Reissner-Sagoci problem for a non-homogeneous half-space with surface constraint

Abstract

This paper deals with the problem of twisting of a non-homogeneous, isotropic, half-space by rotating a circular part of its boundary surface (0⩽r⩽a, z = 0) through a given angle. A ring (a b, z = 0) is rigidly clamped. The shear modulus μ is assumed to vary with the cylindrical coordinates r, z by the power law (μ = μα,β r α z β). Such a dependence is of practical interest in the context of Soil Mechanics. The problem leads to a Fredholm integral equation of the second kind which is solved numerically, giving an evaluation of the influence of non-homogeneity on the torque at the surface and the stress intensity factor. The homogeneous case studied in [16] is recovered. Expressions for some quantities of physical importance such as the torque applied at the surface and stress intensity factor are obtained. It appears from our investigation that the influence of clamping dies out with increasing α and β. Quantitative evaluations are given and some curves for the relative increase, due to clamping, in the torque and in the stress intensity factor are presented.