Topology optimization of smart structures: design of piezoelectric plate and shell actuators

In this paper, a novel approach to the design of piezoelectric plate and shell actuators using topology optimization is described. A new piezoelectric material model PEMAP-P (piezoelectric material with penalization and polarization) is proposed, which is an extension of the SIMP (solid isotropic material with penalization) model used for elastic materials. In addition to the pseudo-density ρ1, which describes the 'amount' of piezoelectric material in each finite element, a new design variable ρ2 is introduced for the polarization of the piezoelectric material. The optimization problem consists in distributing the piezoelectric actuators in such a way as to achieve a maximum output displacement in a given direction at a given point of the structure, while simultaneously minimizing the structural compliance. Sequential linear programming (SLP) is used to solve the optimization problem. Examples are given demonstrating the potential of the proposed approach for the optimal design of piezoelectric actuators for multi-layer plate and shell structures.