Topology Optimization of a Linear Piezoelectric Micromotor Using the Smoothed Finite Element Method

This paper presents the topology optimization design for a linear micromotor, including multitude cantilever piezoelectric bimorphs. Each microbeam in the mechanism can be actuated in both axial and flexural modes simultaneously. For this design, we consider quasi-static and linear conditions, and the smoothed finite element method (S-FEM) is employed in the analysis of piezoelectric effects. Certainty variables such as weight of the structure and equilibrium equations are considered as constraints during the topology optimization design process, then a deterministic topology optimization (DTO) is conducted. To avoid the overly stiff behavior in FEM modeling, a relatively new numerical method known as the cell-based smoothed finite element method (CS-FEM, as a branch of S-FEM) is introduced for our DTO problem. The topology optimization procedure is implemented using a solid isotropic material with a penalization (SIMP) approximation and a method of moving asymptotes (MMA) optimizer. Because of the higher efficiency and accuracy of S-FEMs with respect to standard FEMs, numerical results of our DTO analysis using a softer CS-FEM are substantially improved, compared to FEMs using quadrilateral elements (Q4) and triangular elements (T3) when the same sets of nodes are used.