考虑质量约束的多相材料结构拓扑优化新方法

提出了一种将双向渐进法（BESO）与快速非支配排序遗传算法（NSGA-II）相结合的拓扑优化方法，称为BESO-NSGA-II方法。与传统双向渐进法的体积约束不同，本文算法以质量作为约束条件，并采用多相材料插值方案实现了多相材料的优化分布。通过大量的算例，证明了算法的稳定性和有效性。与传统双向渐进法相比，新算法在相同约束条件下能有效地提高结构刚度。同时，为了获得干净的拓扑，该算法提出了在交叉变异过程中使用的双惩罚算子来实现干净的拓扑结构。结果表明，该算法能较好地实现结构的轻量化设计。

A novel approach to topology optimization of multi-material structures considering mass constraint

This paper proposes a topology optimization method that combines the Bi-directional Evolutionary Structural Optimization (BESO) and the Non-dominated Sorting Genetic Algorithm II (NSGA-II), which is called the BESO-NSGA-II method in this paper.Different from the volume constraint of the traditional two-way progressive method, this algorithm takes mass as the constraint condition and adopts the multiphase material interpolation scheme to achieve the optimal distribution of the multiphase material.Many numerical examples in this paper prove the stability and effectiveness of the algorithm.Compared with the traditional Bi-directional Evolutionary Structural Optimization, the new algorithm can effectively improve the stiffness of the structure under the same constraints.At the same time, to obtain a clean topology, the algorithm proposes a double penalty operator used in the cross-mutation process.The results show that the algorithm can better realize the lightweight design of the structure.