Axial displacement dislocations for the hollow cone and the hollow sphere

Simple solutions in closed form are given for the dislocational states of stress in a hollow cone (Fig. 3) or a hollow sphere (Fig. 5) induced by making an axial cut, and imposing a rigid-body displacement of one face of the cut relative to the other, in the axial direction. The problems are solved by adaptations of the Saint-Venant torsion theory, and of J. H. Michell’s theory of torsion of non-uniform shafts.