Stress optimization of smooth continuum structures based on the distortion strain energy density

This paper presents an evolutionary structural optimization method of designing continuum structures with clear and smooth boundaries for stress minimization. The stress optimization problem is formulated with the P-norm function based on the distortion strain energy density, so as to avoid the stress relaxation and the local nature of the maximum stress. In order to obtain a smooth topology, the surrogate design variables on the volume fraction of elements are defined based on the proportion of solid and void points within an element. Based on sensitivity analysis, topology optimization evolves the structure by gradually decreasing the structural volume to the optimized one with the prescribed volume. 2D and 3D numerical examples are presented and discussed to demonstrate the effectiveness of the proposed topology optimization method for minimizing the maximum stress of continuum structures and alleviating stress concentration.