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

and Applied Analysis 3 In this contribution we have applied cg-FEM to a structural shape optimization analysis. This type of processes will benefit from the computational efficiency and accuracy of cg-FEM but also from the data structure that will allow for sharing information between different geometries analyzed during the process, further improving the behavior of the optimization process. The paper is organized as follows. The problem to be solved is defined in Section 2. The main characteristics of the proposed cg-FEMmethodology are presented in Sections 3 and 4, respectively, devoted to the use of Cartesian grids independent of the geometry for the FE analysis and to the hadaptive procedures specially adapted to the use of Cartesian grids. Numerical examples will be used in Section 5 to evaluate the performance of the cg-FEMmethodology. 2. Problem Statement Let us consider the 2D linear elastic problem. Let u be the displacement field defined in Ω ⊂ R, the solution of the boundary value problem: −∇ ⋅ σ (u) = b in Ω,