Stress distribution in a rotating elastic functionally graded material hollow sphere with spherical isotropy

Abstract

The stress distribution in a rotating, spherically isotropic, functionally graded material (FGM) spherical shell that has its elastic constants and mass density as functions of the radial coordinate is exactly investigated in the paper. Three displacement functions are employed to simplify the basic equations of equilibrium for a spherically isotropic, radially inhomogeneous elastic medium. By expanding the displacement functions in terms of spherical harmonics, the basic equations are finally turned into an uncoupled second-order ordinary differential equation and a coupled system of two such equations. Exact analysis of a steadily rotating spherical shell with the material constants being power functions of the radial coordinate is carried out and a numerical example is presented.