Three-Dimensional Semi-Analytical Thermo-Elasticity Solution for a Functionally Graded Solid and an Annular Circular Plate

Three-dimensional analysis of a functionally graded (FG) solid and an annular circular plate subjected to thermo-mechanical load with various boundary conditions are carried out in this paper. At first, the temperature gradient can be derived by solving the heat conduction equation exactly and then by applying the differential quadrature method (DQM) along the radial direction and by using the state-space method in the thickness direction to the governing state equations results in a system of first-order differential equations, which can be solved analytically. The thermo-elastic constants of the plate are assumed to vary exponentially through the thickness, and the Poisson ratio is held to be constant. To verify the accuracy of the present work, a comparison is made with previously published results. The effects of temperature change, mechanical load, gradient index, edges conditions and thickness to radial length ratio on the behavior of the plate are examined.