Thermo-mechanical analysis of functionally graded thick spheres with linearly time-dependent temperature

An analysis of the unsteady-state thermo-mechanical problem of functionally graded thick-walled spheres is presented in this paper. the material properties, except poisson's ratio, are assumed to be an arbitrary function of radial direction. considering linearly increasing boundary temperature and employing laplace transform techniques, the time-dependent temperature is obtained. in a special case, by assuming the material properties to follow a power-law function, the navier equation is solved for an arbitrary time. this led to radial displacement, radial stress, and hoop stress as a function of radial direction. in the numerical results calculated by fem software, abaqus is compared to the analytical results. the present results agree well with existing analytical results.