Topology optimization of piezoelectric actuators considering geometric nonlinearities

This work shows a methodology for the optimum design of piezelectric actuators undergoing large deformations. An equilibrium formulation for the finite movement of a piezoelectric body is introduced, as well as its finite element discretization. The solution of the nonlinear finite element equations is acomplishied through a new coupled-field arc-length algorithm. The optimization consists in the maximization of the output displacements subject to volume and displacement constraints. Sensitivities are derived with respect to mechanical displacements and electric potentials. The Generalized Method of Moving Asymptotes (GMMA) is used for the solution of the optimization problem. The results obtained with the proposed formulation are shown and the influence of the geometric nonlinearities is discussed.