Theoretical Approach of Optimum Design for a Plate of Functionally Gradient Materials under Thermal Loading

Abstract

A Functionally Gradient Material (FGM) is one of the most advanced composite materials, composed of light metal and engineering ceramics. These materials are now developed for the purpose of general use as structural elements for the extremely high temperature environments. In the present article, transient heat conduction problems and the associated thermal stress problems of nonhomogeneous material such as FGM are treated theoretically. As one of the analytical models, a thick plate with infinitely long extent and composed of nonhomogeneous material is considered. Thereafter, transient heat conduction problems for such materials are solved using the laminated composite method, and the temperature solution is given by the integral form of arbitrary non-homogeneous material properities. And then, the optimization problem of the abovementioned nonhomogeneous plate is discussed. The optimum material composition for the purpose of reducing the thermal stress distribution is given by numerical results.