An efficient approach for shape optimization of components

The optimization problem of finding the optimal shape of a mechanical component is investigated with the aim of presenting a simple and efficient numerical approach for minimizing stress concentration factor. The proposed approach is based on finite element method in conjunction with the widely used fully stressed design criterion (or the axiom of uniform stress), i.e. for structural shape optimization, an essential requirement for optimality is the achievement of constant tangential stresses along a section of the boundary to be optimized. The design boundary is modeled by using cubic splines, which are determined by a number of control points. The optimal shape of the design boundary with constant stress is achieved iteratively by adjusting the design boundary shape based on a simple logic and algorithm. The result quality in terms of accuracy and efficiency are tested and discussed with finite element analysis examples. The approach presented has the attractive properties that it can be very simply implanted into standard finite element codes.