An accurate modelling of piezoelectric multi-layer plates

The present work proposes a new approach to laminated plates with piezoelectric layers based on a refinement of the electric potential as function of the thickness coordinate and accounting for shearing correction of the elastic displacement. The approach deals with the combination of an equivalent single-layer approach for the mechanical displacement with a layerwise-type modelling of the electric potential considered as an additional degree of freedom. Such an approach offers flexibility in accommodating electric conditions at the layer interfaces. The equations governing the force, moment and electric charge resultants of the laminated piezoelectric plate are then deduced from a variational formulation involving mechanical surface loads or prescribed electric potential on the top and bottom faces of the plate as well as at layer interfaces. A particular attention is devoted to the interface conditions which are enforced by using Lagrange multipliers in the variational principle. Emphasis is placed on the performances, advantages and limitations of the present approach. The quality of the predictions of the global and local responses (the through-the-thickness variation of elastic displacements, stresses, electric potential and induction) is quantified for particular structures of practical interest such as piezoelectric bimorph, bilayer structure and piezoelectric sandwich undergoing applied density of force and electric potential. Moreover, comparisons of the results provided by the refined approach to those of finite element computations and simplified model are also presented. The comparisons assess of the effectiveness of the present laminated piezoelectric plate model that improves, in significant way, the predictions given by a simplified approach.