Coupled three-dimensional piezoelasticity solution for edge effects in Levy-type rectangular piezolaminated plates using mixed field extended Kantorovich method

A coupled three-dimensional piezoelasticity solution for rectangular piezoelectric laminated plates with Levy-type boundary conditions is presented using the mixed-field multi-term extended Kantorovich method (EKM) and Fourier series expansion. The solution considers two-way electromechanical coupling, and satisfies all the essential and natural boundary conditions as well as the continuity conditions at the interface exactly at all points. The objective is to accurately characterize the edge effects in finite dimensional piezolaminated plates under mechanical and actuation potential loading, and also to provide a benchmark for assessing the accuracy of the two-dimensional laminate theories. The interlaminar shear stress is also accompanied by a singular stress field of the transverse normal (peel) stress near the edge. The numerical study is conducted for both single layer PZT plates for sensory applications and hybrid sandwich plates for smart structural applications. It is shown that the EKM solution predicts the displacement, stress, electric potential and electric displacement fields very accurately including the sharp variations of stresses near the edge, under the potential loading with just two/three terms in the trial function.