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--Poincare 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.
['R. Amigo', 'Sebastian Miguel Giusti', 'A. A. Novotny', 'E. C. N. Silva', 'Jan Sokołowski']
Optimum design of flextensional piezoelectric actuators into two spatial dimensions