A two-scale concurrent topology optimization method based on the couple stress theory is proposed for maximizing structural fundamental eigenfrequency. Because of the fact that the classical mechanics theory cannot reveal the size effect because of neglecting the influence of microstructure, the theory of couple stress including the microscopic properties of materials can be used to describe the size effect in deformations. On the foundation of the couple stress theory, the two-scale optimization model for finding optimal configurations of macrostructures and their periodic composite material microstructures is built. And the fundamental eigenfrequency of the macrostructure is maximized. The effective macroscopic couple stress constitutive constants of macrostructures are calculated by the representative volume element method. And a modified solid isotropic material with a penalization model is used to effectively avoid the localized mode. The optimization algorithm based on the bidirectional evolutionary structural optimization method is proposed. The optimal results of numerical examples show that the optimal topologies and natural frequencies obtained by the couple stress theory may differ significantly from those obtained by the typical Cauchy theory. It is obvious that couple stress theory can effectively describe the size effect in topology optimization.

提出了基于偶应力理论的两尺度并发拓扑优化方法，以最大化结构的基本特征频率。由于经典力学理论由于忽略了微观结构的影响而无法揭示尺寸效应，因此可以将包括材料微观特性在内的耦合应力理论用于描述变形中的尺寸效应。在偶应力理论的基础上，建立了寻找宏观结构及其周期性复合材料微观结构最优构型的两尺度优化模型。并且宏观结构的基本特征频率被最大化。通过代表体积元法计算出有效的宏观结构宏观耦合应力本构常数。并采用带有惩罚模型的改性固体各向同性材料来有效避免局部化。提出了基于双向进化结构优化方法的优化算法。数值算例的最佳结果表明，耦合应力理论获得的最佳拓扑和固有频率可能与典型柯西理论获得的最佳拓扑和固有频率明显不同。显然，耦合应力理论可以有效地描述拓扑优化中的尺寸效应。数值算例的最佳结果表明，耦合应力理论获得的最佳拓扑和固有频率可能与典型柯西理论获得的最佳拓扑和固有频率明显不同。显然，耦合应力理论可以有效地描述拓扑优化中的尺寸效应。数值算例的最佳结果表明，耦合应力理论获得的最佳拓扑和固有频率可能与典型柯西理论获得的最佳拓扑和固有频率明显不同。显然，耦合应力理论可以有效地描述拓扑优化中的尺寸效应。