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• Lagrangian finite element model for the 3D simulation of glass forming processes

  P. Ryzhakov, J. García-Espinosa, E. Oñate

  Computers and Structures (2016). 117, 126-140 (preprint)

  
  

  Abstract

  We propose here a numerical model for a three-dimensional simulation of glass forming processes. Using the basic philosophy of the Particle Finite Element method (PFEM), we introduce several new features adapting the strategy to suit the problem of interest. A modified fractional step method for the solution of the flow equations is applied. This approach, on the one hand, inherits the computational efficiency of the original fractional step approach, and on the other hand shows better mass conservation features. These features are particularly attractive taking into account the importance of the correct prediction of the glass product's wall thickness. A smart mesh update strategy and a simple mechanical contact scheme are introduced. In order to account for temperature-dependent viscosity, the heat equation is coupled to the mechanical model. Viscosity is obtained from the temperature field via an empirical law. The model is validated and an example modeling the processes in the final blow mold of the bottle manufacturing process is proposed.

  Abstract
  We propose here a numerical model for a three-dimensional simulation of glass forming processes. Using the basic philosophy of the Particle Finite Element method (PFEM), we [...]

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• Unified Lagrangian formulation for fluid and solid mechanics, fluid-structure interaction and coupled thermal problems using the PFEM

  A. Franci, E. Oñate, J. Carbonell

  Monograph CIMNE (2015). M155

  
  

  Abstract

  The objective of this work is the derivation and implementation of a unified Finite Element formulation for the solution of fluid and solid mechanics, Fluid-Structure Inter- action (FSI) and coupled thermal problems. The unified procedure is based on a stabilized velocity-pressure Lagrangian formulation. Each time step increment is solved using a two-step Gauss-Seidel scheme: first the linear momentum equations are solved for the velocity increments, next the continuity equation is solved for the pressure in the updated configuration. The Particle Finite Element Method (PFEM) is used for the fluid domains, while the Finite Element Method (FEM) is employed for the solid ones. As a consequence, the domain is remeshed only in the parts occupied by the fluid. Linear shape functions are used for both the velocity and the pressure fields. In order to deal with the incompressibility of the materials, the formulation has been stabilized using an updated version of the Finite Calculus (FIC) method. The procedure has been derived for quasi-incompressible Newtonian fluids. In this work, the FIC stabilization procedure has been extended also to the analysis of quasi-incompressible hypoelastic solids. Specific attention has been given to the study of free surface flow problems. In particular, the mass preservation feature of the PFEM-FIC stabilized procedure has been deeply studied with the help of several numerical examples. Furthermore, the conditioning of the problem has been analyzed in detail describing the effect of the bulk modulus on the numerical scheme. A strategy based on the use of a pseudo bulk modulus for improving the conditioning of the linear system is also presented. The unified formulation has been validated by comparing its numerical results to ex- perimental tests and other numerical solutions for fluid and solid mechanics, and FSI problems. The convergence of the scheme has been also analyzed for most of the prob- lems presented. The unified formulation has been coupled with the heat tranfer problem using a staggered scheme. A simple algorithm for simulating phase change problems is also described. The numerical solution of several FSI problems involving the temperature is given. The thermal coupled scheme has been used successfully for the solution of an industrial problem. The objective of study was to analyze the damage of a nuclear power plant pressure vessel induced by a high viscous fluid at high temperature, the corium.  The numerical study of this industrial problem has been included in this work.

  Abstract
  The objective of this work is the derivation and implementation of a unified Finite Element formulation for the solution of fluid and solid mechanics, Fluid-Structure Inter- [...]

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• Applications of turbulence modeling in civil engineering

  J. Cotela, E. Oñate, R. Rossi

  Monograph CIMNE (2016). M159

  
  

