Functionally graded hollow spheres under non-axisymmetric thermo-mechanical loads

An analytical method is developed to obtain the solution for the two-dimensional (r,θ)(r,θ) steady state thermal and mechanical stresses in a hollow thick sphere made of functionally graded material. The material properties are assumed to vary through the thickness according to the power law functions. The temperature profile is obtained solving the functionally graded energy equation. The Navier equations are solved analytically using the Legendre polynomials and the system of Euler differential equations. Temperature, displacement components and stresses distributions are obtained and plotted for different power law indices. The results are validated with the known data in literature.