Exact Thermoelasticity Solution for Cylindrical Bending Deformations of Functionally Graded Plates

Abstract

The abrupt change in material properties across the interface between discrete layers in composite structures can result in large interlaminar stresses leading to delamination. One way to overcome these adverse effects is to use “functionally graded materials” which are inhomogeneous materials with continuously varying material properties. There are several three-dimensional (3D) solutions available for the thermoelastic analysis of inhomogeneous plates. Most of these studies have been conducted for laminated plates that have piecewise constant material properties in the thickness direction. Rogers et al. [1] have employed the method of asymptotic expansion to analyze 3D deformations of inhomogeneous plates. However, the boundary conditions on the edges of the plate in their theory are applied in an average sense like those in 2D plate theories and the plate is assumed to be only moderately thick. Tarn and Wang [2] have also presented an asymptotic solution that may be carried out to any order, but the manipulations become more and more involved as one considers higher order terms. Cheng and Batra [3] have also used the method of asymptotic expansion to study the 3D thermoelastic deformations of a functionally graded elliptic plate. Tanaka et al. [4] designed property profiles for functionally graded materials to reduce the thermal stresses. Reddy [5] has presented solutions for rectangular plates based on the third-order shear deformation plate theory. Reiter and Dvorak [6, 7] performed detailed finite element studies of discrete models containing simulated skeletal and particulate microstructures and compared results with those computed from homogenized models in which effective properties were derived by the Mori-Tanaka and the self-consistent methods. Cheng and Batra [8] have related the deflections of a simply supported functionally graded polygonal plate given by the first-order shear deformation theory (FSDT) and a third-order shear deformation theory (TSDT) to that of an equivalent homogeneous Kirchhoff plate.