Optimization of Functionally Graded Materials in the Slab Symmetrically Surface Heated Using Transient Analytical Solution

Abstract

Functionally graded materials (FGMs) have been introduced to significantly reduce the temperature and thermal stresses on structures at severe thermal loading. Design and development of FGMs as the heat treatable and energy-absorbing materials for high-temperature and thermal protection systems requires understanding of exact temperature and thermal stress distribution, in order to optimize their resistance to failure. In this study, transient temperature and associated thermal stresses in a functionally graded slab symmetrically heated on both sides are determined by separation of the variables scheme. This method is applied to the heat conduction equation in terms of heat flux for obtaining the temperature profile. Further, the method of the thermo-elastic problem solution can be readily extended for non-homogenous problems with arbitrary temperature profile. Exponential space dependent function of physical properties is considered. Role of heat and stress wave propagation speeds on the problem is illustrated. Effect of the inhomogeneity parameter and the Fourier number on the distribution of temperature, displacement, and stress is discussed. Moreover, determination of the dynamical thermal stresses magnitude due to end effects is investigated. Based on findings, the optimal designs of FGMs are shown for stress reduction and improving heat treatable behavior.