Analytical and numerical analysis of an internally and/or externally pressurized thick-walled sphere made of radially nonuniform material

In this work, a thick-walled spherical vessel made of nonhomogeneous materials subjected to internal and/or external pressure was analyzed within the context of three-dimensional elasticity theory. A closed-form analytical solution was obtained for computing the displacement and stress fields. It has been assumed that the elastic stiffness is varying through thickness of the functionally graded material according to a nonlinear general expression, while Poisson’s ratio is considered as constant. In order to check the relevance of the analytical solution, a finite element model of the pressurized vessel were constructed, taking into account variations in Young's modulus. Very good agreement has been found between the numerical results and the predictions of the analytical solution, which confirms the accuracy of our model. Thus, the inhomogeneity in material properties can be exploited to optimize the distribution of displacement and stress fields.