. Rossi, B. Suárez, R. Morán

(2012). Research Report, Nº PI374

Abstract
We present some developments in the Particle Finite Element Method (PFEM) for analysis of coupled problems in mechanics involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of material points in both the fluid and the solid domains (the later including soil/rocks and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The procedure to model frictional contact conditions and material erosion at fluid-solid and solid-solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of river beds, the stability of breakwaters and constructions under sea waves, the falling of landslides on houses and into a reservoir and the failure of rockfill dams in overspill situations.
Abstract
We present some developments in the Particle Finite Element Method (PFEM) for analysis of coupled problems in mechanics involving fluid-soil-structure interaction (FSSI). [...]
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Validation of the particle finite element method (PFEM) for simulation of rock slides in lakes and reservoirs
J. Irazábal, F. Salazar, E. Oñate

(2012). Research Report, Nº PI390

Abstract
The analysis of landslides in reservoirs is particularly interesting because the oscillation of the water surface elevation (especially rapid drawdowns) can foster their occurrence. The existence of the reservoir for a long enough time makes the material of the slopes turn saturated, thus its pore pressure raises and, as a consequence, its effective stress is reduced. This unstabilizing effect is partially compensated by the raise of total stress due to hydrostatic pressure generated by the water in the reservoir. A rapid drawdown eliminates the stabilization in a lapse which is frequently not enough for the pore pressure to be dissipated (this depends on the permeability of the material as well as on the velocity of the water level drop, but is quite frequent). In this situation, the probability of occurrence of a landslide is greater. In this report some validation cases are described, where the impact of sliding blocks against a mass of water is simulated, as well as the generation and propagation of the subsequent impulse wave. They are based on the experiments performed by Sælevik et al. [21].
Abstract
The analysis of landslides in reservoirs is particularly interesting because the oscillation of the water surface elevation (especially rapid drawdowns) can foster their occurrence. [...]
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El reto de la transferencia de los resultados de la investigación a la industria
E. Oñate

(2012). Research Report, Nº PI386

Abstract
En este trabajo se analizan algunas de las razones que dificultan y favorecen la transferencia de los resultados de la investigación que se desarrolla en entornos científicos al sector industrial. En concreto se analiza el proceso de la innovación y sus factores de impulso e inhibición. También se describe el ciclo que siguen las ideas, desde que se originan en un entorno científico hasta que se transforman en productos de éxito comercial. Finalmente, se presentan algunas recomendaciones para favorecer el proceso de transferencia de los resultados de la investigación a la industria y se propone la creación de un nuevo modelo de centro de I+D+I.
Abstract
En este trabajo se analizan algunas de las razones que dificultan y favorecen la transferencia de los resultados de la investigación que se desarrolla en entornos científicos [...]
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Benchmarking on bifurcation and localization in J2 plasticity for plane stress and plane strain conditions
M. Cervera, M. Chiumenti, D. Di Capua

(2011). Research Report, Nº PI370

Abstract
This paper studies the phenomenon of strain bifurcation and localization in J2 plasticity under plane stress and plane strain conditions. Necessary conditions for the outcome of bifurcation, localization, stress boundedness and decohesion are analytically established. It is shown that the explicit consideration of these conditions allows for the determination of localization angles in certain situations of interest that can be used to conduct benchmark tests on finite element formulations. The relative merits of irreducible, (stabilized) mixed and (displacement and/or strain) enhanced formulations are discussed. Numerical examples show that the mixed displacement/pressure formulation is to be preferred to the standard irreducible schemes in order to predict correct failure mechanisms with localized patterns of plastic deformation. Mixed elements are shown to be practically free from mesh directional bias dependence.
Abstract
This paper studies the phenomenon of strain bifurcation and localization in J2 plasticity under plane stress and plane strain conditions. Necessary conditions for the outcome [...]
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Análisis de flujos en lámina libre y su interacción con sólidos y estructuras por el método de partículas y elementos finitos (PFEM)
E. Oñate, B. Suárez, F. Salazar, R. Morán, M. Celigueta, S. Latorre

(2011). Research Report, Nº PI365

Abstract
Se describen los conceptos básicos del método de partículas y elementos finitos (PFEM) para análisis de flujos de fluidos en lámina libre y su interacción con objetos sólidos y estructuras flotantes o sumergidas. Se presentan diversas aplicaciones del PFEM en los ámbitos de la ingeniería de puertos e hidráulica y al estudio de la caída de una avalancha sobre un embalse.
Abstract
Se describen los conceptos básicos del método de partículas y elementos finitos (PFEM) para análisis de flujos de fluidos en lámina libre [...]
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An adaptive finite point method for aeroelastic analysis
E. Ortega, E. Oñate, S. Idelsohn

(2011). Research Report, Nº PI368

Abstract
An adaptive Finite Point Method (FPM) for solving aeroelastic compressible flow problems is presented. The numerical methodology is based on a meshless upwind-biased discretization of the Euler equations, written in arbitrary Lagrangian-Eulerian (ALE) form, and integrated in time by means of a dual-time steeping technique. This procedure allows achieving accurate solutions circumventing stability constraints of time marching schemes but profiting from its explicit features. In order to exploit the meshless potential of the method, the domain deformation approach implemented is based on the spring network analogy and ''h''-adaptivity is also employed in the computations. Several numerical examples involving typical aeroelastic problems illustrate the performance of the proposed technique. Moreover, evidence about the computational cost and parallel performance of the method is given.
Abstract
An adaptive Finite Point Method (FPM) for solving aeroelastic compressible flow problems is presented. The numerical methodology is based on a meshless upwind-biased discretization [...]
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Modelització del deflectòmetre d’impacte amb el mètode dels elements finits i les partícules
M. Font, E. Oñate, J. Carbonell

(2011). Research Report, Nº PI366

Abstract
El deflectòmetre d’impacte segurament és l’aparell més utilitzat per realitzar assaigs no destructius dels ferms. Els enginyers utilitzen el deflectòmetre d’impacte per estimar els mòduls elàstics de les diferents capes que conformen el ferm assumint una aproximació quasi estàtica del fenomen. Amb la utilització del Mètode dels Elements Finits i les Partícules (PFEM), per una banda es pot simular l’impacte que provoca el deflectòmetre d’impacte sobre el ferm, i de l’altra validar el PFEM com a model axisimètric de resposta dinàmica d’un ferm. La validació consisteix a comparar la concavitat de deflexions mesurada pel deflectòmetre d’impacte amb la concavitat de deflexions calculada amb el PFEM utilitzant els mòduls elàstics que proporciona el càlcul invers. Els capítols 2 i 3 inclouen el marc teòric en el qual es desenvolupa el treball. El capítol 2 inclou una introducció als ferms, presenta el concepte de deflexió, fa un repàs dels equips d’avaluació no destructiva i presenta un resum dels diferents mètodes existents per al càlcul de paviments flexibles. El capítol 3 és una introducció al Mètode dels Elements Finits i les Partícules. El capítol 4 presenta els desenvolupaments dels objectius plantejats. Per últim, es presenten unes consideracions finals, que inclouen les conclusions, possibles millores del programa d’ordinador emprat i propostes de futures línies d’investigació. Els annexes inclouen els resultats de tots els casos calculats amb les taules i les gràfiques corresponents.
Abstract
El deflectòmetre d’impacte segurament és l’aparell més utilitzat per realitzar assaigs no destructius dels ferms. Els enginyers utilitzen [...]
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Development of a 6-DoF simulator for analysis and evaluation of autonomous parafoil systems
E. González, C. Sacco, E. Ortega, R. Flores

(2011). Research Report, Nº PI356

Abstract
The role parachutes have in many civil, humanitarian and military applications call for new and improved computational tools aimed at tackling the current lack of software applications in the field. The present project, which is part of a research line being developed at CIMNE for these purposes, involves the development of numerical tools for the analysis and evaluation of autonomous parafoil systems. These tools, which are based on a 6-DOF dynamic parachute model and a GNC system implemented by means of PID algorithms, facilitate the user to test designs, develop and evaluate control strategies and analyze real-life drop scenarios. As an example of potential use, lateral and altitude control strategies were successfully developed and tested. Future implementations will include Monte Carlo simulations for statistical analysis of landing precision, parameter identification for flight-tests data reduction and an advanced GUI. The dynamic simulator presented in this work, together with the aerodynamic and structural tools developed by CIMNE, allow simulating the complete parachute-payload system, letting the designer to analyse design variations before building prototypes, the control system engineer to test different control strategies and the flight test engineer to predict the real performance of the system even before flying it once. In brief, involving simulation in the whole development process increases chances of success, shortening development time and costs.
Abstract
The role parachutes have in many civil, humanitarian and military applications call for new and improved computational tools aimed at tackling the current lack of software [...]
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Explicit dynamic analysis of thin membrane structures
R. Flores, E. Ortega, E. Oñate

(2011). Research Report, Nº PI351

Abstract
An explicit dynamic structural solver developed at CIMNE for the analysis of parachutes is presented. The canopy fabric has a negligible out-of-plane stiffness, therefore its numerical study presents important challenges. Both the large changes in geometry and the statically indeterminate character of the system are problematic from the numerical point of view. This report covers the reasons behind the particular choice of solution scheme as well as a detailed description of the underlying algorithm. Both the theoretical foundations of the method and details of implementation aiming at improving computational efficiency are given. Benchmark cases to assess the accuracy of the solution as well as examples of practical application showing the performance of the code are finally presented.
Abstract
An explicit dynamic structural solver developed at CIMNE for the analysis of parachutes is presented. The canopy fabric has a negligible out-of-plane stiffness, therefore [...]
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Advances on Finite Element Methods and Particle-based Methods for Metal Forming Processes
E. Oñate

(2011). Research Report, Nº PI360

Abstract
The paper presents an overview of the advances in recent years on the finite element method (FEM) and on particle-based methods for the simulation of industrial metal forming processes. More specifically, we present the evolution of the FEM in the field from the early plastic/viscoplastic flow approaches to the new stabilized FEM for analysis of multiphysics bulk forming processes. Also the paper describes the state of the art in the new rotation-free shell elements for simulation of sheet stamping processes. Finally, we present the so-called Particle Finite Element Method (PFEM), as a component of a family of new computational techniques integrating particle-based methods and mesh-based procedures. The PFEM is particularly suited for large deformation problems in solids and fluids involving nonlinear mechanical and geometrical effects, fluid-structure interactions and frictional contact situations. Applications of the FEM and the PFEM to several metal and material forming processes are presented.
Abstract
The paper presents an overview of the advances in recent years on the finite element method (FEM) and on particle-based methods for the simulation of industrial metal forming [...]
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The Cycle of Ideas in research, development and technology transfer
E. Oñate

(2011). Research Report, Nº PI358

Abstract
When people talks about research, development and technology transfer (RTD in short) and commercial industrial activities, it is quite usual to mix up objectives, resources and responsibilities. There is a growing opinion, spread by some public administrators and the media, that research groups at universities and RTD centers must be "profitable". In few words, many persons would wish that research is funded with competitive funds or even loans (either public or private) and that the outcomes of the research get into the market rapidly, so that the profits from marketing the corresponding products will allow research groups to be financially self-sustaining.
Abstract
When people talks about research, development and technology transfer (RTD in short) and commercial industrial activities, it is quite usual to mix up objectives, resources [...]
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A 3D low-order panel method for unsteady aerodynamic problems
E. Ortega, R. Flores, E. Oñate

