Thermal deformations of plates produced by temperature distributions satisfying poisson's equation

Abstract

Small-deflection plate equations are presented in terms of the midplane plate deformations and the temperature distribution within the plate, which is assumed independent of the plate deformation. The plate boundary conditions are presented in a general form and are suitable for solutions involving either fixed, free, or hinged edge conditions.

The temperature distribution within the plate is assumed to be governed by Poisson's equation and a specified temperature distribution over the surfaces of the plate. Solutions for the temperature distribution are given in terms of a power series with respect to the plate thickness coordinate, the coefficients of which are dependent on the midplane temperature distribution and the midplane temperature gradient in the plate thickness direction.

Out-of-plane plate deformations are discussed for plates with fixed edges. Discussions of plate deformations are also presented in which the temperature distributions result from constant heat generation within the plate and from radiation absorption.