Optimum design of flextensional piezoelectric actuators into two spatial dimensions

Abstract

Piezoelectric actuators are in common use for control of distributed parameter systems. We consider the topology optimization of a multiphysic model in piezoelectricity into two spatial dimensions. 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 the elastic energy of an actuator. The domain decomposition technique and the Steklov Poincaŕe pseudodifferential 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 new method of sensitivity analysis is general and can be used for shape-topological optimization in a broad class of multiphysics models. Our numerical results confirm the efficiency of the proposed approach to optimum design in multiphysics.