(2010). Research Report, Nº PI343

Abstract
An unsteady low-order panel method for three-dimensional subsonic analyses is presented. The method, which is based on well-established techniques in computational aerodynamics, is intended to achieve a cost-effective solution of unsteady flows around arbitrary aerodynamic configurations. This work has two main objectives. First, to relax geometry discretization requirements and, second, to simplify the treatment of problems in which the analysis configuration moves along specified flight paths and/or changes its geometry during the simulation. Following this aim, a time-marching solution procedure is adopted in conjunction with a free-wake model which avoids iterative solutions for wake shape and position. The suitability of the present approach for solving typical aerodynamic problems is illustrated by means of several numerical examples.
Abstract
An unsteady low-order panel method for three-dimensional subsonic analyses is presented. The method, which is based on well-established techniques in computational aerodynamics, [...]
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Advances in the simulation of multi-fluid flows with the Particle Finite Element Method. Application to bubble dynamics
M. Mier-Torrecilla, S. Idelsohn, E. Oñate

(2010). Research Report, Nº PI342

Abstract
In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking interfaces. We develop a numerical scheme able to deal with large jumps in the physical properties, included surface tension, and able to accurately represent all types of discontinuities in the flow variables. The scheme is based on decoupling the velocity and pressure variables through a pressure segregation method which takes into account the interface conditions. The interface is defined to be aligned with the moving mesh, so that it remains sharp along time, and pressure degrees of freedom are duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity. Furthermore, the mesh is refined in the vicinity of the interface to improve the accuracy and the efficiency of the computations. We apply the resulting scheme to the benchmark problem of a two-dimensional bubble rising in a liquid column presented in [1], and propose two breakup and coalescence problems to assess the ability of a multi-fluid code to model topology changes.
Abstract
In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well [...]
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Advances in the particle finite element method (PFEM) for solving coupled problems in engineering
E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi, J. Marti, J. Carbonell, P. Ryzhakov, B. Suárez

(2010). Research Report, Nº PI347

Abstract
We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems on fluid and solid mechanics in engineering accounting for fluid-structure interaction and coupled thermal effects, material degradation and surface wear. The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations are solved, as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. The procedure for modelling frictional contact conditions at fluid-solid and solid-solid interfaces via mesh generation are described. A simple algorithm to treat soil erosion in fluid beds is presented. An straight forward extension of the PFEM to model excavation processes and wear of rock cutting tools is described. Examples of application of the PFEM to solve a wide number of coupled problems in engineering such as the effect of large waves on breakwaters and bridges, the large motions of floating and submerged bodies, bed erosion in open channel flows, the wear of rock cutting tools during excavation and tunneling and the melting, dripping and burning of polymers in fire situations are presented.
Abstract
We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems on fluid and solid mechanics in engineering [...]
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Two-noded beam element for composite and sandwich beams using Timoshenko theory and refined zigzag kinematics
E. Oñate, A. Eijo, S. Oller

(2010). Research Report, Nº PI346

Abstract
The so-called zigzag theory has been developed in recent years as an extension of the classical layer-wise theory for modeling composite laminated beams, plates and shells. An advantage of the zigzag theory is that the number of kinematic variables is independent of the number of layers. In this work we present a simple linear two-noded beam element adequate for the analysis of composite and sandwich beams based on the combination of classical Timoshenko beam theory and the refined zigzag kinematics recently proposed by Tessler et al. [19]. The accuracy of the new beam element is tested in a number of examples of applications for composite laminated beams.
Abstract
The so-called zigzag theory has been developed in recent years as an extension of the classical layer-wise theory for modeling composite laminated beams, plates and shells. [...]
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Análisis numérico de los fenómenos hidrodinámicos en escolleras con aplicaciones a presas de materiales sueltos
R. Hernández, A. Larese, E. Oñate

(2010). Research Report, Nº PI348

Abstract
Actualmente las presas de materiales sueltos son la tipología cuya elección es más frecuente debido, en parte, a los grandes avances que se han hecho en el estudio de los materiales que se utilizan en este tipo de estructuras, a la gran facilidad de encontrarlos y a su bajo coste y, por otra parte, a su adaptabilidad a una amplia variedad de emplazamientos. Sin embargo, hay que tener en cuenta su gran vulnerabilidad frente a fenómenos de sobrevertido, que pueden comprometer seriamente la estructura e incluso causar su colapso. Es por todo esto que en los últimos años se está manifestando un interés creciente en el estudio del comportamiento de las presas de material sueltos frente a fenómenos extremos. Esta tesina se enmarca en el contexto del proyecto XPRES del Plan Nacional I+D del Ministerio de Educación y Ciencia [2], cuyo principal objetivo es desarrollar un método computacional para el análisis de la evolución de la filtración, así como el seguimiento del proceso de rotura en las presas de escollera en caso de sobrevertido. Este objetivo requiere el desarrollo de dos modelos numéricos acoplables, uno que modelice el proceso de filtración en el cuerpo de la presa y otro que modelice la respuesta estructural. Se pretende abordar la validación de los algoritmos desarrollados por CIMNE para la modelización de la filtración y determinar cuál de ellos presenta las mejores características para su aplicación en casos reales. La validación se llevará a cabo utilizando Kratos, un código abierto C++ que se está desarrollando en CIMNE pensado para resolver problemas de multifísica mediante el método de los elementos finitos. Los resultados numéricos se compararán los datos experimentales proporcionados por CEDEX y UPM y los modelos teóricos obtenidos por UPM. Esta validación se centrará, principalmente, en el modelo en dos dimensiones, aunque se hará extensible al caso en tres dimensiones.
Abstract
Actualmente las presas de materiales sueltos son la tipología cuya elección es más frecuente debido, en parte, a los grandes avances que se han hecho [...]
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Innovative numerical tools for the simulation of parachutes
E. Ortega, R. Flores, E. Oñate, C. Sacco, E. González

(2010). Research Report, Nº PI341

Abstract
The design and evaluation of parachute-payload systems is an important field of applications in which numerical analysis tools can make very important contributions. This work describes new numerical developments carried out at CIMNE in this field, which involve a coupled fluid-structural solver intended for the unsteady simulation of ram-air type parachutes and a set of complementary tools aimed at studying trajectory and control systems effects. For an efficient solution of the aerodynamic problem, an unsteady panel method has been chosen exploiting the fact that large areas of separated flow are not expected under nominal flight conditions of ram-air parachutes. Besides, a dynamic explicit solver based on a finite element technique is chosen for the structure. This approach yields a robust solution even when highly non-linear effects due to large displacements and material asymmetric behaviours are present. The numerical results show considerable accuracy and robustness. An added benefit of the proposed aerodynamic and structural techniques is that they can be easily vectored and thus suitable for use in parallel architectures. The main features of the developed computational tools are described in this work and several numerical examples are provided to illustrate the good performance and potential of the proposed techniques. Further improvements of the methodology being carried out and future lines of investigation are also presented.
Abstract
The design and evaluation of parachute-payload systems is an important field of applications in which numerical analysis tools can make very important contributions. This [...]
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Possibilities of the particle finite element method in computational mechanics
E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi, S. Latorre

(2010). Research Report, Nº PI345

Abstract
We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in fluid and solid mechanics accounting for fluid-structure interaction and coupled thermal effects. The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. Extensions of the PFEM to allow for frictional contact conditions at fluid-solid and solid-solid interfaces via mesh generation are described. A simple algorithm to treat erosion in the fluid bed is presented. Examples of application of the PFEM to solve a number of coupled problems such as the effect of large wave on structures, the large motions of floating and submerged bodies, bed erosion situations and melting and dripping of polymers under the effect of fire are given.
Abstract
We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in fluid and solid mechanics accounting [...]
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Interface GiD-SAP2000-VRML. Aplicación práctica a la modelización virtual de edificios del patrimonio histórico
F. Muñoz, J. Maristany, J. López-Rey

(2010). Research Report, Nº PI344

Abstract
The numerical modeling of historic buildings is an essential tool for understanding the structural behavior, even more whit the aim is to assume an analysis for conservation and / or rehabilitation. At present time, most building’s numerical simulation software is divided into three parts: the preprocessor, which prepares all the necessary information (geometry, boundary conditions, loads, etc.), the Analysis, where all calculations take place (FEM) and the postprocessing where decisions are taking based on the analysis of the results obtained in the previous steps (Muñoz, Maristany 1999). At that last point is, where the user of the computer programs usually find limitations in the graphical interpretation of the results. Some numerical results with endless list of numbers are not the best way to address the problem and its graphical output is not yet fully developed. That is, graphic interface is still very basic, let alone a real-time dynamic visualization in 3D. It`s important to have both powerful hardware and software tools to visualize the obtained results. Currently, there are emerging many structural analysis programs that have highly advanced postprocessing, but they still display limitations in space, they operate only on 2 or 3 dimensions with space constraints. For this reason, this paper seeks to integrate different current computer programs with 3D graphical representation. Thus, the visualization of numerical results (tension, stress and strain values) can be much more interesting. This is to enable users to virtually navigate in real time, through any 3D structure and better understand their behavior. In short, this research aims to develop an interface between the computer programs of structural calculations and representation software with virtual 3D graphics (vrml- virtual reality modeling language), with practical application to historic buildings. As a closure for the paper we develop a practical example based on Mexico City’s Cathedral tabernacle.
Abstract
The numerical modeling of historic buildings is an essential tool for understanding the structural behavior, even more whit the aim is to assume an analysis for conservation [...]
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Modeling thermoplastic melt spread over different flooring materials
K. Butler, E. Oñate, R. Rossi, J. Marti, S. Idelsohn

(2010). Research Report, Nº PI349

Abstract
The effects of the thermal properties of three flooring materials on the spread rate of polymer melt over the surface were studied using a model based on the Particle Finite Element Method (PFEM). The high thermal conductivity of steel keeps the steel floor at a nearly uniform temperature throughout, whereas the ceramic and oak floors are able to sustain a higher temperature beneath the point at which the hot melt is dripping onto the surface. In general, the spread rate is controlled by the viscosity at the outer edges of the melt pool. The spread rate over steel is therefore fastest, especially for a thin floor that rapidly increases in temperature. The low thermal inertia of oak results in rapid changes in surface temperature, which traps the heat close to the interface between the floor and the melt and maintains a high temperature and low viscosity in the center of the melt pool. The ceramic floor transports heat more readily and may develop a hot spot underneath. The material properties of ceramic lie between those of oak and steel, but although the spread rate over a steel floor is always faster than over ceramic, the spread rate over oak may not always be slower.
Abstract
The effects of the thermal properties of three flooring materials on the spread rate of polymer melt over the surface were studied using a model based on the Particle Finite [...]
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La ciencia a l'enginyeria. El llegat de l'école polytechnique
X. Oliver

(2009). Research Report, Nº PI338
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Size effect and localization in J2 plasticity
M. Cervera, M. Chiumenti

(2009). Research Report, Nº PI331

Abstract
This paper studies the phenomenon of structural size effect and strain localization in J2 plasticity. Size effect is here understood as the change in the response of a given structure when the spatial dimensions are scaled up or down while the geometry and other relevant properties of the structure are preserved. The work exploits the advantages of the mixed displacement–pressure formulation in incompressible or quasi-incompressible situations. Elasto-J2-plastic constitutive behaviour with regularized softening is considered. Stability issues are discussed to ensure existence and uniqueness of the solution of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is able to solve a wide range of structural scales, including real life engineering applications. The results obtained do not suffer from spurious mesh dependence. Furthermore, the formulation includes the classical theories of perfect plasticity and linear fracture mechanics as limit cases.
Abstract
This paper studies the phenomenon of structural size effect and strain localization in J2 plasticity. Size effect is here understood as the change in the response of a given [...]
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Fuel cells state of the art
A. Jarauta, J. Pons Prats

(2009). Research Report, Nº PI340
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Las ingenierias: Unas profesiones de largo recorrido
B. Suarez

(2009). Research Report, Nº PI339
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A finite point method to solve shallow water equations.
C. Buachart, E. Ortega, E. Oñate

