Abstract and Applied Analysis
Volume 2013 (2013), Article ID 953786, 19 pages
Research Article

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

Centro de Investigación de Tecnología de Vehículos (CITV), Universidad Politècnica de València, 46022 Valencia, Spain

Received 25 January 2013; Accepted 20 February 2013

Academic Editor: Juan J. Nieto

Copyright © 2013 E. Nadal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.