The finite and semi-infinite tilted, flat but rounded punch

The problem of a tilted flat punch having a rounded edge, and with a sufficiently large angle of tilt for contact to be lost along the flat face, is considered. A complete solution to the contact problem, within the context of an elastic half-plane formulation, is derived, including the effects of a shearing force either sufficient or insufficient to cause sliding. The solution is then modified by making the punch semi-infinite in extent, so as to render it effective as an asymptote useful in both quantifying fretting damage, and in improving the precision of approximate numerical solutions. The asymptote is then applied to an example problem.