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

Autor: J. E. Tarancón, F. J. Fuenmayor, Manuel Tur, Enrique Nadal, Juan José Ródenas, J. Albelda
Rok vydání: 2013
Předmět:
CRACK-GROWTH
Mathematical optimization
Article Subject
INGENIERIA MECANICA
MathematicsofComputing_NUMERICALANALYSIS
02 engineering and technology
BOUNDARY-CONDITIONS
01 natural sciences
Mathematics::Numerical Analysis
law.invention
Regular grid
MULTIPOINT CONSTRAINTS
0203 mechanical engineering
law
Shape optimization
Polygon mesh
Cartesian coordinate system
0101 mathematics
ComputingMethodologies_COMPUTERGRAPHICS
Mathematics
SIMPLE ERROR ESTIMATOR
lcsh:Mathematics
Applied Mathematics
Numerical analysis
Linear elasticity
lcsh:QA1-939
DOMAIN DECOMPOSITION METHOD
SUPERCONVERGENT PATCH RECOVERY
Finite element method
PART I
010101 applied mathematics
EQUILIBRIUM
020303 mechanical engineering & transports
Computer Science::Sound
Mesh generation
ACOUSTIC SCATTERING
Algorithm
Analysis
APPROXIMATION
Zdroj: Abstr. Appl. Anal.
Abstract and Applied Analysis, Vol 2013 (2013)
RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname
ISSN: 1687-0409
1085-3375
2010-2054
DOI: 10.1155/2013/953786
Popis: 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.
This work has been developed within the framework of research project DPI2010-20542 of the Ministerio de Economia y Competitividad (Spain). The financial support of the FPU program (AP2008-01086), the funding from Universitat Politecnica de Valencia, and Generalitat Valenciana (PROMETEO/2012/023) are also acknowledged. The authors also thank the support of the Framework Programme 7 Initial Training Network Funding under Grant no. 289361 "Integrating Numerical Simulation and Geometric Design Technology."
Databáze: OpenAIRE
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