Optimal topologies in structural design of micropolar materials

Abstract

The authors developed the finite element method (FEM) for micropolar elastic solids and applied it to the problem of topology optimization. The weighted residual method and 8-node isoparameteric elements were employed for the FEM analysis. The solid isotropic material with penalization (SIMP) method and the gravity control function were employed in the optimization procedure. For the designing area, rectangular plates under several types of boundary conditions were analysed. In this analysis, the effects of the engineering material constants for micropolar elasticity, the coupling number N, which is related to stresses, and the characteristic length l, which is related to couple stresses, are researched. The optimal structures of micropolar materials are strongly influenced by material properties of bending. Though the optimal topologies of classical elastic solids are generally truss frames, those of micropolar materials are rigid frames, which are simple topologies. At the joint of members loaded moments, holes are more apt to appear in the optimization process for micropolar solids than classical solids, that is, optimal topologies becomes finer, in micropolar elasticity. Obtained results are determined by the tradeoff between simplification and refinement of structures. The proposed method could potentially solve the optimization problems of bio-materials such as bone tissue.