Two-dimensional modelling of laminated piezoelectric composites: analysis and numerical results

We propose a new approach to laminated piezoelectric plates based on a refi nement of the electric potential as function of the thickness coordinate of the laminate and accounting for shear effects, Moreover, the variation of the electric potential as function of the thickness coordinate is modelled for each layer of the laminate, The equation for the laminated piezoelectri c plate are then obtained by using a variational formulation involving mech anical surface Loads or prescribed electric potential on the top and bottom faces of the plate, In addition to the equations fur the generalized stres s resultants (due to the shear effects), the equation of the electric charg e conservation is also deduced for the 2D model, Particular attention is devoted to the single piezoelectric plate and bimor ph structure and the through-thickness distribution of the displacements. e lectric potential as well as stresses are given for different kinds of elec tromechanical loads, The results thus obtained are compared to those provid ed by a finite element method performed for the full 3D model, A good agree ment is observed for plates made of layers of PZT-4 piezoelectric material. The comparison ascertains the effectiveness of the present 2D approach to piezoelectric laminates. (C) 2001 Elsevier Science Ltd, All rights reserved .