Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization

This work presents an analysis methodology based on the use of the Finite Element Method (FEM) nowadays considered one of the main numerical tools for solving Boundary Value Problems (BVPs). The proposed methodology, so-called cg-FEM (Cartesian grid FEM), has been implemented for fast and accurate n...

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Main Authors: E. Nadal, J. J. Ródenas, J. Albelda, M. Tur, J. E. Tarancón, F. J. Fuenmayor
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/953786
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author E. Nadal
J. J. Ródenas
J. Albelda
M. Tur
J. E. Tarancón
F. J. Fuenmayor
author_facet E. Nadal
J. J. Ródenas
J. Albelda
M. Tur
J. E. Tarancón
F. J. Fuenmayor
author_sort E. Nadal
collection DOAJ
description This work presents an analysis methodology based on the use of the Finite Element Method (FEM) nowadays considered one of the main numerical tools for solving Boundary Value Problems (BVPs). The proposed methodology, so-called cg-FEM (Cartesian grid FEM), has been implemented for fast and accurate numerical analysis of 2D linear elasticity problems. The traditional FEM uses geometry-conforming meshes; however, in cg-FEM the analysis mesh is not conformal to the geometry. This allows for defining very efficient mesh generation techniques and using a robust integration procedure, to accurately integrate the domain’s geometry. The hierarchical data structure used in cg-FEM together with the Cartesian meshes allow for trivial data sharing between similar entities. The cg-FEM methodology uses advanced recovery techniques to obtain an improved solution of the displacement and stress fields (for which a discretization error estimator in energy norm is available) that will be the output of the analysis. All this results in a substantial increase in accuracy and computational efficiency with respect to the standard FEM. cg-FEM has been applied in structural shape optimization showing robustness and computational efficiency in comparison with FEM solutions obtained with a commercial code, despite the fact that cg-FEM has been fully implemented in MATLAB.
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institution OA Journals
issn 1085-3375
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language English
publishDate 2013-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-dc07b8752257481aa8bb99795e1db1ac2025-08-20T02:21:16ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/953786953786Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape OptimizationE. Nadal0J. J. Ródenas1J. Albelda2M. Tur3J. E. Tarancón4F. J. Fuenmayor5Centro de Investigación de Tecnología de Vehículos (CITV), Universidad Politècnica de València, 46022 Valencia, SpainCentro de Investigación de Tecnología de Vehículos (CITV), Universidad Politècnica de València, 46022 Valencia, SpainCentro de Investigación de Tecnología de Vehículos (CITV), Universidad Politècnica de València, 46022 Valencia, SpainCentro de Investigación de Tecnología de Vehículos (CITV), Universidad Politècnica de València, 46022 Valencia, SpainCentro de Investigación de Tecnología de Vehículos (CITV), Universidad Politècnica de València, 46022 Valencia, SpainCentro de Investigación de Tecnología de Vehículos (CITV), Universidad Politècnica de València, 46022 Valencia, SpainThis work presents an analysis methodology based on the use of the Finite Element Method (FEM) nowadays considered one of the main numerical tools for solving Boundary Value Problems (BVPs). The proposed methodology, so-called cg-FEM (Cartesian grid FEM), has been implemented for fast and accurate numerical analysis of 2D linear elasticity problems. The traditional FEM uses geometry-conforming meshes; however, in cg-FEM the analysis mesh is not conformal to the geometry. This allows for defining very efficient mesh generation techniques and using a robust integration procedure, to accurately integrate the domain’s geometry. The hierarchical data structure used in cg-FEM together with the Cartesian meshes allow for trivial data sharing between similar entities. The cg-FEM methodology uses advanced recovery techniques to obtain an improved solution of the displacement and stress fields (for which a discretization error estimator in energy norm is available) that will be the output of the analysis. All this results in a substantial increase in accuracy and computational efficiency with respect to the standard FEM. cg-FEM has been applied in structural shape optimization showing robustness and computational efficiency in comparison with FEM solutions obtained with a commercial code, despite the fact that cg-FEM has been fully implemented in MATLAB.http://dx.doi.org/10.1155/2013/953786
spellingShingle E. Nadal
J. J. Ródenas
J. Albelda
M. Tur
J. E. Tarancón
F. J. Fuenmayor
Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization
Abstract and Applied Analysis
title Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization
title_full Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization
title_fullStr Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization
title_full_unstemmed Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization
title_short Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization
title_sort efficient finite element methodology based on cartesian grids application to structural shape optimization
url http://dx.doi.org/10.1155/2013/953786
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