基于双尺度拓扑优化的多相材料结构设计方法

Structure Design Method of Multiphase Materials Based on Two-scale Topology Optimization

针对双尺度优化问题,研究小组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。通过基于能量的均匀化理论推导非均质材料的有效性质,并采用多相材料插值方案实现双尺度结构多相材料的拓扑优化。为了获得“干净”的拓扑,BESO-NSGA-Ⅱ算法提出了在交叉变异过程中使用双惩罚算子来实现“干净”的拓扑结构。通过算例并与经典BESO算法进行对比,验证了BESO-NSGA-Ⅱ算法的稳定性和有效性及其获得收敛解的能力,以期为后续的双尺度拓扑优化研究提供参考依据。

Aiming at the dual-scale optimization problem, the research team proposes a topology optimization method that combines Bi-directional Evolutionary Structural Optimization(BESO) and Non-dominated Sorting Genetic Algorithm Ⅱ(NSGA-Ⅱ), called BESO-NSGA-Ⅱ method. The effective properties of heterogeneous materials are deduced by energy-based homogenization theory, and the multiphase material interpolation scheme is adopted to realize the topology optimization of twoscale structure multiphase materials. In order to obtain a “clean” topology, BESO-NSGA-Ⅱ proposes a double penalty operator used in the crossover mutation process to achieve a “clean” topology. The stability and effectiveness of BESO-NSGA-Ⅱ algorithm and its ability to obtain convergent solutions are verified by calculation examples and comparison with the classic BESO algorithm, in order to provide a reference for subsequent two-scale topology optimization research.