Finite Difference Solution to Thermoelastic Field in a Thin Circular FGM Disk with a Concentric Hole

This study pays attention to the analysis of thermoelastic filed in a thin circular functionally graded material (FGM) disk with a concentric hole subjected to thermal loads. The material distribution in the disk is assumed to vary in the radial direction only. The mechanical and thermal properties of the FGM disk are simulated by the power function and exponential variation with the radius of the disk. As the range of variation of Poisson's ratio is small and its effect on the thermoelastic characteristics is negligible, it is reasonably assumed to be constant throughout the disk. Based on the two dimensional thermoelastic theories, the problem is reduced to the solution of a second order differential equation which is converted to a system of algebraic linear equations with the help of finite difference discretization. Solution of these equations is obtained by Gauss elimination method for an Al2O3/Al FGM disk. Numerical results of different components of stress and displacement are presented and analyzed. The analysis of the results reveals that the thermoelastic characteristics of an FGM disk are substantially dependant on material distribution as well as difference of temperatures at the inner and outer surfaces of the disk.