Analytical and numerical solutions of pressurized thick-walled FGM spheres

The elastic analysis of thick-walled spheres made of functionally graded materials (FGMs) is considered to be one of the most important areas in many engineering designs. This paper presents the stresses and displacement fields in an FGM thick-walled sphere under constant interior and exterior pressure. The investigation was carried out using analytical and numerical methods. Exact and finite element (FE) models of the pressurized spherical vessel were created, assuming and implementing continuous changing of Young modulus along the radial direction. It is considered that the elastic modulus of the FGMs varies with thickness according to the nonlinear generalized formula. For a pressurized FGM sphere, the analytical solutions for displacement and stress distribution were developed and demonstrated in the radial direction. Finally, the analytical results are compared to the results from the FE analysis.