  Abstract

  This work explores the use of stabilized finite element formulations for the incompressible Navier-Stokes equations to simulate turbulent flow problems. Turbulence is a challenging problem due to its complex and dynamic nature and its simulation if further complicated by the fact that it involves fluid motions at vastly different length and time scales, requiring fine meshes and long simulation times. A solution to this issue is turbulence modeling, in which only the large scale part of the solution is retained and the effect of smaller turbulent motions is represented by a model, which is generally dissipative in nature. In the context of finite element simulations for fluids, a second problem is the apparition of numerical instabilities. These can be avoided by the use of stabilized formulations, in which the problem is modified to ensure that it has a stable solution. Since stabilization methods typically introduce numerical dissipation, the relation between numerical and physical dissipation plays a crucial role in the accuracy of turbulent flow simulations. We investigate this issue by studying the behavior of stabilized finite element formulations based on the Variational Multiscale framework and on Finite Calculus, analyzing the results they provide for well-known turbulent problems, with the final goal of obtaining a method that both ensures numerical stability and introduces physically correct turbulent dissipation. Given that, even with the use of turbulence models, turbulent flow problems require significant computational resources, we also focused on programming and parallel implementation aspects of finite element codes, and in particular in ensuring that our solver can perform efficiently on distributed memory architectures and high-performance computing clusters. Finally, we have developed an adaptive mesh refinement technique to improve the quality of unstructured tetrahedral meshes, again with the goal of enabling the simulation of large turbulent flow problems. This technique combines an error estimator based on Variational Multiscale principles with a simple refinement procedure designed to work in a distributed memory context and we have applied it to the simulation of both turbulent and non-Newtonian flow problems.

  Abstract
  This work explores the use of stabilized finite element formulations for the incompressible Navier-Stokes equations to simulate turbulent flow problems. Turbulence is a challenging [...]

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• Nonlinear Analysis of Orthotropic Membrane and Shell Structures Including Fluid-structure Interaction

  J. Valdés, E. Oñate, J. Miquel

  Monograph CIMNE (2007). M107

  
  

  Abstract

  Nowadays, fluid-structure interaction problems are a great challenge of different fields in engineering and applied sciences. In civil engineering applications, wind flow and structural motion may lead to aeroelastic instabilities on constructions such as long-span bridges, high-rise buildings and light-weight roof structures. On the other hand, biomechanical applications are interested in the study of hemodynamics, i.e. blood flow through large arteries, where large structural membrane deformations interact with incompressible fluids.   In the structural part of this work, a new methodology for the analysis  of geometrically nonlinear orthotropic membrane and rotation-free  shell elements is developed based on the principal fiber orientation  of the material. A direct consequence of the fiber orientation strategy is the possibility to analyze initially out-of-plane prestressed membrane and shell structures. Additionally, since conventional membrane theory  allows compression stresses, a wrinkling algorithm based on modifying the constitutive equation is presented. The structure is modeled with finite elements emerging from the governing equations of elastodynamics.   The fluid portion of this work is governed by the incompressible Navier-Stokes equations, which are modeled by stabilized equal-order interpolation finite elements. Since the monolithic solution for these equations has the disadvantage that take great computer effort to solve large algebraic system of equations, the fractional step methodology is used to take advantage of the computational efficiency given by the uncoupling of the pressure from the velocity field.  In addition, the generalized-a time integration scheme for fluids is  adapted to be used with the fractional step technique.   The fluid-structure interaction problem is formulated as a three-field system: the structure, the fluid and the moving fluid mesh solver. Motion of the fluid domain is accounted for with the arbitrary  Lagrangian-Eulerian formulation with two different mesh update strategies. The coupling between the fluid and the structure is performed with the strong coupling block Gauss-Seidel partitioned technique.  Since the fluid-structure interaction problem is highly nonlinear,  a relaxation technique based on Aitken's method is implemented in the strong coupling formulation to accelerate the convergence.   Finally several example problems are presented in each field to verify the robustness and efficiency of the overall algorithm,  many of them validated with reference solutions.

  Abstract
  Nowadays, fluid-structure interaction problems are a great challenge of different fields in engineering and applied sciences. In civil engineering applications, wind flow [...]

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• Development of an integrated system for geometry modelling, mesh generation and data management for the analysis by the finite element method

  R. Ribó, E. Oñate, G. Bugeda

  Monograph CIMNE (2000). M56

  
  

  Abstract

  En esta tesis se describe el desarrollo e implementación de un sistema informático para el tratamiento de toda la información necesaria para un análisis por el Método de los Elementos Finitos o por otros métodos numéricos (diferencias finitas, volúmenes finitos, métodos de contorno, métodos de puntos, etc.).Algunas de sus partes se refieren principalmente al diseño y organización de un sistema de estas características. En otras, se describen los nuevos algoritmos que ha sido necesario desarrollar para cumplir los objetivos propuestos.Las diversas disciplinas que se describen a lo largo de la tesis se pueden diferenciar en:* Organización del sistema. Consiste en definir el tratamiento de todos los datos de un análisis genérico de manera uniforme. También se dan criterios sobre el ordenamiento interno de los datos.* Modelación geométrica. Se presenta una serie de algoritmos que se han desarrollado para tratar y modificar la geometría del modelo.* Generación de malla. Se describen diferentes técnicas y algoritmos para poder realizar la generación de la malla.* Adaptabilidad del sistema a diferentes análisis. Se describe como se ha diseñado y como se realiza la adaptación del sistema a un código de análisis cualquiera.La implementación del conjunto de criterios y algoritmos descritos a lo largo de esta tesis, ha permitido la creación de un sistema que da soporte al proceso de análisis mediante métodos numéricos de modelos, tanto a nivel académico como industrial.

