One-Dimensional Transient Heat Conduction and Associated Thermal Stress Problems of a Plate with Nonhomogeneous Material Properties.

Abstract

The one-dimensional transient heat conduction problem of a nonhomogeneous plate with arbitrarily distributed and continuously varied material properties, such as FGM (functionally gradient materials), is treated theoretically in this paper. For such a nonhomogeneous plate, the heat conduction equation becomes nonlinear, therefore the theoretical treatment is very difficult and the exact solution is almost impossible to obtain. Introducing the analytical procedure of the laminated plate model, and thereafter, taking into account the constraint that the number of lamine becomes sufficiently large, the analytical temperature solution for such a completely nonhomogeneous plate is derived. Furthermore, the associated thermal stress components for an infinitely long non-homogeneous plate are formulated under the mechanical condition of being traction free. As a numerical example, the plate composed of alumina and aluminum alloy is considered. The numerical results for temperature change and the associated thermal stress distributions are shown in the figures, and the effects of nonhomogeneity (change of the volume fraction of two different materials)on thermoelastic behaviors are briefly examined.