(2009). Research Report, Nº PI337
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Optimizing rock cutting through computer simulation
J. Rojek, E. Oñate, C. Labra, H. Kazal, J. Akerman

(2009). Research Report, Nº PI336

Abstract
This paper presents an original thermomechanical model of rock cutting with evaluation of tool wear. The model has been developed within the framework of the discrete element method, which is a suitable numerical method to study problems of multiple material fractures likes those of rock cutting. The paper presents brief overview of the theoretical formulation, calibration of the discrete element model, and a number of numerical results obtained in simulation of rock cutting processes typical for underground excavation, using both roadheaders and TBMs.
Abstract
This paper presents an original thermomechanical model of rock cutting with evaluation of tool wear. The model has been developed within the framework of the discrete element [...]
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A neural networks approach to aerofoil noise prediction
K. Lau, R. López, E. Oñate

(2009). Research Report, Nº PI335

Abstract
A neural network noise prediction model for a turbulent boundary layer noise mechanism has been created using a feed forward multilayer perceptron and a noise spectrum database collected from a family of NACA 0012 areofoils. The results of the neural network model were compared against the Brooks model and it was found that the quality of the prediction was improved was improved over the entire range of the data. The model was also validated against experimental data not utilized the training of the neural, with positive results.
Abstract
A neural network noise prediction model for a turbulent boundary layer noise mechanism has been created using a feed forward multilayer perceptron and a noise spectrum database [...]
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Melting and spread of polymer in fire with the particle finite element method
E. Oñate, R. Rossi, K. Butler, S. Idelsohn

(2009). Research Report, Nº PI333

Abstract
A new computational procedure for analysis of the melting and flame spread of polymers under fire conditions is presented. The method, termed Particle Finite Element Method (PFEM), combines concepts from particle-based techniques with those of the standard finite element method (FEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in the thermoplastic material. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of melting and dripping of polymer particles. A mesh connects the nodes defining the discretized domain where the governing equations are solved as in the standard FEM. An incremental iterative scheme for the solution of the nonlinear transient coupled thermal-flow problem, including loss of mass by gasification, is used. Examples of the possibilities of the PFEM for the modelling and simulation of the melting and flame spread of polymers under different fire conditions are described. Numerical results are compared with experimental data provided by NIST.
Abstract
A new computational procedure for analysis of the melting and flame spread of polymers under fire conditions is presented. The method, termed Particle Finite Element Method [...]
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A numerical investigation of wind tunnel model deformations caused by the twin-sting support system
R. Flores, E. Ortega, E. Oñate

(2009). Research Report, Nº PI334

Abstract
This work presents a wing deformation analysis of a twin-sting-mounted commercial aircraft model. Twin-sting arrangements minimize flow disturbances around the model fuselage and tail; on the other hand, they cause important changes in the flow field around the wing and also increase aerodynamic interference at the wing and aeroelastic effects on the wing. In some cases, these effects can alter the normal downwash developed behind the wing, modifying the flow pattern at the tail. Consequently, when tail aerodynamics is a major concern, this kind of support interference should be carefully evaluated. The methodology developed in this work employs an unstructured FEM-based flow solver for computing aerodynamic loads. These loads are then transferred to a finite element structural model in order to assess the geometrical deformation of the wing caused by torsional moment exerted by supporting mechanism. The analysis described involves three different twin-sting support configurations taking into account angle of attack variations and Mach numbers spanning from subsonic of high transonic ranges.
Abstract
This work presents a wing deformation analysis of a twin-sting-mounted commercial aircraft model. Twin-sting arrangements minimize flow disturbances around the model fuselage [...]
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Robust design methods in aerospace engineering
M. Kouhi, E. Oñate, G. Bugeda

(2008). Research Report, Nº PI328

Abstract
This document is an introduction to some important methodologies that have been developed in robust design in aerospace engineering. After describing the concept of robustness and uncertainty, multipoint, minimax, expected value, second order second moment and Taguchi methods are mentioned. At the end of this report, Game Theory, as one of the approach for multi objective optimization problems has been introduced.
Abstract
This document is an introduction to some important methodologies that have been developed in robust design in aerospace engineering. After describing the concept of robustness [...]
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Implementation of a general algorithm for incompressible and compressible flows within the multi-physics code Kratos and preparation of fluid-structure coupling
R. Rossi, E. Oñate, A. Maymó

(2008). Research Report, Nº PI327

Abstract
This diploma thesis deals with the implementation of a fluid solver for incompressible and compressible flows within the multi-physics framework Kratos. The presentation of this environment based on the finite element method (FEM) and an introduction to multidisciplinary problems in general are the starting point of this work and help understanding the following steps more easily. Originating from the basic conservation equations for mass, momentum and energy, the Euler equations for inviscid flow are derived. In this context some approximations are presented that avoid the solution of the energy equation and allow the use of a general approach for the simulation of incompressible, slightly compressible and barotropic flow. The implementation of the incompressible case is outlined step-by-step: Having discretized the continuous problem, a fractional step scheme is presented in order to uncouple pressure and velocity components by a split of the momentum equation. Emphasis is placed on the nodal implementation using an edge-based data structure. Moreover, the orthogonal subscale stabilization - necessary because of the finite element discretization - is explained very briefly. Subsequently, the solver is extended to compressible regime mentioning the respective modifications. For validation purposes numerical examples of incompressible and compressible flows in two and three dimensions round of this first part. In a second step, the implemented flow solver is prepared for the fluid-structure coupling. After presenting solving procedures for multi-disciplinary problems, the arbitrary Lagrangian Eulerian (ALE) formulation is introduced and the conservation equations are modified accordingly. Some preliminary tests are performed, particularly with regard to mesh motion and adjustment of the boundary conditions. Finally, expectations for the envisaged fluid-structure coupling are brought forward.
Abstract
This diploma thesis deals with the implementation of a fluid solver for incompressible and compressible flows within the multi-physics framework Kratos. The presentation of [...]
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PUMI: An explicit ED unstructural finite element solver for the Euler equations
R. Flores, E. Ortega

(2008). Research Report, Nº PI326

Abstract
The PUMI flow solver has been developed at CIMNE in to address the need for fast solutions of the flow field around complex geometries. Nowadays calculations involving a number of cells on the order of ten million are performed routinely. PUMI was created to deal with this kind of large-scale problem using modest hardware, therefore special emphasis was placed on the computational efficiency of the code. Design guidelines where minimum memory requirement, very fast single-threaded performance as well as satisfactory parallel scaling up to a moderate number of threads (as found on current desktop hardware using a small number of multi-core CPUs. In order to speedup the mesh generation activities an unstructured finite element formulation was selected. This papers describes the theoretical basis of the algorithms as well as detail of the implementation that increase the robustness and efficiency of the code.
Abstract
The PUMI flow solver has been developed at CIMNE in to address the need for fast solutions of the flow field around complex geometries. Nowadays calculations involving a number [...]
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A cooling system for a hybrid PV/thermal linear concentrator
D. Chemisana, J. Cipriano, M. Ibáñez, B. Mesih, A. Mellor

(2008). Research Report, Nº PI325

Abstract
This paper presents the thermal evaluation of an evacuated PVT collector designed to operate under concentrated radiation (15 suns). Finite volume 3D numerical computations have been carried out in order to study the thermal characteristics of different rectangular cross section aluminium pipes and to test the performance of the PVT collector with several laminar flow rates. Experiments with the same laminar flows show the same behavior than in the numerical results.
Abstract
This paper presents the thermal evaluation of an evacuated PVT collector designed to operate under concentrated radiation (15 suns). Finite volume 3D numerical computations [...]
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A finite point method for adaptive three-dimensional compressible flow calculation
E. Ortega, E. Oñate, S. Idelsohn

(2008). Research Report, Nº PI323

Abstract
The Finite Point Method (FPM) is a meshless technique which is based on both, a Weighted Least-Squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a major investigation into the capabilities of the FPM to deal with threedimensional applications concerning real compressible fluid flow problems. In the first part of this work, the upwind biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting meshless capabilities, an h-adaptive methodology for two and three-dimensional compressible flow calculations is developed. This adaptive technique applies a solution-based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are highly encouraging. Several numerical examples are provided throughout the article in order to illustrate their performance.
Abstract
The Finite Point Method (FPM) is a meshless technique which is based on both, a Weighted Least-Squares numerical approximation on local clouds of points and a collocation [...]
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Lift maximization with uncertainties for high lift devices optimization
Z. Tang, J. Periaux, G. Bugeda, E. Oñate

(2008). Research Report, Nº PI322

Abstract
In this paper, the aerodynamic shape optimization problems with uncertain operating conditions has been addressed. After a review of robust control theory and the possible approaches to take into account uncertainties, the use of Taguchi robust design methods in order to overcome single point design problems in Aerodynamics is proposed. Under the Taguchi concept, a design with uncertainties is converted into an optimization problem with two objectives which are the mean performance and its variance, so that the solutions are as less sensitive to the uncertainty of the input parameters as possible. Furthermore, the Multi-Criterion Evolutionary Algorithms (MCEAs) are used to capture a set of compromised solutions (Pareto front) between these two objectives. The flow field is analyzed by Navier-Stokes computation using an unstructured mesh. The proposed approach drives to the solution of a multi-objective optimization problem that is solved using a modification of a Nondominated Sorting Genetic Algorithm (NSGA). In order to reduce the number of expensive evaluations of the fitness function a Response Surface Modeling (RSM) is employed to estimate the fitness value using the polynomial approximation model. During the solution of the optimization problem a Semi-torsional Spring Analogy is used for the adaption of the computational mesh to all the obtained geometrical configurations. The proposed approach is applied to the robust optimization of the 2D high lift devices of a business aircraft by maximizing the mean and minimizing the variance of the lift coefficients with uncertain free-stream angle of attack at landing and takeoff flight conditions, respectively.
Abstract
In this paper, the aerodynamic shape optimization problems with uncertain operating conditions has been addressed. After a review of robust control theory and the possible [...]
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Validación experimental del Particle Finite Element Method (PFEM)
E. Oñate, A. Larese, S. Idelsohn, M. Celigueta, R. Rossi

(2008). Research Report, Nº PI318
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Desarrollo de un soporte metálico intravascular
M. Bordone, E. Oñate, E. Soudah, M. Chiumenti

(2008). Research Report, Nº PI317

Abstract
Las enfermedades cardiovasculares son la primera causa de muerte de la población Europea. Se estima que la mortalidad por enfermedades cardiovasculares es la mitad de la mortalidad total en toda Europa y provoca 4,35 millones de fallecidos cada año en los 52 estados miembros de la Región Europea. Según la Organización Mundial de la Sanidad (OMS) más de 1,9 millones de muertos en la Unión Europea, además de ser la principal causa de deshabilitad y reducción de calidad de vida. Estos tipos de enfermedades afectan sobre todo a la mayor parte de la población, y, sabiendo que el porcentaje de ancianos en la nuestra sociedad sigue subiendo, se puede fácilmente entender que las cardio-patologías puedan constituir siempre un riesgo elevado para la salud de los países occidentales. La cirugía moderna busca cada día soluciones menos invasivas, como por ejemplo a través de cirugía llamada mini-invasiva. La cirugía mini-invasiva es la técnica quirúrgica que consiente acceder a cavidades internas sin operar incisiones (cirugía en abierto). En esta definición, es trivial intuir que entran sobre todo las técnicas endoscópicas que han permitido realizar muchas operaciones de diferente grado de peligrosidad produciendo numerosos beneficios y reduciendo los índices de riesgo. En la cirugía cardiovascular no es raro encontrar problemáticas de tener que insertar aparatos como stent, válvulas cardiacas, sondas y muchas cosas más a través pequeños orificios (como vasos sanguíneos, por ejemplo, la femoral, la aorta la carótida o la subclavia). Estos aparatos van a ser posicionados o conducidos a través de guías (catéteres) que los conducen hasta el sitio destinado. El hecho de utilizar catéteres que tienen que penetrar por estas vías obliga a que estos aparatos respecten dimensiones muy pequeñas. Es interesante entonces estudiar como estas estructuras deben de soportar esfuerzos de compresión y de expansión cuando vienen insertadas en el catéter y luego se sueltan. El ejemplo en el cual enfocaremos nuestro estudio va a ser un soporte metálico intravascular para cualquier aparato necesite ser anclado en el interior de una vena o arteria.
Abstract
Las enfermedades cardiovasculares son la primera causa de muerte de la población Europea. Se estima que la mortalidad por enfermedades cardiovasculares es la mitad [...]
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Numerical validation of hemodynamic factors in vascular diseases
M. Bordone, E. Oñate, E. Soudah

