基于偶应力理论的双向进化结构优化法

Bi-directional Evolutionary Structural Optimization Based on Couple Stress Theory

拓扑优化是实现传统结构创新式构型设计的常用技术。在此领域内,变密度法已经成为目前结构优化设计的主流算法。这种算法基于经典介质理论,不包括材料尺度参数,无法捕捉微观结构的信息。为此,应用双向进化结构优化法取代变密度法,并结合偶应力理论而不是经典理论构建了优化列式来进行拓扑优化设计,最终将两种优化算法得到的结果作对比,以呈现出不同尺度下结构的不同构型。结果表明,在以结构刚度最大化为目标的设计中,偶应力介质的结果取决于尺度参数的大小,最优结果具有明显的尺度效应。通过几个数值算例证明了这种方法适用于具有与单元尺寸相当的固体材料的结构单元设计,并且拓展了针对微型结构设计问题的技术手段。

Topology optimization is a common technology to realize the innovative configuration design of traditional structures.In this field,solid isotopic material with penalization(SIMP)has become the mainstream algorithm of structural optimization design.This algorithm is based on classical medium theory and does not include material scale parameters,so it can not capture the information of microstructure.Therefore,bi-directional evolutionary structural optimization(BESO)was used to replace SIMP method,and combined with couple stress theory rather than classical theory,an optimization formula was constructed for topology optimization design.Finally,the results of the two optimization algorithms were compared to show different configurations of structures at different scales.The results show that in the design aimed at maximizing the structural stiffness,the result of couple stress medium depends on the size of scale parameters,and the optimal result has obvious scale effect.Several numerical examples show that the method is suitable for structural element design with solid materials equivalent to the element size,and expands the technical means for micro structure design.