Actuator effect of a piezoelectric anisotropic plate model

Abstract

This paper addresses the actuator e ect of a piezoelectric anisotropic plate model, depending on the location of the applied electric potentials, and for di erent clamped boundary conditions. It corresponds to integer optimization problems, whose objective functions involve the displacement of the plate. We adopt the two-dimensional piezoelectric anisotropic nonhomogeneous plate model derived in Figueiredo and Leal [1]. This model is rst discretised by the nite element method. Then, we describe the associated integer optimization problems, which aim to nd the maximum displacement of the plate, as a function of the location of the applied electric potentials. In this sense, we also introduce a related multi-objective optimization problem, that is solved through genetic algorithms. Several numerical examples are reported. For all the tests, the sti ness matrices and force vectors have been evaluated with the subroutines planre and platre, of the CALFEM toolbox of MATLAB [2], and, the genetic algorithms have been implemented in C++.