Three-dimensional asymptotic approach to inhomogeneous and laminated piezoelectric plates

An asymptotic theory is developed for anisotropic inhomogeneous and laminat ed piezoelectric plates on the basis of three-dimensional linear piezoelect ricity. The inhomogeneity is assumed in the thickness direction and include s the important piezoelectric laminates as a special case. Through asymptot ic expansions, the resulting two-dimensional differential equations are of the same form for each order, with different nonhomogeneous terms being det ermined systematically by preceding-order solutions. The governing equation s of the leading-order, when degenerated to pure elasticity, are shown to b e the same as those for equivalent classical thin elastic plates. The propo sed methodology is illustrated by considering a rectangular piezoelectric p late subject to both mechanical and electric loadings with its edges simply supported and grounded. A three-dimensional solution for the fully electro mechanically coupled problem is obtained by successively solving the two-di mensional field equations from the leading order to higher orders, Excellen t agreement is observed with established results and new results are presen ted, from which significant physical insights are discussed. (C) 2000 Elsev ier Science Ltd. All rights reserved.