A hollow sphere of inner radius b and outer radius a is subject to normal pressures on its inner and outer surfaces...

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A hollow sphere of inner radius b and outer radius a is subject to normal pressures on its inner and outer surfaces. The sphere is made up of an isotropic material, the displacements and stress fields are spherically symmetric. The only non-vanishing displacement component is the radial displacement ur, and is a function of r only. Based on this we can assume the following strains. lu lur dr The only non-vanishing stress components are the radial stress σ, and the circumferential stresses σθ-g. These stresses are goverened by the following differential equation for equilibrium. =0. dr Given the following constitutive equations in spherical coordinates. Determine the following (a) Derive the differential equation for σ (b) Solve the differential equation for σ (c) Use your solution for σ, to determine σ6- (d) Use the boundary conditions given to derive expressions for σ, and σθ in terms of a, b, r, Po and Pi (Group equations in terms of Po and Pi).

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