(2008). Research Report, Nº PI315
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Desarrollo de modelos constitutivos avanzados para análisis del comportamiento no lineal de materiales de construcción
M. Cervera

(2008). Research Report, Nº PI316

Abstract
En este informe se describen algunos de los desarrollos recientes en modelos constitutivos avanzados para el comportamiento no lineal de materiales de construcción. El trabajo se centra especialmente en los modelos de simulación numérica del fenómeno de fisuración en hormigón estructural y otros geomateriales tales como la mampostería y la obra de fábrica. En la primera parte del informe se describen los enfoques principales para la simulación numérica de la fisuración a tracción en estructuras de hormigón: el de fisura discreta y el de fisura distribuida, para centrarse en el segundo. Dentro de éste, el informe describe en detalle un modelo escalar de daño continuo desarrollado en CIMNE. Este modelo de daño se basa en la partición del tensor de tensiones para poder capturar el comportamiento unilateral del hormigón al pasar de tracción a compresión y viceversa. El modelo propuesto adopta un formalismo basado en las deformaciones totales, lo cual aumenta su eficiencia algorítmica y lo hace especialmente apto para aplicaciones sísmicas y problemas de gran tamaño, tal como se muestra en las aplicaciones presentadas. En la última parte del informe se trata el tema de la localización de deformaciones y de daño y de la simulación numérica del colapso estructural. En esta parte se combina el modelo de daño distribuido presentado anteriormente con un algoritmo de rastreo de fisuras. La mejoría de las capacidades del modelo se hace patente en las aplicaciones mostradas y, especialmente, en el estudio de un arco semicircular de obra de fábrica con carga asimétrica, cuyos resultados son mucho más realistas que los que se obtienen con el modelo de daño distribuido en su forma original. El informe concluye con algunas observaciones sobre la utilidad de los modelos constitutivos avanzados y su aplicación por parte de los usuarios finales de programas comerciales o de propósito específico.
Abstract
En este informe se describen algunos de los desarrollos recientes en modelos constitutivos avanzados para el comportamiento no lineal de materiales de construcción. [...]
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Development and characterization of semitransparent double skin PV façades
J. Cipriano, C. Lodi, D. Chimisana, G. Houzeaux, O. Perpiñan

(2008). Research Report, Nº PI324

Abstract
This research aims at developing new standardized typologies of semitransparent double skin façades formed by PV laminates in the outer skin. At present there are many buildings in Europe which incorporate such active façades, but all have been designed as user defined projects and very few accurately evaluate the feasibility of using the heat produced within the air gap. There is actually a lack of effective methodology to allow non-specialist architects to design and evaluate such façades. This research tries to address this situation: the Spanish PV manufacturer ISOFOTON, together with the partners of the PVTBUILDING project: CIMNE, the UdL, PICHAguilera, DOMUS and BSC have begun a collaboration to design industrialized modules constituted by an external semitransparent PV layer, a wide air gap and an internal glass layer. This paper describes the results of four stages of a more wide research: a detailed analysis of the existing double skin façades in office buildings and the definition of a family of standard PV modules and ventilated façades; an intensive evaluation of the existing heat transfer relations for asymmetrical heated vertical air channels; the programming of a dynamic transient solver based on TRNSYS and the validation of the codes with the set up of prototypes and the beginning of an experimental campaign.
Abstract
This research aims at developing new standardized typologies of semitransparent double skin façades formed by PV laminates in the outer skin. At present there are many [...]
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Análisis elasto-viscoplástico en problemas bidimensionales con Stampack
W. Castelló, F. Flores

(2008). Research Report, Nº PI329

Abstract
Este informe presenta los avances logrados en la implementación dentro del código Stampack, de un modelo constitutivo elasto-viscoplástico del tipo de Perzyna para materiales isótropos con endurecimiento por deformación. El objetivo principal de incluir un modelo elasto-viscoplástico en Stampack, es la posibilidad de tener en cuenta como influye la velocidad de deformación en problemas industriales como el forjado o la extrusión. En estos problemas las temperaturas elevadas (más de un tercio de la temperatura de fusión) juegan un rol importante, provocando un estado viscoso en el material de manera que el flujo plástico resulta ser función de la velocidad de deformación del sólido. El modelo elegido resulta una extrapolación directa del modelo elasto-plástico basado en el gradiente de deformaciones propuesto por Garino [1]. El modelo elasto-visco-plástico unificado se corresponde al propuesto por Ponthot [2]. Aquí se ha empleado el trabajo de Garino y Ponthot et al.[3] para la definición de un benchmark aceptable para la comparación de resultados. En este informe se presenta el modelo elasto-viscoplástico implementado en el código de elementos finitos Stampack, y se muestra la primera etapa de prueba asociada con problemas en pequeñas deformaciones. Anteriormente Stampack no poseía un modelo elasto-viscoplástico para tratar problemas bidimensionales en deformaciones finitas. El contenido del informe es el siguiente: la sección 2 presenta la cinemática asociada al modelo, el modelo de endurecimiento viscoso y el esquema numérico de integración de la ecuación constitutiva. La sección 3 muestra el ingreso de datos a Stampack y cuáles son las rutinas involucradas en proceso de integración del modelo elasto-viscoplástico. Por último, la sección 4 contiene un problema de aplicación y se comparan los resultados del presente trabajo con los obtenidos por otros investigadores.
Abstract
Este informe presenta los avances logrados en la implementación dentro del código Stampack, de un modelo constitutivo elasto-viscoplástico del tipo de [...]
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Nuevos elementos de lámina cusdrilateros sin rotaciones
C. Estrada, F. Flores

(2008). Research Report, Nº PI330

Abstract
El contenido de este informe semestral es el siguiente. En la Sección 3 se presentan los aspectos básicos de la formulación original del elemento BSQ. Se muestra la geometría donde se define “la parcela de elementos” y el sistema de coordenadas a utilizar y el cálculo de las curvaturas en función de las coordenadas de los nudos de la parcela. En la Sección 4 se describe una forma alternativa de tratar el campo de curvatura con motivos de extender las capacidades del BSQ al tratamiento de superficies quebradas y ramificadas. El cálculo de las deformaciones membranales se muestra en la Sección 5. En la Sección 6 se muestra el nuevo esquema particular de estabilización física y una forma alternativa de tratar las fuerzas de estabilización flexional. También se dan algunos detalles respecto al cálculo de fuerzas nodales equivalentes. En la Sección 7 se presenta algunos ejemplos de los elementos presentado incluyendo ejemplos no lineales. Finalmente se resumen algunas conclusiones.
Abstract
El contenido de este informe semestral es el siguiente. En la Sección 3 se presentan los aspectos básicos de la formulación original del elemento BSQ. [...]
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Lift maximization with uncertainties for the optimization of high‐lift devices
Z. Tang, J. Périaux, E. Oñate, G. Bugeda

(2008). Research Report, Nº PI314

Abstract
In this paper, the aerodynamic shape optimization problems with uncertain operating conditions have been addressed. After a review of robust control theory and the possible approaches to take into account uncertainties, the use of Taguchi robust design methods in order to overcome single point design problems in aerodynamics is proposed. Under the Taguchi concept, a design with uncertainties is converted into an optimization problem with two objectives which are the mean performance and its variance, so that the solutions are as less sensitive to the uncertainty of the input parameters as possible. Furthermore, the modified non‐dominated sorting genetic algorithms are used to capture a set of compromised solutions (Pareto front) between these two objectives. The flow field is analyzed by Navier–Stokes computation using an unstructured mesh. In order to reduce the number of expensive evaluations of the fitness function a response surface modeling is employed to estimate the fitness value using the polynomial approximation model. During the solution of the optimization problem, a semi‐torsional spring analogy is used for the adaption of the computational mesh to all the obtained geometrical configurations. The proposed approach is applied to the robust optimization of the 2D high‐lift devices of a business aircraft by maximizing the mean and minimizing the variance of the lift coefficients with uncertain free‐stream angle of attack at landing flight condition.
Abstract
In this paper, the aerodynamic shape optimization problems with uncertain operating conditions have been addressed. After a review of robust control theory and the possible [...]
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Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE). Vint anys d'historia
E. Oñate

(2007). Research Report, Nº PI312

Abstract
El CIMNE (www.cimne.com), un centre de recerca consorci entre la Universitat Politècnica de Catalunya i la Generalitat de Catalunya, fa vint anys. El CIMNE està especialitzat en el desenvolupament i l’aplicació de mètodes numèrics avançats per a la solució d’un ampli ventall de problemes en enginyeria, que van des de la mecánica de sòlids i estructures, fins als processos de fabricació, passant per les TIC i els sistemes de suport a la decisió per a la prevenció i el tractament de catàstrofes naturals, com poden ser les inundacions o els vessaments de productes tòxics. El CIMNE es posiciona com un centre clau en el paper del desenvolupament d’idees originades en entorns de recerca bàsica i la seva transferència al sector industrial, per a la seva posterior industrialització i comercialització.
Abstract
El CIMNE (www.cimne.com), un centre de recerca consorci entre la Universitat Politècnica de Catalunya i la Generalitat de Catalunya, fa vint anys. El CIMNE està [...]
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A finite point method for three-dimensional compressible flow
E. Ortega, E. Oñate, S. Idelsohn

(2007). Research Report, Nº PI310
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Analysis of ship hydrodynamics using the overlapping domain decomposition level set method
K. Lam

(2007). Research Report, Nº PI307

Abstract
This report investigates the free surface capture of the Overlapping Domain Decomposition Level Set Method (ODDLS). The CFD software Tdyn is used to carry out computations in unison with GiD a pre/post processor to prepare the model and to analysis data. The Arbitrary Lagrangian-Eulerian method is also applied to allow deformation of the model mesh to allow the hull to sink and trim and to optimise free surface capture. The offshore patrol vessel NT-130 developed by Navtec in Chile is the focus of the computations. Experimental towing tank data for still water conditions was compared to Tdyn results to asses its performance. Also, data from tests in wave conditions is presented in this report.
Abstract
This report investigates the free surface capture of the Overlapping Domain Decomposition Level Set Method (ODDLS). The CFD software Tdyn is used to carry out computations [...]
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Shape optimization in aeronautical applications using neural networks
A. Daring, R. López, R. Flores, G. Bugeda, E. Oñate

