Generalized Plane Solution for Monoclinic Piezoelectric Laminates

An efŽ cient method has been developed for analyzing the three-dimensional electromechanical deformations of a monoclinic piezoelectric laminate subjected to surface tractions and electric displacements on the top and bottom surfaces. The procedure combines the transfer matrix method with the asymptotic expansion technique. The electromechanical coupled formulation is reduced to a hierarchy of problems referred to as a reference plane. A closed-form solution is obtained for the generalized plane deformations of a piezoelectric laminate with the top and bottom surfaces subjected to uniform electric displacements andmechanical normal tractions and edges at the midplane rigidly clamped and grounded. The closed-form solution is obtained because the asymptotic expansion terminates after a few terms. For some loadings the in-plane electric Ž elds can bemuch larger than the out-of-plane electric Ž elds.