Modied Fi xed-grid Finite element method in shape optimization problems based on the 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 basedon minimization of the stress along the design boundary calculated by the modied fixedgrid finite element method (mfgfem). using mfgfem eliminates mesh adaptationand re-meshing processes, as needed in the standard nite element method, and reducesthe analysis cost signicantly. in this study, a new approach for computing the stinessmatrix of boundary intersecting elements is also presented and the optimal shape of theproblem domain is obtained via a simple optimization algorithm. the performance of theproposed approach is investigated for shape optimization problems. it is concluded thatthe results of the present method are in good agreement with other analytical and niteelement solutions.