A piezoelectric anisotropic plate model

Abstract

We mathematically justify a reduced piezoelectric plate model. This is achieved considering the three-dimensional static equations of piezoelectricity, for a nonhomogeneous anisotropic thin plate, and using the asymptotic analysis to compute the limit of the displacement vector and electric potential, as the thickness of the plate approaches zero. We prove that the three-dimensional displacement vector converges to a Kirchhoff-Love displacement, that solves a two-dimensional piezoelectric plate model, defined on the middle surface of the plate. Moreover, the three-dimensional electric potential converges to a scalar function that is a second order polynomial with respect to the thickness variable, with coefficients that depend on the transverse component of the Kirchhoff-Love displacement. We remark that the results of this paper generalize a previous work of A. Sene (2001) for homogeneous and isotropic materials.