Reliability Based Topology Optimization of a Linear Piezoelectric Micromotor Using the Cell-Based Smoothed Finite Element Method

This paper presents integration of reliability analysis with topology optimization design for a linear mircroactuator, including multitude cantilever piezoelectric bimorphs. Each microbimoph in the mechanism can be actuated in both axial and flexural modes simultaneously. We consider quasi-static and linear conditions, and the smoothed finite element method (S-FEM) is employed in the analysis of piezoelectric effects. Since microfabrication methods are used for manufacturing this type of actuator, uncertainty variables become very important. Hence, these variables are considered as constraints during our topology optimization design process and reliability based topology optimization (RBTO) 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) has been introduced first time for our RBTO problem. Reliability analysis has been conducted using performance measure approach (PMA), advanced mean value (AMV) and first order reliability method (FORM). After finding random design points, topology optimization procedure is implemented using a solid isotropic material with a penalization (SIMP) and method of moving asymptotes (MMA) optimizer. Numerical tests show that the accuracy and efficiency of numerical results using softer CS-FEM in RBTO problems are substantially improved compared to the FEM.