  Abstract
  En esta tesis se describe el desarrollo e implementación de un sistema informático para el tratamiento de toda la información necesaria para un análisis [...]

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• Calculation of shells by analytical methods

  M. Tort, E. Oñate

  (2009). Technical Report, IT587

  
  

  Abstract

  The forms of revolution generated by shell structures are the simplest of classical art. Thus, the main motivation of this paper is present the basic tools for understanding shell behavior and the reader can design it without any problems. The text will focus on analyzing the two most common shells. First the dome and second cylindrical wall. Having analyzed the two types we will look the union between these two types and see the ring edge necessary in many cases.

  Abstract
  The forms of revolution generated by shell structures are the simplest of classical art. Thus, the main motivation of this paper is present the basic tools for understanding [...]

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• An isotropic damage model for geomaterials in the KRATOS framework

  I. de-Pouplana, E. Oñate

  Monograph CIMNE (2015). M153

  
  

  Abstract

  Progressive fracture in quasi-brittle materials such as concrete, rocks, soils, is often treated as strain softening in continuum damage mechanics. Such constitutive relations favour spurious strain localization and ill-posedness of boundary value problems, and call for some kind of regularization. In the present work, two different approaches are presented: a partially regularized local damage model that adjusts the softening part of a stress-strain law depending on the size of the element, and a fully regularized non-local damage model that introduces the characteristic length as an additional material parameter controlling the size of the fracture process zone.In addition, the strain softening of such models usually results in highly complex structural responses, including the snap-back type, and thus in this work we will be discussing non-linearity associated to damage modelling, and a global arc-length method for tracing the equilibrium path will be exposed.Furthermore, in the context of non-local damage models it is crucial to work with fine spatial discretizations at the damage progress zone, so that elements are smaller than the characteristic length. In this regard, a mesh-adaptive technique has been implemented with the purpose of enhancing the efficiency of the numerical analysis.Finally, two classical examples, the three-point bending test, and the single-edge notched beam test, are performed in order to analyse the mesh objectivity of the implemented integral-type non-local damage model, and assess the strengths and limitations of the mesh-adaptive procedure.

  Abstract
  Progressive fracture in quasi-brittle materials such as concrete, rocks, soils, is often treated as strain softening in continuum damage mechanics. Such constitutive relations [...]

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• A finite element method for fluid-structure interaction with surface waves

  E. Oñate, J. García-Espinosa

  (2001). Trends in Computational Structural Mechanics. W. A. Wall, K.-U. Bletzinger and K. Schweizerhof (Eds.), CIMNE, Barcelona, Spain

  
  

  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 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 fractional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized [...]

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• A FEM fluid-structure interaction algorithm for analysis of the seal dynamics of a Surface-Effect Ship

  J. García-Espinosa, B. Servan Camas, E. Oñate, D. Di Capua, P. Ubach de Fuentes

  Comp. Meth. App. Mech. Eng. (2015). 295, 290-304 (preprint)

  
  

  Abstract

  This paper shows the recent work of the authors in the development of a time-domain FEM model for evaluation of the seal dynamics of a surface effect ship. The fluid solver developed for this purpose, uses a potential flow approach along with a stream-line integration of the free surface. The paper focuses on the free surface-structure algorithm that has been developed to allow the simulation of the complex and highly dynamic behavior of the seals in the interface between the air cushion, and the water. The developed fluid-structure interaction solver is based, on one side, on an implicit iteration algorithm, communicating pressure forces and displacements of the seals at memory level and, on the other side, on an innovative wetting and drying scheme able to predict the water action on the seals. The stability of the iterative scheme is improved by means of relaxation, and the convergence is accelerated using Aitken’s method. Several validations against experimental results have been carried out to demonstrate the developed algorithm.  

  Abstract
  This paper shows the recent work of the authors in the development of a time-domain FEM model for evaluation of the seal dynamics of a surface effect ship. The fluid solver [...]

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