Stress constrained multi-material topology optimization with the ordered SIMP method

Abstract

To date, both the stress-related and multi-material topology optimization problems have been extensively studied. However, there are few works addressing the stress-constrained multi-material topology optimization (SMMTO) problem. Hence, a novel solution to the SMMTO problem is proposed in this paper based on the ordered SIMP method. To be specific, description of the multi-material elastic model is achieved with the ordered SIMP interpolation. More importantly, a novel ordered SIMP-like interpolation function is proposed to realize the relaxed and scaled stress interpolation, so that only a unique set of density variables are required for the SMMTO problem. Scaling of the stress measure plays a vital role in properly addressing the different yield limits. The global stress constraint is established with the p-norm function combined with the stability transformation method to close the gap between the p-norm stress and the exact maximum local stress. The adjoint sensitivity analysis is performed and the optimization problem is solved using a MMA optimizer. Several benchmark numerical examples are investigated and discussed to illustrate the effectiveness of the proposed approach.