An old elasticity problem in a unilateral setting

Abstract

A limiting case of the Michell problem involving an elastic wedge is the unbounded solid with a semi-infinite cut, the tip of which is subjected to a concentrated force. For the limiting case, the classical solution leads to overlapping of material whenever the component of the force along the axis of symmetry is directed away from the cut, and the problem must be solved anew using unilateral boundary conditions. The required mathematics is simple, and the subject is suitable for classroom discussion. Two examples are solved explicitly, and additional exercise problems are suggested.