ASYMPTOTIC THERMOELASTIC ANALYSIS OF ANISOTROPIC INHOMOGENEOUS AND LAMINATED PLATES

Abstract

On the basis of three-dimensional elasticity without a priori assumptions, we develop an asymptotic theory for the thermoelastic analysis of anisotropic inhomogeneous plates subject to general temperature variations and under the action of lateral loads. The inhomogeneities considered are in the thickness direction, and the laminated plate represents an important special case. Through reformulation of the basic equations and nondimensionalization of the field variables, we find that the method of asymptotic expansions is well suited for the problem. Upon using the asymptotic expansion, we obtain sets of recurrence equations that can be integrated successively to determine the solution for a problem. We show that the classical laminated plate theory (CLT) is merely the leading-order approximation in the asymptotic theory. Furthermore, the higher-order equations are essentially the same as the CLT equations, only with nonhomogeneous terms that are completely determined from the lower-order solutions. As a result, the three-dimensional asymptotic solution for a thermoelasticity problem of the laminated plate can be obtained in a systematic way no more difficult than the CLT. The theory is illustrated by considering an inhomogeneous plate subject to a temperature variation and a laminated plate subject to a general thermomechanical loading.