Analysis of a Rocking and Walking Punch—Part II: General Numerical Solution Using Quadratic Programming

This paper pursues a numerical approach to the solution of the contact problem of a rigid punch on an incompressible half-plane, subjected to a shearing force together with a normal force which may be offset from the centerline of the punch. A piecewise-linear representation of the shear tractions is employed and quadratic programming techniques are used to solve the problem. This method enables an arbitrary load history to be followed. Results are presented which show excellent agreement with other solutions to the special cases of monotonic and steady-state cyclic loading. It is shown that the traction distribution reaches a steady-state cycle after only a few cycles of loading. The existence of an interesting stick-slip regime, where a central zone of slip is bordered by two stick regions is highlighted.