Compliance Under a Small Torsional Couple of an Elastic Plate Pressed Between Two Identical Elastic Spheres

Abstract

The object of the analysis is to calculate the surface shear traction and the torsional compliance of an elastic system comprising a plate pressed between identical spheres. The problem is formulated in terms of an integral equation which is solved numerically. The parameters are the plate thickness and ratio of shear moduli. Solutions are obtained for all except extremely thin plates, for which a previous approximate solution is shown to be valid. The contact stress distribution is always close to the well-known distribution appropriate to the half-space, with a singularity at the edge of the contact circle, unless the plate is simultaneously thin and flexible. A thin flexible plate confines the singularity to a very small region at the edge of the contact circle, the stress elsewhere being essentially proportional to radius. The torsional compliance predicted by the analysis agrees well with experiment.