Stress-based multi-material structural topology optimization considering graded interfaces

For the multi-material structural topology optimization, most of works are based on the ideal interface hypothesis (the interfaces of material are considered to be ideal connection), which leads to the optimized structures tend to dangerous. Thus, this paper proposes a topology optimization method to minimize the maximum von Mises stress of multi-material structures with graded interfaces. A filter-based method is proposed to search and determine the locations of the multi-material interfaces, and the widths of the interfaces are determined by the filter radius. The mechanical properties of the multi-material interfaces are interpolated by gradient, and the gradient transition between the multi-material interface is realized. An extended Bi-directional Evolutionary Structural Optimization (BESO) method based on discrete variables is adopted to avoid the stress singularity problem. The maximum stress is measured by the global p-norm stress aggregation method. The adjoint method is used to derive the sensitivities of elements. Benchmark numerical examples are investigated to validate the effectiveness of the proposed method. Results show that the multi-material structure with graded interface can be described and optimized effectively. The width of the interfacial zone and the properties of the graded interface can be well controlled and defined, respectively. The topological results, for stress design, indicate that the maximum stress can be effectively reduced compared with stiffness design. The maximum stress of the topological structure considering the graded interface is higher than that without the graded interface, which indicates that the structure designed considering the graded interface is more safe. 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 with graded interfaces.