Scipedia: Eugenio Oñate's Research Reports

A finite point method for elasticity problems

María Jesús Samper — Tue, 02 Jul 2019 09:59:03 +0200

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.

Possibilities of finite calculus in computational mechanics

María Jesús Samper — Tue, 02 Jul 2019 09:36:07 +0200

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.

A finite element methodology for local global damage evaluation in civil engineering structures

María Jesús Samper — Tue, 02 Jul 2019 09:28:53 +0200

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.

Posibilidades de los métodos numéricos en el mundo industrial

María Jesús Samper — Tue, 02 Jul 2019 09:17:10 +0200

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.

A finite element method for fluid-structure interaction with surface waves using finite calculus formulation

María Jesús Samper — Tue, 02 Jul 2019 09:10:06 +0200

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.

A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation

María Jesús Samper — Thu, 11 Jul 2019 14:57:46 +0200

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.

The Monte Carlo method. Application to the stochastic analysis of sheet stamping processes

María Jesús Samper — Thu, 11 Jul 2019 14:22:35 +0200

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.

Prediction of damage and failure in civil engineering structures using a finite element model.

María Jesús Samper — Thu, 11 Jul 2019 12:13:09 +0200

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.

Límites de los métodos numéricos

María Jesús Samper — Fri, 05 Jul 2019 10:40:56 +0200

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

El bucle de los números

María Jesús Samper — Fri, 05 Jul 2019 10:31:36 +0200

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.

Simulación por ordenador del comportamiento resistente de estructuras: El laboratorio virtual de estructuras

María Jesús Samper — Fri, 05 Jul 2019 10:23:25 +0200

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.

Del ábaco de fichas a Internet

María Jesús Samper — Fri, 05 Jul 2019 10:13:17 +0200

The braid of numbers

María Jesús Samper — Fri, 05 Jul 2019 10:09:39 +0200

Meshless analysis of incompressible flows using the Finite Point Method

María Jesús Samper — Fri, 05 Jul 2019 10:05:54 +0200

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.

Métodos avanzados para el cálculo de la resistencia de la última de estructuras de hormigón

María Jesús Samper — Thu, 05 Dec 2019 13:23:39 +0100

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.

Rotation‐free triangular plate and shell elements

María Jesús Samper — Fri, 12 Jul 2019 15:03:18 +0200

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.

A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation

María Jesús Samper — Fri, 12 Jul 2019 14:57:54 +0200

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.

New degrees of freedom in computational mechanics: mesh free finite point method, rotation free shell triangles and moving free meshes

María Jesús Samper — Fri, 12 Jul 2019 14:27:24 +0200

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.

Advances in the stabilized finite point method for structural mechanics

María Jesús Samper — Fri, 12 Jul 2019 10:35:08 +0200

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.

A methodology for analysis of fluid structure interaction accouting for free surface waves

María Jesús Samper — Fri, 12 Jul 2019 10:21:04 +0200

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.