Torsion of a Rigid Smooth Elliptic Insert in an Infinite Elastic Plane

A solution is presented for the non-Hertzian contact stress problem developed during torsion of a smooth rigid elliptic insert in an infinite, linearly elastic plane. The problem is reduced to a singular integro-differential equation which is solved numerically. Results are presented for the contact zones, and for the normal and tangential stresses at the plane-insert interface. The contact region is independent of the magnitude of the applied moment, but depends strongly on the shape of the ellipse, and is weakly dependent on Poisson’s ratio of the plane. Results are also given for the reduction in torsional stiffness between a fully bonded insert and the present solution, (i.e., a completely failed bond).