Three-dimensional asymptotic approach to inhomogeneous and laminated piezoelectric plates

An asymptotic theory is developed for anisotropic inhomogeneous and laminated piezoelectric plates on the basis of three-dimensional linear piezoelectricity. The inhomogeneity is assumed in the thickness direction and includes the important piezoelectric laminates as a special case. Through asymptotic expansions, the resulting two-dimensional differential equations are of the same form for each order, with different nonhomogeneous terms being determined systematically by preceding-order solutions. The governing equations of the leading-order, when degenerated to pure elasticity, are shown to be the same as those for equivalent classical thin elastic plates. The proposed methodology is illustrated by considering a rectangular piezoelectric plate subject to both mechanical and electric loadings with its edges simply supported and grounded. A three-dimensional solution for the fully electromechanically coupled problem is obtained by successively solving the two-dimensional field equations from the leading order to higher orders, Excellent agreement is observed with established results and new results are presented, from which significant physical insights are discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.