Stress analysis of rotating thick-walled nonhomogeneous sphere under thermomechanical loadings

Abstract

In this work, a rotating thick-walled spherical vessel made of nonhomogeneous materials subjected to internal and/or external pressure under thermal loading was analyzed within the context of three-dimensional elasticity theory. An analytical formulation was established for computing the displacement and stress fields. It has been assumed that the mechanical and thermal properties are varying through thickness of the functionally graded material (FGM) according to a power-law nonlinear expression, while Poisson's ratio is considered as constant. Based on equilibrium equation, Hooke's law, stress-strain relationship in the spheres and other theories from mechanics a second-order ordinary differential equation well-known as Navier equation is obtained that represents the thermoelastic field in hollow FGM sphere. Navier equation derived from the mechanical equilibrium equation was solved to obtain the exact solution of the displacement and stress distributions. Different results of thermoelastic field are presented across the thickness of the sphere. The analysis of the different results reveals that stress and strain in the FGM sphere are significantly depend upon variation made in temperature profile, rotation and inhomogeneity parameter on the thermoelastic field. Thus, the inhomogeneity in material properties can be exploited to optimize the distribution of displacement and stress fields.