Topology optimization of stress-constrained structures using distortion energy theory

Abstract The strain energy can be divided into changes in volume and distortions in shape. Distortions in shape are a significant contributing factor to material failure. Therefore, this paper transforms global stress constraints into distortion energy constraint based on the level-set method to optimize the structure design. First, the large and complex stress constraints are transformed into a distortion energy constraint, which is based on the theory of distortion energy causing material yield. Next, due to the challenges in extracting distortion energy from the elements and ensuring design safety, the more easily extractable strain energy constraint is used as a substitute for the distortion energy constraint. Finally, four numerical examples serve to demonstrate the effectiveness and practical applicability of the proposed approach.