A new asymptotic model for a composite piezoelastic plate

A new asymptotic homogenization piezoelastic composite plate model is obtai ned. Derivation is based on a modified two-scale asymptotic homogenization technique applied to a rigorously formulated piezoelectric problem for a th ree-dimensional thin composite layer of a periodic structure. The obtained model makes it possible to determine both local fields and the effective pr operties of piezoelectric plate by means of solution of the obtained three- dimensional local unit cell problems and a global two-dimensional piezoelas tic problem for a homogenized anisotropic plate. It is shown, in particular that the effective stiffnesses generally depend on the local piezoelectric constants of the material. The general symmetry properties of the effectiv e stiffnesses and piezoelectric coefficients of the homogenized plate are d erived. The general model is applied to a practically important case of a l aminated anisotropic piezoelastic plate, for which the analytical formulas for the effective stiffnesses, piezoelectric and dielectric coefficients ar e obtained. Theory is illustrated by a numerical example of a piezoelectric laminated plate of a specific structure. (C) 2001 Elsevier Science Ltd. Al l rights reserved.