The Reissner–Sagoci Problem for a Non-homogeneous Half-space with a Surface Constraint

Abstract

This paper deals with the problem of twisting 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 < r < b, z = 0) outside the circle is stress-free and the remaining part (r > b, z = 0) is rigidly clamped. The shear modulus is assumed to vary with the cylindrical coordinates, r, z by the relation μ(z) = μ₁(c + z)^α, c ≠ 0 where μ₁, c and α are real constants. Expressions for some quantities of physical importance, such as torque applied at the surface of the disk and stress intensity factors, are obtained. The effects of non-homogeneity on torque and stress intensity factor are illustrated graphically.