Static analysis of cross-ply laminated plates with integrated surface piezoelectric layers using differential quadrature

The three-dimensional solution for static analysis of cross-ply rectangular plate imbedded in piezoelectric layers is presented using differential quadrature method (DQM) and Fourier series approach. The plate is assumed to be simply-supported at one pair of opposite edges and arbitrary conditions at the other pair. Applying the DQM to the governing differential equations and to the boundary conditions along the longitudinal or latitudinal directions, new state equations about state variables at discrete points are derived. The stress, displacement and electric potential distributions are obtained by solving these state equations. Both the direct and the inverse piezoelectric effects are investigated and the influence of piezoelectric layers on the mechanical behavior of plate is studied. The method is validated by comparing numerical results for the plate without piezoelectric layers and simply-supported edges with that available in the literature.