Analytical and numerical modelling of laminated composites with piezoelectric layers

Abstract
An accurate and efficient modelling for laminated piezoelectric plates is presented. The approach is based mostly on a refinement of the elastic displacement including a shear correction and accounting for a layerwise approximation for the electric potential. The equation of the model are deduced from a variational formulation accounting for continuity conditions at the layer interfaces by using Lagrange multipliers. The resolution of different situations is considered for various types of electromechanical loads : (i) density of applied forces and (ii) applied electric potential. The results for bimorph and sandwich structures are given and compared to the finite element computations performed on the 3D model. The problem of vibration of piezoelectric laminated composites is also discussed. A quite good accuracy is shown for the electromechanical local (the trough-the-thickness variation) and global (deflection, frequencies, etc.) responses of the present plate model.