Topology optimization of couple-stress material structures

Conventional topology optimization is concerned with the structures modeled by classical theory of mechanics. Since it does not consider the effects of the microstructures of materials, the classical theory can not reveal the size effect due to material's heterogeneity. Couple-stress theory, which takes account of the microscopic properties of the material, is capable of describing the size effect in deformations. The purpose of this paper is to investigate the formulation for topology optimization of couple-stress material structures. The artificial material density of each element is chosen as design variable. Based on the basic idea of SIMP (Solid Isotropic Material with Penalization) method, the effective material stiffness matrix of couple-stress material is related to the artificial density by power law with penalty. The structural analysis is implemented by finite element method for couple-stress materials, and a 4-noded quadrilateral couple-stress element is formulated in which C (1) continuity requirement is relaxed. Some typical problems are solved and the optimal results based on the couple-stress theory are compared with the conventional ones. It is found that the optimal topologies of couple-stress continuum show remarkable size effect.