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. To test the numerical solutions, the bending problem of the cantilever was used. 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 1, 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 truss frames, in general, those of micropolar materials are rigid frames. Since the checkerboard structures are more apt to appear in the optimization process for micropolar solids than in classical elasticity, filtering (the gravity control function employed in this paper) or other techniques are required to obtain practical solutions. The proposed method could potentially solve the optimization problems of biomaterials such as bone tissue.
