Moderately large deflection analysis of simply supported piezo-laminated composite plates under uniformly distributed transverse load

Abstract

This paper presents the structural analysis of simply supported piezo-laminated rectangular plates with immovable edges under uniformly distributed transverse load utilizing Kirchhoff’s hypothesis and von Kármán strain displacement relations. The effect of actuation electric potential difference on the transverse deflection of the plate is examined. The study considers linear induced strain in the piezoelectric layer applicable to low electric fields. The vón Kármán’s moderately large deflection equations for laminated elastic plates are derived in terms of stress and transverse deflection functions. The layup of the plate can be general with no limitation on the placement of the piezoelectric layer. A deflection function satisfying the simply supported boundary conditions is assumed and a stress function is then obtained after solving the compatibility equation. Applying modified Galerkin’s method to the governing nonlinear partial differential equations, an expression for the load–deflection relation is obtained. This is the advantage of the current approach compared to the numerical techniques. Results are obtained for isotropic and graphite-epoxy square plates with the proposed load–deflection relation and compared with finite element approach. It is demonstrated that the deflection of the plate can be reduced by applying appropriate electric field on the piezoelectric layer.