Optimum Design of Flextensional Piezoelectric Actuators into Two Spatial Dimensions

In control of distributed parameter systems the piezoelectric actuators are of common use. The topology optimization of a multiphysic model in piezoelectricity is considered. The topological derivative of a tracking-type shape functional is derived in its closed form for the purpose of shape optimization of piezoelectric actuators. The optimum design procedure is applied to a micromechanism which transforms the electrical energy supplemented via its piezoceramic part into elastic energy of an actuator. The domain decomposition technique and the Steklov-Poincaré pseudo-differential boundary operator are employed in the asymptotic analysis of the shape functional defined on a part of the boundary of the elastic body under consideration. The proposed method of sensitivity analysis is general and can be used for the purpose of the shape-topological optimization for a broad class of multiphysics models. The numerical results confirm the efficiency of proposed approach to optimum design in multiphysics.