Generalized plane solution for monoclinic piezoelectric laminates

An efficient method has been developed for analyzing the three-dimensional electromechanical deformations of a monoclinic piezoelectric laminate subje cted to surface tractions and electric displacements on the top and bottom surfaces. The procedure combines the transfer matrix method with the asympt otic expansion technique. The electromechanical coupled formulation is redu ced to a hierarchy of problems referred to as a reference plane. A closed-f orm solution is obtained for the generalized plane deformations of a piezoe lectric laminate with the top and bottom surfaces subjected to uniform elec tric displacements and mechanical normal tractions and edges at the midplan e rigidly clamped and grounded. The closed-form solution is obtained becaus e the asymptotic expansion terminates after a few terms. For some loadings the in-plane electric fields can be much larger than the out-of-plane elect ric fields.