Von Mises Stress and Level Set Method based Structural Topology Optimization with Multi-phase Materials

This paper presents a topology optimization method based on Von Mises stress and the level set method for the multiple materials design. Since the level set method can naturally handle topological changes during the interface propagation, the level set model based material implicit representation has been applied to structural topology optimization. However, the level set method can not generate new holes during the optimization process and the final result depends on the initial topological guess. In this paper, the new holes are generated according to the distribution of Von Mises stress in material region to suppress the dependence of the initialization. We establish the replacement strategy of multiple materials to make the objective function minimum. And then, the shape optimization is implemented by the propagating using the level set method with the descent gradient direction. Numerical examples demonstrate the validity of the proposed method.