(2007). Research Report, Nº PI306

Abstract
An optimization methodology based on neural networks was developed for use in 2D optimal shape design problems. Neural networks were used as a parameterization scheme to represent the shape function, and an edge-based high-resolution scheme for the solution of the compressible Euler equations was used to model the flow around the shape. The global system incorporates neural networks and the Euler fluid solver into the C++ Flood optimization framework containing a library of optimization algorithms. The optimization scheme was applied to a minimal drag problem in an unconstrained optimization case and a constrained case in hypersonic flow using evolutionary training algorithms. The results indicate that the minimum drag problem is solved to a high degree of accuracy but at high computational cost. For more complex shapes, parallel computing methods are required to reduce computational time.
Abstract
An optimization methodology based on neural networks was developed for use in 2D optimal shape design problems. Neural networks were used as a parameterization scheme to represent [...]
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Sistema de predicción de resistencia basado en redes neuronales
I. Ortigoza, J. García-Espinosa

(2007). Research Report, Nº PI305

Abstract
In this work we will be based on two experimental-based statistical techniques, which allow us to determine approximately the residual resistance coefficient of the sailboat and the viscous coefficient and wave resistance coefficient in the case of merchants. For the calculation of the residual resistance in sailboats the most used method is the Delft series, and for the calculation of the residual resistance in merchants the most widespread method is that of Holtrop and Mennen. Both methods used experimental data to adjust a function, the results obtained with the functions are quite reliable, but it is difficult to improve the model since the statistical adjustment is complicated. For this reason, in this work we try to overcome that limitation and develop a tool that is capable of performing the same calculations, with the same or better reliability and also that allows to be constantly improved with experimental data. The tool used is the neural network.
Abstract
In this work we will be based on two experimental-based statistical techniques, which allow us to determine approximately the residual resistance coefficient of the sailboat [...]
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Computation of turbulent flows using a finite element formulation
E. Oñate, A. Valls, J. García-Espinosa

(2007). Research Report, Nº PI304

Abstract
We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization terms introduced by the FIC approach allow to solve a wide range of fluid flow problems at different Reynolds numbers, including turbulent flows, without the need of a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows at large Reynolds numbers exhibiting turbulence features are presented.
Abstract
We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization [...]
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Enhanced Rotation-Free Basic Shell Triangle. Applications to Sheet Metal Forming
E. Oñate, F. Flores, L. Neamtu

(2007). Research Report, Nº PI302

Abstract
An enhanced rotation-free three node triangular shell element (termed EBST) is presented. The element formulation is based on a quadratic interpolation of the geometry in terms of the six nodes of a patch of four triangles associated to each triangular element. This allows to compute an assumed constant curvature field and an assumed linear membrane strain field which improves the in-plane behaviour of the element. A simple and economic version of the element using a single integration point is presented. The implementation of the element into an explicit dynamic scheme is described. The efficiency and accuracy of the EBST element and the explicit dynamic scheme are demonstrated in many examples of application including the analysis of a cylindrical panel under impulse loading and sheet metal stamping problems.
Abstract
An enhanced rotation-free three node triangular shell element (termed EBST) is presented. The element formulation is based on a quadratic interpolation of the geometry in [...]
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Membranes structures formed by low pressure inflatable tubes. New analysis methods and recent constructions
E. Oñate, F. Flores, J. Marcipar

(2007). Research Report, Nº PI303

Abstract
This paper shows applications of a recently developed thin shell element adequate for the analysis of membrane and inflatable structures. The element is a three node triangle with only translational degrees of freedom that uses the configuration of the three adjacent elements to evaluate the strains in terms of the nodal displacements only. This allows to compute (constant) bending strains and (linear) membrane strains using a total Lagrangian formulation. Several examples, including inflation and deflation of membranes and some practical applications to the analysis, design and construction of membrane structures formed by low pressure inflatable tubes are presented.
Abstract
This paper shows applications of a recently developed thin shell element adequate for the analysis of membrane and inflatable structures. The element is a three node triangle [...]
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NURBS-Enhanced finite element method for eular equations
R. Sevilla, S. Fernández-Méndez, A. Huerta

(2007). Research Report, Nº PI309

Abstract
In this work the NURBS-Enhanced Finite Element Method (NEFEM) is combined with a Discontinuous Galerkin (DG) formulation for the numerical solution of the Euler equations of gas dynamics. With the NEFEM approach numerical fluxes along curved boundaries are computed much more accurately due to the exact geometric representation of the computational domain. The proper implementation of the wall boundary condition provides accurate results even with a linear interpolation of the solution. A detailed comparison of the NEFEM in front of isoparametric finite elements (FE) is presented, demonstrating the superiority of the NEFEM approach for both linear and higher order computations.
Abstract
In this work the NURBS-Enhanced Finite Element Method (NEFEM) is combined with a Discontinuous Galerkin (DG) formulation for the numerical solution of the Euler equations [...]
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NURBS-Enhanced finite element methods (NEFEM)
R. Sevilla, S. Fernández-Méndez, A. Huerta

(2007). Research Report, Nº PI308

Abstract
An improvement of the classical finite element method is proposed. It is able to exactly represent the geometry by means of the usual CAD description of the boundary with Non-Uniform Rational B-Splines (NURBS). Here, the two-dimensional case is presented. For elements not intersecting the boundary, a standard finite element interpolation and numerical integration is used. But elements intersecting the NURBS boundary need a specifically designed piecewise polynomial interpolation and numerical integration. A priori error estimates are also presented. Finally, some examples demonstrate the applicability and benefits of the proposed methodology. NEFEM is at least one order of magnitude more precise than the corresponding isoparametric finite element in every numerical example shown. This is the case for both continuous and discontinuous Galerkin formulations. Moreover, for a desired precision NEFEM is also more computational efficient, as shown in the numerical examples. The use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details. The possibility of computing accurate solution with coarse meshes and high order interpolations, makes NEFEM a more efficient strategy than classical isoparametric FE.
Abstract
An improvement of the classical finite element method is proposed. It is able to exactly represent the geometry by means of the usual CAD description of the boundary with [...]
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Posibilidades de los métodos numéricos en obras subterráneas
E. Oñate, B. Suárez, J. Canet

(2007). Research Report, Nº PI301

Abstract
Se presenta un resumen de las posibilidades de diversos métodos numéricos basados en la combinación de técnicas de elementos finitos y de partículas para la simulación de problemas típicos de obras subterráneas, tales como la excavación de túneles y la inundación de cavidades.
Abstract
Se presenta un resumen de las posibilidades de diversos métodos numéricos basados en la combinación de técnicas de elementos finitos y de partículas [...]
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Estado del arte sobre aplicación de métodos numéricos y la simulación de escenarios de riesgo y al cálculo de la seguridad estructural
A. Barbat, L. Pujades, O. Cardona

(2007). Research Report, Nº PI300

Abstract
En este informe se estudian los métodos numéricos orientados hacia el cálculo de la seguridad de las estructuras, a la evaluación de su vulnerabilidad y riesgo, así como al desarrollo de escenarios de riesgo. Partiendo de una amplia revisión bibliográfica, se realiza una descripción del marco conceptual del riesgo, insistiéndose en las formulaciones que se han dado a los conceptos de amenaza, vulnerabilidad, fragilidad y daño involucrados en la definición del riesgo. A pesar de que los conceptos analizados son válidos para cualquier tipo de elemento en riesgo, para responder al principal objetivo de este estudio se pone énfasis en las estructuras de edificación y en las zonas urbanas. Dicho objetivo es el de estudiar los métodos de última generación orientados a la evaluación del daño esperado tanto en edificios individuales (lo que implica examinar su seguridad y vulnerabilidad) como en zonas urbanas (para las que se describirán procedimientos de simulación de escenarios de riesgo.) Después de incluir los principios relacionados con la evaluación de diferentes amenazas naturales (terremotos, tsunamis, erupciones volcánicas, huracanes, inundaciones, deslizamientos, avalanchas, etc.) para las que se introduce el concepto de escenario de amenaza, el presente estudio se centra más en la amenaza sísmica, al tener esta una mayor influencia en la seguridad de las estructuras que se hallan en zonas urbanas. Se describe, primeramente, del método del índice de vulnerabilidad, desarrollado en el ámbito del riesgo sísmico, que permite caracterizar la vulnerabilidad de las estructuras. Unas funciones de vulnerabilidad semiempíricas permite estimar el daño estructural para diferentes intensidades de la acción y para diferentes índices de vulnerabilidad estructural. En el segundo lugar, se examina el método del espectro de capacidad que se fundamenta en modelos de análisis no lineal de las estructuras y de curvas de fragilidad estructural. La acción se define mediante el espectro de demanda. El método proporciona las probabilidades de ocurrencia para diferentes estados mencionados, utilizándose como ejemplo la ciudad de Barcelona para la se han desarrollado escenario de riesgo para la amenaza sísmica.
Abstract
En este informe se estudian los métodos numéricos orientados hacia el cálculo de la seguridad de las estructuras, a la evaluación de su vulnerabilidad [...]
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Bounds of functional outputs for parabolic problems. Part II: Bounds of the exact solution
N. Parés, P. Díez, A. Huerta

(2007). Research Report, Nº PI299

Abstract
The paper introduces a methodology to compute upper and lower bounds for linear-functional outputs of the exact solutions of parabolic problems. In this second part, the bounds account for the error both in space and time. The assumption stating that the error introduced by the time marching scheme is negligible, used in the first part, is removed here. The bounds are computed starting from an approximation of the exact solution, associated with a spatial mesh and a time grid. Nevertheless, the bounds are guaranteed with respect to the exact solution, with no reference to any mesh or time discretization.
Abstract
The paper introduces a methodology to compute upper and lower bounds for linear-functional outputs of the exact solutions of parabolic problems. In this second part, the bounds [...]
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Stabilized solution of the multidimensional advection-diffusion-absorption equation using linear finite elements
E. Oñate, J. Miquel, F. Zárate

(2005). Research Report, Nº PI269

Abstract
A stabilized finite element method (FEM) for the multidimensional steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing differential equations derived via the Finite Calculus (FIC) method. For 1D problems the stabilization terms act as a nonlinear additional diffusion governed by a single stabilization parameter. It is shown that for multidimensional problems an orthotropic stabilizing diffusion must be added along the principal directions of curvature of the solution. A simple iterative algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described. Numerical results for 1D and 2D problems with sharp gradients are presented showing the effectiveness and accuracy of the new stabilized formulation.
Abstract
A stabilized finite element method (FEM) for the multidimensional steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on [...]
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Velocity correction methods based on a discrete pressure Poisson equation an algebraic approach
S. Badia, R. Codina

(2006). Research Report, Nº PI286

Abstract
In this paper we introduce some pressure segregation methods obtained from a non-standard version of the discrete monolithic system, where the continuity equation has been replaced by a pressure Poisson equation obtained at the discrete level. In these methods it is the velocity instead of the pressure the extrapolated unknown. Moreover, predictor corrector schemes are suggested, again motivated by the new monolithic system. Key implementation aspects are discussed, and a complete stability analysis is performed. We end with a set of numerical examples in order to compare these methods with classical pressure correction schemes.
Abstract
In this paper we introduce some pressure segregation methods obtained from a non-standard version of the discrete monolithic system, where the continuity equation has been [...]
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Topology optimization of plates
B. Boroomand, A. Barekatein

