Modi ed Fi xed-grid Finite element method in shape optimization problems based on the gradientless method

This paper presents a methodology for solving shape optimization problems where the unknown is the shape of the problem domain. The proposed algorithm is based on minimization of the stress along the design boundary calculated by the Modied Fixed Grid Finite Element Method (MFGFEM). Using MFGFEM eliminates mesh adaptation and re-meshing processes, as needed in the standard nite element method, and reduces the analysis cost signicantly. In this study, a new approach for computing the stiness matrix of boundary intersecting elements is also presented and the optimal shape of the problem domain is obtained via a simple optimization algorithm. The performance of the proposed approach is investigated for shape optimization problems. It is concluded that the results of the present method are in good agreement with other analytical and nite element solutions.