A new asymptotic model for a composite piezoelastic plate

A new asymptotic homogenization piezoelastic composite plate model is obtained. Derivation is based on a modified two-scale asymptotic homogenization technique applied to a rigorously formulated piezoelectric problem for a three-dimensional thin composite layer of a periodic structure. The obtained model makes it possible to determine both local fields and the effective properties of piezoelectric plate by means of solution of the obtained three-dimensional local unit cell problems and a global two-dimensional piezoelastic 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 effective stiffnesses and piezoelectric coefficients of the homogenized plate are derived. The general model is applied to a practically important case of a laminated anisotropic piezoelastic plate, for which the analytical formulas for the effective stiffnesses, piezoelectric and dielectric coefficients are obtained. Theory is illustrated by a numerical example of a piezoelectric laminated plate of a specific structure.