(2006). Research Report, Nº PI298

Abstract
In this report we propose a stabilization method for topology optimization of planes. The method can be classified in the category of continuation methods. The new continuation method is based on using continuous of design variables (DV) defined on a set meshes different from the one used for the finite element solution. The optimization procedure stars with using a coarse DV-mesh compared to finite element one. Once the convergence is obtained in the optimizations steps, a finer DV-mesh is nominated for further steps. With such a continuation method one can control the bounds of the gradients of the DV while simultaneously smooth the values in a more logical fashion, compared to what conventional filters perform. The DV-mesh refinement can be continued until the final mesh becomes similar to the finite element mesh. Depending on the formulation and elements used for the plate problems, e.g. with Kirchhoff or Mindlin-Reissner hypothesis, the refinement may further be continued so that the DV elements become smaller than the plate elements. Application of the method is shown over a wide range of plate problems. Linear and nonlinear plate behaviors formulated by Kirchhoff or Mindlin Reissner hypothesis, while using several forms of DV, are considered to show the performance of the proposed method. As one of the main DV, density is used in a power-law approach (or in an artificial material approach). This is performed in two forms, on in obtaining the topology of Thickness is also used as a realistic design variable in order to show the performance of the method in a rather well-posed optimization problem. We have also included results from a homogenization approach. Comparison in made with conventional element/nodal based approaches using filter. The results show excellent and robust performance of the proposed method. Due to the wide range of cases studied, some inserting side conclusions are also given in this report.
Abstract
In this report we propose a stabilization method for topology optimization of planes. The method can be classified in the category of continuation methods. The new continuation [...]
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Bounds of functional outputs for parabolic problems. Part I: Exact bounds of the discontinuous Galerkin time discretization
N. Parés, P. Díez, A. Huerta

(2006). Research Report, Nº PI297

Abstract
Classical implicit residual type error estimators require using an underlying spatial finer mesh to compute bounds for some quantity of interest. Consequently, the bounds obtained are only guaranteed asymptotically that is with respect to the reference solution computed with the fine mesh. Exact bounds, that is bounds guaranteed with respect to the exact solution, are needed to properly certify the accuracy of the results, especially if the meshes are coarse. The paper introduces a procedure to compute strict upper and lower bounds of the error in linear functional outputs of parabolic problems. In this first part, the bounds account for the error associated with the spatial discretization. The error coming from the time marching scheme is therefore assumed to be negligible in front of the spatial error. The time discretization is performed using the discontinuous Galerkin method, both for the primal and adjoint problems. In the error estimation procedure, equilibrated fluxes at interelement edges are calculated using hybridization techniques.
Abstract
Classical implicit residual type error estimators require using an underlying spatial finer mesh to compute bounds for some quantity of interest. Consequently, the bounds [...]
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An orthotropic mesh corrected crack model
M. Cervera

(2006). Research Report, Nº PI296

Abstract
This paper recovers the original spirit of the continuous crack approaches, where displacements jumps across the crack are smeared over the affected elements and the behaviour is established through a softening stress–(total) strain law, using standard finite element displacement interpolations and orthotropic localconstitutive models. The paper focuses on the problem of shear locking observed in the discrete problem when orthotropic models are used. The solution for this drawback is found in the form of a mesh corrected crack model where the structure of the inelastic strain tensor is linked to the geometry of the cracked element. The discrete model is formulated as a non-symmetric orthotropic local damage constitutive model, in which the softening modulus is regularized according to the material fracture energy and the element size. The resulting formulation is easily implemented in standard non-linear FE codes and suitable for engineering applications. Numerical examples show that the results obtained using this crack model do not suffer from dependence on the mesh directional alignment, comparing very favourably with those obtained using related standard isotropic or orthotropic damage models.
Abstract
This paper recovers the original spirit of the continuous crack approaches, where displacements jumps across the crack are smeared over the affected elements and the behaviour [...]
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Mesh objective tensile cracking via a local continuum damage model and a crack tracking technique
M. Cervera, M. Chiumenti

(2006). Research Report, Nº PI294

Abstract
This paper describes a procedure for the solution of problems involving tensile cracking using the so-called smeared crack approach, that is, standard finite elements with continuous displacement fields and a standard local constitutive model with strain-softening. An isotropic Rankine damage model is considered. The softening modulus is adjusted according to the material fracture energy and the element size. The resulting continuum and discrete mechanical problems are analyzed and the question of predicting correctly the direction of crack propagation is deemed as the main difficulty to be overcome in the discrete problem. It is proposed to use a crack tracking technique to attain the desired stability and convergence properties of the corresponding formulation. Numerical examples show that the resulting procedure is well-posed, stable and remarkably robust; the results obtained do not seem to suffer from spurious mesh-size or mesh-bias dependence.
Abstract
This paper describes a procedure for the solution of problems involving tensile cracking using the so-called smeared crack approach, that is, standard finite elements [...]
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Modeling bed erosion in free surface flows by the particle finite element method
E. Oñate, M. Celigueta, S. Idelsohn

(2006). Research Report, Nº PI293

Abstract
We present a general formulation for modeling bed erosion in free surface flows using the particle finite element method (PFEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in domains containing fluid and solid subdomains. Nodes are viewed as material points (called particles) which can freely move and even separate from the fluid and solid subdomains representing, for instance, the effect of water drops or soil/rock particles. A mesh connects the nodes defining the discretized domain in the fluid and solid regions where the governing equations, expressed in an integral form, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the nonlinear transient coupled fluid-structure problem is described. The erosion mechanism is modeled by releasing the material adjacent to the bed surface according to the frictional work generated by the fluid shear stresses. The released bed material is subsequently transported by the fluid flow. Examples of application of the PFEM to solve a number of bed erosion problems involving large motions of the free surface and splashing of waves are presented.
Abstract
We present a general formulation for modeling bed erosion in free surface flows using the particle finite element method (PFEM). The key feature of the PFEM is the use of [...]
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Modelo constitutivo para el comportamiento de tejidos biológicos blandos
S. Oller

(2006). Research Report, Nº PI292

Abstract
El objetivo de este trabajo es obtener una formulación constitutiva general que permita representar el comportamiento –crecimiento y decrecimiento natural / patológico, remodelación de absorción y de regeneración- de los tejidos biológicos blandos. Entiéndase por tejidos biológicos blandos a aquellos que conforman la piel y órganos del cuerpo humano y que pueden estás sometidos a acciones externas e internas de origen mecánico y metabólico. Estas acciones pueden producir grandes deformaciones transitorias y permanentes.
Abstract
El objetivo de este trabajo es obtener una formulación constitutiva general que permita representar el comportamiento –crecimiento y decrecimiento natural / patológico, [...]
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A study on the lumped preconditioner and memory requirements of feti and related primal domain decompositions methods
Y. Fragakis

(2006). Research Report, Nº PI291

Abstract
In recent years, Domain Decomposition Methods (DDM) have emerged as advanced solvers in several areas of computational mechanics. In particular, during the last decade, in the area of solid and structural mechanics, they reached a considerable level of advancement and were shown to be more efficient than popular solvers, like advanced sparse direct solvers. The present contribution follows the lines of a series of recent publications by author on DDM. In the papers, the authors developed a unified theory of primal and dual methods and presented a family of DDM that were shown to be more efficient than previous methods. The present paper extends this work, presenting a new family of related DDM, thus enriching the theory of the relations between primal and dual methods. It also explores memory requirement issues, suggesting also a particularly memory efficient formulation.
Abstract
In recent years, Domain Decomposition Methods (DDM) have emerged as advanced solvers in several areas of computational mechanics. In particular, during the last decade, in [...]
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Force and displacement duality in domain decomposition methods for solid and structural mechanics
Y. Fragakis

(2006). Research Report, Nº PI290

Abstract
In recent years, Domain Decomposition Methods (DDM) have emerged as advanced solvers in several of computational mechanics. In particular, during the last decade, in the area of solid and structural mechanics, they reached a considerable level of advancement and were shown to be more efficient than popular solvers, like advanced sparse direct solvers. The present paper explores the extent of application of the general concept of force-displacement duality in DDM. A general framework for the definition of DDM is set up and it is shown that if the definition of a DDM meets some requirements, then it can lead to one primal and one dual formulation. A number of DDM are included in this setting and particular implications for each one of them is researched.
Abstract
In recent years, Domain Decomposition Methods (DDM) have emerged as advanced solvers in several of computational mechanics. In particular, during the last decade, in the area [...]
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Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscale
R. Codina

(2006). Research Report, Nº PI289

Abstract
In this paper we present a stabilized finite element formulation to solve the Oseen equations as a model problem involving both convection effects and the incompressibility restriction. The need for stabilization techniques to solve this problem arises because of the restriction in the possible choices for the velocity and pressure spaces dictated by the inf–sup condition, as well as the instabilities encountered when convection is dominant. Both can be overcome by resorting from the standard Galerkin method to a stabilized formulation. The one presented here is based on the subgrid scale concept, in which unresolvable scales of the continuous solution are approximately accounted for. In particular, the approach developed herein is based on the assumption that unresolved subscales are orthogonal to the finite element space. It is shown that this formulation is stable and optimally convergent for an adequate choice of the algorithmic parameters on which the method depends.
Abstract
In this paper we present a stabilized finite element formulation to solve the Oseen equations as a model problem involving both convection effects and the incompressibility [...]
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LES turbulence models. Relation with stabilized numerical methods
A. Valls, J. García-Espinosa, E. Oñate

(2006). Research Report, Nº PI288

Abstract
One of the aims of this text is to show some important results in LES modelling and to identify which are main mathematical problems for the development of a complete theory. A relevant aspect of LES theory, which we will consider in our work, is the close relationship between the mathematical properties of LES models and the numerical methods used for their implementation. In last years it is more and more common the idea in the scientific community, especially in the numerical community, that turbulence models and stabilization techniques play a very similar role. Methodologies used to simulate turbulent flows, RANS or LES approaches, are based on the same concept: unability to simulate a turbulent flow using a finite discretization in time and space. Turbulence models introduce additional information (impossible to be captured by the approximation technique used in the simulation) to obtain physically coherent solutions. On the other side, numerical methods used for the integration of partial differential equations (PDE) need to be modified in order to able to reproduce solutions that present very high localized gradients. These modifications, known as stabilization techniques, make possible to capture these sharp and localized changes of the solution. According with previous paragraphs, the following natural question appears: Is it possible to reinterpret stabilization methods as turbulence models? This question suggests a possible principle of duality between turbulence modelling and numerical stabilization. More than to share certain properties, actually, it is suggested that the numerical stabilization can be understood as turbulence. The opposite will occur if turbulence models are only necessary due to discretization limitations instead of a need for reproducing the physical behaviour of the flow. Finally: can turbulence models be understood as a component of a general stabilization method?
Abstract
One of the aims of this text is to show some important results in LES modelling and to identify which are main mathematical problems for the development of a complete theory. [...]
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On some fluid-structure iterative algorithms using pressure segregation methods. Applications to aeroelasticity
S. Badia, R. Codina

(2006). Research Report, Nº PI287

Abstract
In this paper we suggest some algorithms for the fluid-structure interaction problem stated using a domain decomposition framework. These methods involve stabilized pressure segregation methods for the solution of the fluid problem and fixed point iterative algorithms for the fluid-structure coupling. These coupling algorithms are applied to the aeroelastic simulation of suspension bridges. We assess flexural and torsional frequencies for a given inflow velocity. Increasing this velocity we reach the value for which the flutter phenomenon appears.
Abstract
In this paper we suggest some algorithms for the fluid-structure interaction problem stated using a domain decomposition framework. These methods involve stabilized pressure [...]
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Analysis of a stabilized finite element approximation of the transient convection-diffusion equation using an ale framework
S. Badia, R. Codina

(2006). Research Report, Nº PI285

Abstract
In this paper we analyze a stabilized finite element method to approximate the convection diffusion equation on moving domains using an ALE framework. As basic numerical strategy, we discretize the equation in time using first and second order backward differencing (BDF) schemes, whereas space is discretized using a stabilized finite element method (the orthogonal subgrid scale formulation) to deal with convection dominated flows. The semi-discrete problem (continuous in space) is first analyzed. In this situation it is easy to identify the error introduced by the ALE approach. After that, the fully discrete method is considered. We obtain optimal error estimates in both space and time in a mesh dependent norm. The analysis reveals that the ALE approach introduces an upper bound for the time step size for the results to hold. The results obtained for the fully discretized second order scheme (in time) are associated to a weaker norm than the one used for the first order method. Nevertheless, optimal convergence results have been proved. For fixed domains, we recover stability and convergence results with the strong norm for the second order scheme, stressing the aspects that make the analysis of this method much more involved.
Abstract
In this paper we analyze a stabilized finite element method to approximate the convection diffusion equation on moving domains using an ALE framework. As basic numerical strategy, [...]
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On some pressure segregation methods of fractional-step type for the finite element approximation of incompressible flow problems
R. Codina, S. Badia

