Stress-related topology optimization via level set approach

► Stress-related topology optimization (STOPT) is studied by level-set method (LSM). ► Problem formulations and the corresponding solution aspects are presented in detail. ► How to solve some intrinsic difficulties in STOPT by LSM are discussed critically. ► Numerous examples demonstrate the effectiveness of the proposed approach. ► LSM is a promising tool for STOPT under appropriate problem formulations. Considering stress-related objective or constraint functions in structural topology optimization problems is very important from both theoretical and application perspectives. It has been known, however, that stress-related topology optimization problem is challenging since several difficulties must be overcome in order to solve it effectively. Traditionally, SIMP (Solid Isotropic Material with Penalization) method was often employed to tackle it. Although some remarkable achievements have been made with this computational framework, there are still some issues requiring further explorations. In the present work, stress-related topology optimization problems are investigated via a level set-based approach, which is a different topology optimization framework from SIMP. Numerical examples show that under appropriate problem formulations, level set approach is a promising tool for stress-related topology optimization problems.