Modified fixed-grid finite element method in shape ‎optimization problems based on gradientless method

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