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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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• Recent advances in unstructured mesh and point generation

  R. Löhner

  (2002). Research Report, Nº PI210

  
  

  Abstract

  Recent advances in mesh and point generation are reviewed. These include: meshing of discrete surfaces, parallel advancing front methods, improvements in RAMS gridding via directional enrichment and tighter sphere packing for discrete particle methods. Several examples are included to illustrate the effectiveness of developed techniques.

  Abstract
  Recent advances in mesh and point generation are reviewed. These include: meshing of discrete surfaces, parallel advancing front methods, improvements in RAMS gridding via [...]

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• Development of an adaptive mesh generator

  J. Olausson, J. Gustafsson, D. Capua, E. Oñate

  (2002). Research Report, Nº PI211

  
  

  Abstract

  This study thoroughly explains the process of implementing Adaptive Mesh Refinement into a Finite Element Analysis program. Using the error norm, a routine for improving an original mesh for an arbitrary 2D structural problem has been developed. By utilizing user-defined relative global error, an optimal mesh for a given level of approximation can be obtained in an iterative manner. The routine (called AMG v1.0) runs with the pre-/postprocessor GiD and the calculation module Calsef, but can easily be tailored to work with other FEA programs. AMG operates with two mesh optimality criteria, which have proven to refine the mesh in a non-oscillatory manner. The open structure, along with the Graphical User Interface, makes AMG suitable for educational and experimental purposes. For validation, six examples within the field of structural engineering have been solved, four of which have been compared favorably with analytical solutions. The mesh optimality routines used are general, why AMG can be extended to handle more types of elements, 3D analysis, and to be applicable to other types of engineering problems. Above all AMG serves as a first step of implementing Adaptive Mesh Refinement procedures into GiD.

  Abstract
  This study thoroughly explains the process of implementing Adaptive Mesh Refinement into a Finite Element Analysis program. Using the error norm, a routine for improving an [...]

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• Cálculo de estructuras con materiales compuestos laminados por el método de elementos finitos

  E. Oñate

  (2002). Research Report, Nº PI212

  
  

  Abstract

   La utilización de materiales compuestos laminados en estructuras es creciente en todos los ámbitos de la ingeniería. El cálculo de esas estructuras requiere tener en cuenta las características de dichos materiales, tanto en cuanto a sus propiedades mecánicas, generalmente ortótropas, como a la peculiaridad de su distribución en capas laminares. Un caso particular de interés práctico de ese tipo de estructuras mixtas de hormigón y acero, e incluso las estructuras de hormigón armado en las que el hormigón y las armaduras se asimilan a capas de materiales con propiedades diferentes. En este capítulo presentamos una panorámica del cálculo por el método de elementos finitos de estructuras formadas por materiales compuestos laminados. Iniciaremos el capítulo con una introducción al cálculo de vigas planas formadas por un apilamiento de capas utilizando elementos de viga de Timoshenko de dos nodos. Tras ello estudiaremos las placas multilaminadas mediante elementos de Reissner-Mindlin, para terminar con el análisis de láminas de forma arbitraria y de revolución utilizando elementos finitos multilaminados planos y troncocónicos respectivamente, basados también en la teoría de Reissner-Mindlin.    

  Abstract
   La utilización de materiales compuestos laminados en estructuras es creciente en todos los ámbitos de la ingeniería. El cálculo de esas estructuras [...]

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• Introducción a la optimización de estructuras

  M. Soboleosky, G. Bugeda, S. Oller

  (2002). Research Report, Nº PI213

  
  

  Abstract

  El presente apunte tiene como meta mostrar, de manera sencilla y conceptual, los objetivos y procedimientos de la optimización orientada a la ingeniería. Es el resultado de una pasantía en el Centro Internacional de Métodos Numéricos en Ingeniería de la Universidad Politécnica de Catalunya, bajo la dirección de los profesores Gabriel Bugeda y Sergio Oller.

  Abstract
  El presente apunte tiene como meta mostrar, de manera sencilla y conceptual, los objetivos y procedimientos de la optimización orientada a la ingeniería. Es [...]

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