(2006). Research Report, Nº PI284

Abstract
In this paper we treat several aspects related to time integration methods for the incompressible Navier-Stokes equations that allow to uncouple the calculation of the velocities and the pressure. The first family of schemes consists of classical fractional step methods, of which we discuss several possibilities for the pressure extrapolation and the time integration of first and second order. The second family consists of schemes based on an explicit treatment of the pressure in the momentum equation followed by a Poisson equation for the pressure. It turns out that this “staggered” treatment of the velocity and the pressure is stable. Finally, we present predictor-corrector methods based on the above schemes that aim to converge to the solution of the monolithic time integration method. Apart from presenting these schemes and check its numerical performance, we also present a complete set of stability results for the fractional step methods that are independent of the space stability of the velocity-pressure interpolation, that is, of the classical inf-sup condition.
Abstract
In this paper we treat several aspects related to time integration methods for the incompressible Navier-Stokes equations that allow to uncouple the calculation of the velocities [...]
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Variational formulation of the finite calculus equations in solid mechanics and diffusion-reaction problems
E. Oñate, C. Felippa

(2006). Research Report, Nº PI283

Abstract
We present a variational formulation of the finite calculus (FIC) equations for problems in mechanics governed by differential equations with symmetric operators. Applications considered include solid mechanics, diffusion-transport and diffusion-reaction problems. The key of the variational formulation is the identification of the FIC governing equations with the classical differential equations of mechanics written in terms of modified non-local variables. A total potential energy (TPE) functional is found in terms of the modified variables. The FIC equations in the domain and the boundary are recovered as the Euler-Lagrange equations and the natural boundary condition of the TPE functional, respectively. Symmetric finite element equations are obtained after discretization of the TPE functional, therefore preserving the symmetry of the governing infinitesimal equations. The variational FIC expression is reinterpreted as a Petrov Galerkin weighted residual form of the original FIC equations with non-local weighting functions. The analogy of the variational FIC-FEM formulation with a discontinuous Galerkin method is recognized. Extensions to multidimensional linear elastostatics and diffusion-reaction problems are presented.
Abstract
We present a variational formulation of the finite calculus (FIC) equations for problems in mechanics governed by differential equations with symmetric operators. Applications [...]
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FIC/FEM formulation with matrix stabilizing terms for incompressible floes at low and high Reynolds numbers
E. Oñate, A. Valls, J. García-Espinosa

(2006). Research Report, Nº PI282

Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus method using a matrix form of the stabilization parameters. This allows to model a wide range of fluid flow problems for low and high Reynolds numbers flows without introducing a turbulence model. Examples of application to the analysis of incompressible flows with moderate and large Reynolds numbers are presented.
Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and [...]
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On the simulation of flows with violent free surface motion
R. Löhner, C. Yang, E. Oñate

(2006). Research Report, Nº PI281

Abstract
A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms to obtain velocities and pressure in the gas region near the free surface have been implemented. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from smoothed particle hydrodynamics (SPH) calculations. These and a series of other examples demonstrate that the present CFD method is capable of simulating violent free surface flows with strong nonlinear behavior.
Abstract
A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate [...]
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Coupling of Feflo with Simpact
J. Arteaga-Gomez, R. Löhner, J. Rojek, E. Oñate

(2006). Research Report, Nº PI280

Abstract
This paper describes the coupling of FEFLO, a general purpose compressible and incompressible flow solver base on adaptive unstructured grids with SIMPACT, a general purpose, large deformation, explicit structural dynamics code developed at the Center for Numerical Methods in Engineering (CIMNE). Details on the codes, as well as the compiling strategy employed are given. Examples illustrate the possibilies the present fluid-structure capability offers.
Abstract
This paper describes the coupling of FEFLO, a general purpose compressible and incompressible flow solver base on adaptive unstructured grids with SIMPACT, a general purpose, [...]
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Programación y gestión de redes de notas via Internet I
J. Jiménez, A. Priegue, F. Guzmán, E. Oñate

(2005). Research Report, Nº PI279

Abstract
Este trabajo presenta los desarrollos llevados a cabo en CIMNE en la programación y gestión de redes de motas utilizando Internet. El trabajo se enmarca dentro de la línea de I+D de CIMNE en el estudio, desarrollo y aplicación de redes de sensores inteligentes sin hilos en diversos ámbitos de la ingeniería. En las referencias [(1-3)] se describen los resultados de investigaciones anteriores del equipo de CIMNE sobre el tema. El trabajo se ha llevado a cabo en el marco de las actividades del proyecto "Desarrollo de tecnologías para investigación y gestión de procesos constructivos utilizando redes de sensores sin hilos.(PROSENSOR)" financiado por el programa PROFIT del Ministerio de Educación y Ciencia. El proyecto se inició en Noviembre de 2005 y su finalización está prevista en Diciembre, 2007. Los autores agradecen a la empresa Sensoria S.A., el asesoramiento y colaboración en la realización del trabajo.
Abstract
Este trabajo presenta los desarrollos llevados a cabo en CIMNE en la programación y gestión de redes de motas utilizando Internet. El trabajo se enmarca [...]
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Plataforma WSN/NIMS I
J. Piazzese, J. Jiménez, E. Oñate

(2005). Research Report, Nº PI268
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Discrete Green's functions for unbounded using finite element method
B. Boroomand, F. Mossaiby

(2005). Research Report, Nº PI267

Abstract
In this report dynamic solution of unbounded domains using pure finite element method is presented. The problems of concern are those with governing differential equations of constant coefficient. When the grid is of repeatable pattern the solution of an unbounded domain is reducible to a solution over a smaller domain with a grid consisting of few numbers of repeatable patterns. It is shown that by use of the proportionality property, having roots in governing equations, both conditions required for a unique solution, i.e. the decay and radiation of energy, are met through a spectral formulation. As a key point, a consistent transformation approach is proposed in order to employ such a spectral formulation for the solution. The transformation technique is analogous to those conventionally used for solution of partial differential equations but of course in a matrix form. To demonstrate the applicability of method, Green’s functions for two dimensional scalar and elastic wave equations are obtained numerically in frequency domain. The method is also capable of giving Green’s functions for dynamic solution of domains with repeatable material properties. Comprehensive discussions are given for accuracy and convergence of the solution.
Abstract
In this report dynamic solution of unbounded domains using pure finite element method is presented. The problems of concern are those with governing differential equations [...]
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El método de partículas y elementos finitos. Aplicaciones en ingeniería de puertos
E. Oñate, M. Celigueta, S. Idelsohn, F. Del Pin

(2005). Research Report, Nº PI278
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Plataforma WSN/NIMS III. Programación básica de motas
J. Jiménez, A. Priegue, J. Piazzese, E. Oñate

(2005). Research Report, Nº PI277
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Large membranes structures for scientific remote sensing and space exploration
M. Tessler

(2005). Research Report, Nº PI276

Abstract
As part of the NASA Floyd L.Thompson Fellowship, the author spent four months in the beginning of 2005 at the International Center for Numerical Methods in Engineering (CIMNE) in Barcelona, Spain. During this visit, he had many opportunities to discuss the new NASA Space Exploration Program with graduate students and faculty at CIMNE, and worked closely with several researchers focusing on the modeling and analysis of thin-film membranes. Here, a brief overview of the space exploration technologies that use very large structural membranes is presented, together with some comments related to computational mechanics issues for simulating the response of large membrane structures.
Abstract
As part of the NASA Floyd L.Thompson Fellowship, the author spent four months in the beginning of 2005 at the International Center for Numerical Methods in Engineering (CIMNE) [...]
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An edge-based solver for compressible flow
E. Ortega, R. Flores, E. Oñate

(2005). Research Report, Nº PI275

Abstract
An edge-based high-resolution scheme for the solution of the compressible Euler equations on unstructured finite elements grids is presented. The flow solver adopted in the present work is the approximate Riemann solver developed by Roe. A high-order spatial approximation is achieved by means of a piecewise linear reconstruction of the interface variables according to the MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) formulation. Finally, non-linear limiters are introduced in order to prevent the generation of oscillations. The proposed approach corresponds with the methodology presented by Löhner in [1].
Abstract
An edge-based high-resolution scheme for the solution of the compressible Euler equations on unstructured finite elements grids is presented. The flow solver adopted in the [...]
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Goal oriented adaptivity: Una introducción a través del problema elástico lineal
J. Ródenas

(2005). Research Report, Nº PI274

Abstract
En este documento se presenta el estudio iniciado por el autor durante su estancia en el Centro Internacional de Métodos Numéricos en Ingeniería de la Universitat Politècnica de Catalunya (CIMNE-UPC-Barcelona) durante los meses de Julio, Agosto y Septiembre de 2004 y continuado posteriormente en el Departamento de Ingeniería Mecánica y de Materiales de la Universidad Politécnica de Valencia (DIMM-UPV). El autor desea expresar su agradecimiento a los directores de ambos centros, Eugenio Oñate (CIMNE) y Javier Fuenmayor (DIMM-UPV), por el apoyo prestado para la realización de la estancia y la elaboración de este informe, así como al resto de miembros de dichos centros, sin olvidar, por supuesto, a Pedro Diez (Laboratori de Càlcul Numèric, LACAN-UPC-Barcelona) por su inestimable ayuda. El objetivo del documento es el de proporcionar una introducción a la adaptatividad en magnitudes de interés (Goal Oriented Adaptivity, GOA) siguiendo, en la medida de lo posible, un planteamiento intuitivo. Para ello, este trabajo se centra exclusivamente en la aplicación de esta técnica al problema Elástico Lineal resuelto mediante el Método de los Elementos Finitos (MEF) y procedimientos h-adaptativos. La calidad de la solución que proporciona un modelo de Elementos Finitos (EF) depende, entre otras cosas, de la selección adecuada de los parámetros de la discretización, es decir, del tamaño de los elementos, el grado de las funciones de forma utilizadas en la interpolación de desplazamientos, etc. Como resultado de la simulación numérica se puede obtener una aproximación a la magnitud de interés y también ciertos indicadores de calidad de la solución que pueden venir dados como aportaciones de cada uno de los elementos al error global del análisis. Estos indicadores de calidad de la solución pueden ser utilizados para mejorar automáticamente el modelo de EF y conseguir así una solución más precisa del problema. En el procedimiento tradicional se realiza una estimación local del error de discretización en norma energética para, posteriormente, utilizar técnicas de adaptación automática de la malla a fin de obtener modelos de EF que proporcionen soluciones con un error global en norma energética inferior al especificado por el analista. En todo caso, la norma energética de la solución no suele ser una magnitud de interés para el analista. En este trabajo se describirá una nueva técnica llamada Goal Oriented Adaptivity que permite la estimación de error a-posteriori y la adaptación de la malla de modelos de EF a fin de controlar el error de la magnitud de interés para el analista.
Abstract
En este documento se presenta el estudio iniciado por el autor durante su estancia en el Centro Internacional de Métodos Numéricos en Ingeniería de la [...]
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Plataforma WSN/NIMS II. Primeras experiencias en CIMNE
J. Jiménez, A. Priegue, E. Oñate

(2005). Research Report, Nº PI272
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Identificación modal mediante ajuste local de la respuesta
L. Villa

