Extended layerwise method for laminated piezoelectric and composite plates with delaminations, cracks or debonding of a piezoelectric patch

Extended layerwise method (XLWM) is applied to the static analysis problems of laminated piezoelectric plates and laminated composite plates with a piezoelectric patch in this paper. A piezoelectric XLWM is first developed for the laminated piezoelectric plates with multiple delaminations and transverse cracks. The discontinuities of displacements and electric potential resulted from delamination are described in the assumptions along the thickness direction. In the in-plane displacement and electric potential fields, the transverse cracks are modeled by using the extended finite element method (XFEM). The coupled electromechanical variational principle is employed to derive the Euler equations, boundary conditions and finite element formulations. And then, this piezoelectric XLWM is employed to establish a coupling analysis model for the damaged laminated composite plates with a piezoelectric patch. The damaged composite plate is discretized by the XLWM as well, so the surface displacement freedoms are included into the governing equations of composite plate and piezoelectric patch. The displacement continuity and internal force equilibrium conditions at the interface of the laminated composite plate and piezoelectric patch are considered in the final governing equations.