Topology Optimization for Static Shape Control of Piezoelectric Plates With Penalization on Intermediate Actuation Voltage

Abstract

This paper investigates the simultaneous optimal distribution of structural material and trilevel actuation voltage for static shape control applications. In this optimal design problem, the shape error between the actuated and the desired shapes is chosen as the objective function. The energy and the material volume are taken as constraints in the optimization problem formulation. The discrete-valued optimization problem is relaxed using element-wise continuous design variables representing the relative material density and the actuation voltage level. Artificial interpolation models which relate the mechanical/piezoelectrical properties of the material and the actuation voltage to the design variables are employed. Therein, power-law penalization functions are used to suppress intermediate values of both the material densities and the control voltage. The sensitivity analysis procedure is discussed, and the design variables are optimized by using the method of moving asymptotes (MMA). Finally, numerical examples are presented to demonstrate the applicability and effectiveness of the proposed method. It is shown that the proposed method is able to yield distinct material distribution and to suppress intermediate actuation voltage values as required.