A nonlinear formulation of piezoelectric plates

A nonlinear piezoelectric plate model capable of accurately expressing the direct and converse piezoelectric effects is presented. The developed semi-intrinsic theory is meant to encompass large strains, displacements, and rotations that can occur in the plate as a consequence of a complete coupling between the mechanical and the electrical fields. Based on the assumption that a linear dependence of the electric potential on the plate thickness is not adequate to represent the potential electric energy, a specific structure to the field of admissible displacement is taken into account. A nonlinear regression technique is successively developed to detect the nonlinear dependence of the obtained solutions on the through-the-thickness coordinate. Particular warping functions characterized by the use of an ad hoc polynomial expansion adopted to express their dependence on the plate thickness direction are here considered to describe the shear and the extensional deformability of the plate transverse fibers. Linear constitutive relations for a transversely isotropic continuum are considered. The governing equations of motions for the model are finally obtained.