Multi-material microstructure topology optimization design considering macroscopic structural performance

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Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (11) : 185-193.

ZHANG Lei1,2, NI Shaohao1,2, JIANG Guozhang1,2,3, ZHANG Yan1,2,3, GONG Yiwen1,2

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Abstract

Porous microstructure materials are widely used in aerospace and other engineering fields due to their excellent mechanical properties, such as lightweight, high specific stiffness/strength, and impact resistance. Compared with conventional design with one single material, topological design with multiple materials can provide a microstructure with better mechanical properties. And topology optimization is one of the effective design methods for multi-material layouts. This paper proposes a parametric level set-based multi-material microstructural topology optimization method by combining a difference-set-based multi-material level set description model and an alternating active phase algorithm. In this method, firstly, a difference-set-based multi-material level set description model is constructed to accurately describe the topologies of N+1 phase materials only by using N level set functions. Then, an alternating active phase algorithm is employed to split the original N+1 phase multi-material optimization problem into N(N+1)/2 binary-phase sub-problems, so as to reduce design variables and constraint conditions for improving computational efficiency. Finally, a numerical homogenization method is used to calculate the effective elastic tensor of a multi-material microstructure. With the minimum macrostructural compliance as objective function, and the allowable material amount of each phase as constraint condition, a topology optimization model for the multi-material microstructure is constructed. The optimization criteria algorithm is used to numerally solve the above optimization model. The numerical results show that the proposed method can effectively achieve the topological design of multi-material microstructures, and the resulting microstructures have also smooth structural boundaries and distinct material interfaces.

Key words

topology optimization / multi-material microstructure / level set method / homogenization method / alternating active-phase algorithm

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ZHANG Lei1,2, NI Shaohao1,2, JIANG Guozhang1,2,3, ZHANG Yan1,2,3, GONG Yiwen1,2. Multi-material microstructure topology optimization design considering macroscopic structural performance[J]. Journal of Vibration and Shock, 2024, 43(11): 185-193

References

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