Nonlinear static response of piezoelectric plates considering electro-mechanical coupling

Nonlinear static analysis of piezoelectric plates has been carried out using nonlinear finite element method considering electro-mechanical coupling. The geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the plate thickness. The governing equations are obtained using potential energy and Hamilton's principle that includes elastic and piezoelectric effects. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements. Results are presented for piezoelectric plate under different mechanical boundary conditions. Numerical results for the plate are given in dimensionless graphical forms. Effects of boundary conditions on linear and nonlinear response of the plate are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.