(2005). Research Report, Nº PI271
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Evolutionary methods for optimal shape design
A. Fung, E. Pahl, G. Bugeda, E. Oñate

(2005). Research Report, Nº PI270

Abstract
An optimization code called Optima has been developed at the International Centre for Numerical Methods in Engineering (CIMNE). This report validates two reputably robust Evolutionary Algorithms available in Optima and employs them on aerodynamic shape optimization problems. The two schemes, Differential Evolution Scheme 1 (DE1) and Evolution Strategy coupled with Covariance Matrix Adaptation (ES-CMA), were tested and verified on three standard parametric optimization objective functions through comparison against existing results. Analysis of the test data allowed trends to be established and from this, settings to enhance the performance of the algorithms were proposed and substantiated. The algorithms and their suggested settings were applied on an inverse and a direct constrained shape optimization problem involving NACA four digit airfoils. The inverse task involves the recovery of an airfoil profile through its pressure distribution combination of lift and drag coefficients. Simulation of the airfoil in turbulent flow was done using a Computational Fluid Dynamics (CFD) setup. Finally, the results are presented and the ES-CMA method, using the setting CMA-B proposed in this paper, was found to be most robust. Suggestions for improvements and further work in the optimization configuration and the problem simulation are also proposed.
Abstract
An optimization code called Optima has been developed at the International Centre for Numerical Methods in Engineering (CIMNE). This report validates two reputably robust [...]
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Advances in the formulation of the rotation-free basic shell triangle
E. Oñate, F. Flores

(2003). Research Report, Nº PI241

Abstract
A family of rotation-free three node triangular shell elements is presented. The simplest element of the family is based on an assumed constant curvature field expressed in terms of the nodal deflections of a patch of four elements and a constant membrane field computed from the standard linear interpolation of the displacements within each triangle. An enhanced version of the element is obtained by using a quadratic interpolation of the geometry in terms of the six patch nodes. This allows to compute an assumed linear membrane strain field which improves the in-plane behaviour of the original element. A simple and economic version of the element using a single integration point is presented. The efficiency of the different rotation-free shell triangles is demonstrated in many examples of application including linear and non linear analysis of shells under static and dynamic loads, the inflation and de-inflation of membranes and a sheet stamping problem.
Abstract
A family of rotation-free three node triangular shell elements is presented. The simplest element of the family is based on an assumed constant curvature field expressed in [...]
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Open tools for electromagnetic simulation programs
J. Mora, R. Otín, P. Dadvand, E. Escolano, M. Pasenau, E. Oñate

(2005). Research Report, Nº PI273

Abstract
Computational electromagnetism requires a wide range of numerical methods depending on the application, the topology of the geometry, the frequency and the quality of the solution. Different efforts have been done to develop a universal software package able to deal with any problem, by integrating existing specific modules in the same interface. Nevertheless, modern computational approaches suggest to use a common basic environment, as high level computing lenguage, to be adapted to the requirements done by the end-user. Following this philosophy, this paper proposes three useful computer tools, combining the most usual requirements, to be customised for any electromagnetic problem.
Abstract
Computational electromagnetism requires a wide range of numerical methods depending on the application, the topology of the geometry, the frequency and the quality of the [...]
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Development of local models and their computational implementation for polymer coated steel sheets
J. Rojek, M. Luege, E. Oñate

(2004). Research Report, Nº PI265

Abstract
This report present review of the state of the art of numerical modelling of polymers and polymer coated metal laminates and gives details of selected numerical models including those that will be used in the work in the project POLYCOAT. The first sections studied in the project. Basic mechanical and thermal properties of the polymers are reviewed. Then constitutive models developed for polymers are reviewed based on literature and own work. Details of selected models are given. Deformation behaviour of polymer coated metal laminates is considered with special attention to the phenomena observed at the polymer-metal interface. The numerical models for the interface are presented finally.
Abstract
This report present review of the state of the art of numerical modelling of polymers and polymer coated metal laminates and gives details of selected numerical models including [...]
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The efects of VaR position limits on endogenous price formation in financial markets
G. Peffer

(2004). Research Report, Nº PI263

Abstract
This paper sets out to study the impact that market risk limits have on the price dynamics in securities markets. We start out from a standard model in which trading patterns are determined for utility-maximising investors in non-clearing markets with a particularly simple price formation mechanism. To make trading conditions more realistic, we add borrowing and short-selling constraints and incorporate a stochastic information arrival process into the standard model. We present a VaR position limit formulation that allows us to integrate market risk limit considerations into our model and solve the respective utility maximization problems. Simulation results are then discussed which show an increase in price instability in a scenario of widespread adoption of VaR as a mechanism to limit portfolio risk.
Abstract
This paper sets out to study the impact that market risk limits have on the price dynamics in securities markets. We start out from a standard model in which trading patterns [...]
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On application of robustness test for error estimators to patches near kinked boundaries in three dimensional problems: Part II, Test results for error estimators using SPR and REP
B. Boroomand, F. Mossaiby

(2004). Research Report, Nº PI251

Abstract
In this part of the paper we shall use the formulation given in the first part to assess the quality of recovery based error estimators using two recovery methods, i.e. Superconvergent Patch Recovery (SPR) and Recovery by Equilibrium in Patches (REP). The recovery methods have been shown to be asymptotically robust and superconvergent when applied to two dimensional problems. In this study we shall examine the behavior of the recovery methods on several three dimensional mesh patterns for patches located either inside or at boundaries. This is performed by first finding an asymptotic finite element solution, irrespective of boundary conditions at far ends of the domain, and then applying the recovery methods. The test procedure near kinked boundaries is explained in a step by step manner. The results are given in a series of tables and figures for various cases of three dimensional mesh patterns. It has been experienced that the full superconvergent property is generally lost due to presence of boundary layer solution and the definition of the recoveries near boundaries though the results of the robustness test is still within an acceptable range.
Abstract
In this part of the paper we shall use the formulation given in the first part to assess the quality of recovery based error estimators using two recovery methods, i.e. Superconvergent [...]
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Desenvolupament d’un nou codi d’elements finits per l’estudi de la hidrodinàmica de vaixells. Aplicacions al disseny de velers de la Copa Amèrica
E. Oñate, J. García-Espinosa

(2004). Research Report, Nº PI257

Abstract
The objective of the project that is presented at the IV Prize Duran i Farell Award for Research and Technology is the development of a new computational code based on the finite element method for the fluid-dynamics analysis of vessels. The code allows to accurately reproduce the model basin tests (MBT) usually used for the experimental evaluation of the hydrodynamic resistance of ships. The new code, called Tdyn, is a much more economical and precise alternative to model basin tests, by allowing the analysis of the behavior of vessels in real scale, thus eliminating the usual scale errors in the experimental tests. Tdyn incorporates new mathematical models and advanced finite elements methods that have led to numerous international publications. Tdyn was jointly developed by researchers from the Technical University of Catalonia (UPC) of the Department of Strength of Materials and Structural Engineering of the Barcelona School of Civil Engineering and of the Department of Nautical Engineering and Science of the Faculty of Nautical Studies of Barcelona in the framework of several European and national projects carried out in collaboration with the research center CIMNE and the company Compass IS, as well as other prestigious companies in the naval architecture sector. Tdyn was applied to the design of several America’s Cup yachts (in particular, of the ALINGHI team, winner of the 2003 edition). Tdyn is currently commercialized worldwide through Compass IS, a spin-off of the UPC.
Abstract
The objective of the project that is presented at the IV Prize Duran i Farell Award for Research and Technology is the development of a new computational code based on the [...]
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Aplicaciones de algoritmos que conservan la energía-momentum en dinámica no-lineal
W. Matias Silva

(2004). Research Report, Nº PI259

Abstract
En este trabajo se estudia los algoritmos de integración en el tiempo que se basan en el método α generalizado. Para realizar dicho estudio se adoptan los planteamientos desarrollados en KUHL & CRISFIELD [1999]. Por tanto, el principal objetivo es investigar el comportamiento, en el análisis dinámico no-lineal, de los siguientes algoritmos: 1. La regla de trapecio - RT; 2. La regla del punto medio - RPM; 3. El método de Newmark - NM; 4. El método α de Bossak - MαB; 5. El método α de Hilber - MαH; 6. El método α generalizado - MαG; 7. El método de energía-momentum - MEM; 8. El método de energía-momentum modificado - MEM+ξ; 9. El método de energía-momentum generalizado - MEMG; 10. El método de energía-momentum generalizado modificado - MEMG+ξ; Según las siguientes características deseables: 1. Estabilidad numérica; 2. Conservación y decaimiento de la energía total; 3. Mínima disipación de frecuencias bajas; 4. Máxima disipación de frecuencias altas; 5. Convergencia durante el proceso iterativo; Para ello se ha analizado el problema del péndulo simple no-lineal discretizado con el elemento de barra bi-articulado. En la primera simulación numérica se ha tratado el péndulo como rígido mientras que en la segunda simulación se considera el péndulo elástico.
Abstract
En este trabajo se estudia los algoritmos de integración en el tiempo que se basan en el método α generalizado. Para realizar dicho estudio se adoptan [...]
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Stability and robustness issues in numerical modeling of material failure in the strong discontinuity approach
J. Oliver, A. Huespe, S. Blanco, D. Linero

(2004). Research Report, Nº PI258

Abstract
Robustness and stability of the Continuum Strong Discontinuity Approach (CSDA) to material failure are addressed. After identification of lack of symmetry of the finite element formulation and material softening in the constitutive model as possible causes of loss of robustness, two remedies are proposed: 1) a symmetric version of the elementary enriched finite element with embedded discontinuities, and 2) an implicit explicit integration of the internal variable, in the constitutive model, that renders the tangent constitutive algorithmic operator positive definite and constant. The combination of both developments leads to finite element formulations with constant and non-singular tangent structural stiffness, these allowing dramatic improvements in terms of robustness and computational costs. After assessing the convergence properties of the new strategies, three-dimensional numerical simulations of failure problems illustrate the performance of the proposed procedures.
Abstract
Robustness and stability of the Continuum Strong Discontinuity Approach (CSDA) to material failure are addressed. After identification of lack of symmetry of the finite element [...]
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Optimization. An attempt at describing the State of the Art
E. Pahl

(2004). Research Report, Nº PI256

Abstract
This paper is an attempt at describing the State of the Art of the vast field of continuous optimization. We will survey deterministic and stochastic methods as well as hybrid approaches in their application to single objective and multiobjective optimization. We study the parameters of optimization algorithms and possibilities for tuning them. Finally, we discuss several methods for using approximate models for computationally expensive problems.
Abstract
This paper is an attempt at describing the State of the Art of the vast field of continuous optimization. We will survey deterministic and stochastic methods as well as hybrid [...]
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El método de Level Set: Revisión y nuevas propuestas

A. Valls, J. García-Espinosa, E. Oñate

(2004). Research Report, Nº PI254

Abstract
El método Level Set utilizado en un amplio espectro de problemas de distinta índole, como la simulación de interfaces entre fluidos, el tratamiento de imágenes, la combustión,…tiene como principal objetivo la simulación numérica de la evolución de interfaces entre distintas regiones en contacto. El presente estudio es una revisión y aportación de nuevas propuestas para el método Level Set, en particular para su aplicación a la interfaz entre fluidos. Este método formulado independiente del tipo de método utilizado para la integración numérica de las ecuaciones en derivadas parciales que gobiernan el fenómeno a simular, disfruta de gran aceptación en el mundo de las diferencias finitas y existe abundante literatura al respecto. En este estudio se ha considerado la combinación del método Level Set y el método de Elementos Finitos no tan usual como en el caso anterior, dotando a este estudio de cierta singularidad. El estudio se ha organizado en 9 secciones o capítulos. En capítulos del 1 al 5 se presenta una introducción teó