Stress Amplification/Shielding Phenomena of Spherically Anisotropic and Radially Inhomogeneous Linear Elastic Hollow Spheres

Abstract

Exact solutions of radially symmetric deformation of a spherically anisotropic and radially inhomogeneous linear elastic hollow sphere subjected to uniform radial tractions on the surfaces are derived. The power-law function is assumed to represent the radially inhomogeneity. Stress amplification/shielding phenomena are fully investigated and the benefits of using functionally graded materials are indicated. For a solid sphere under external uniform loadings, the conditions in which infinite stresses occur at the centre of the sphere regardless of applied traction magnitudes are specified. Also, circumferential stresses might have opposite sign of the applied loadings. Cavitation and blackhole phenomena at the centre of the sphere are also discussed.