Boundary layer effects in Levy-type rectangular piezoelectric composite plates using a coupled efficient layerwise theory

Abstract

Abstract The edge effect in rectangular piezoelectric laminated plates is studied using a coupled efficient layerwise theory. For this purpose, an analytical solution is presented for the fully coupled electromechanical, combined active/sensory response of Levy-type rectangular plates. Using a mixed formulation, the governing differential equations are reduced to a set of ordinary differential equations in terms of displacements, electric potential, stress resultants and electric displacement resultants that appear in the boundary conditions at the arbitrary edges. Numerical results are presented for piezoelectric bimorph, and hybrid composite and sandwich plates. Their accuracy is assessed by comparing with the three dimensional finite element solution. Like the mechanical loading, for electrical loading too the strongest edge effect occurs at the free edge followed by the soft-simply supported and clamped ones. The effect of electromechanical coupling and electric boundary conditions on the distributions of stress resultants near the edges is investigated. The effect of inclusion of layerwise terms in the displacement approximation of the efficient layerwise theory is examined by comparing the results with those of the coupled smeared third order theory.