Stress-based bi-directional evolutionary topology optimization for structures with multiple materials

Both multi-material and stress-based topology optimization problems have been extensively investigated. However, there are few studies on the stress-based topology optimization of multi-material structures. Hence, this work proposes a novel topology optimization method for minimizing the maximum von Mises stress of structures with multiple materials under volume constraints. An extended Bi-directional Evolutionary Structural Optimization (BESO) method based on discrete variables which can mitigate the well-known stress singularity problem is adopted. The global von Mises stress is established with the p-norm function, and the adjoint sensitivity analysis is derived. Two benchmark numerical examples are investigated to validate the effectiveness of the proposed method. The effects of key parameters including p-norm, sensitivity and density filter radii on the optimized results and the stress distributions are discussed. The influence of varying mesh densities on the optimized topologies are investigated in comparison with the multi-material stiffness maximization design. The topological results, for multi-material stress design, indicate that the maximum stress can be reduced compared with multi-material stiffness design. It concludes that the proposed approach can achieve a reasonable design that effectively controls the stress level and reduces the stress concentration effect at the critical stress areas of multi-material structures.