Thermal and mechanical stresses in thick spheres with an extended FGM model

Abstract

In this study, an exact solution for the one-dimensional steady-state thermal and mechanical stresses in a hollow thick sphere made of functionally graded material with a new graded model is presented. The temperature distribution is assumed to be a function of radius. The material properties are graded along the radial direction according to exponential functions of radial direction. The advantage of this model, compared to the other models (linear or power law models), is in satisfaction of the material boundary conditions for several types of material variation profiles. Employing the model, the energy and Navier equations are solved using the generalized Bessel function and the Lagrange method. In addition, a method for solving the governing equations in spherical coordinates is presented. The analytical solution of the heat conduction equation and the Navier equation lead to the temperature profile, radial displacement, radial stress, and hoop stress as a function of radial direction.