Synthesis of Compliant Piezomechanical Actuators
In control of distributed parameter systems the piezoelectric actuators are of common use. The topology optimization of a multiphysics model in piezoelectricity into two spatial dimensions 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 new method of sensitivity analysis is general and can be used for the purpose of the shape-topological optimization in a broad class of multiphysics models. The numerical results confirm the efficiency of proposed approach to optimum design in multiphysics. This chapter is based on the paper by Ricardo Amigo, Sebastián Miguel Giusti, Antonio André Novotny, Emílio Carlos Nelli Silva and Jan Sokolowski (Amigo, Giusti, Novotny, Silva, Sokolowski, SIAM J Control Optim, 52(2):760–789, (2016), ).