Periodical contact problems for a half-space involving frictional heating

A periodical system of rigid parabolic punches moving steadily over the surface of a half-space is considered. Frictional shear tractions are developed with the heat generation along the interface. It is assumed that the surfaces of the punches are insulated and that the half-space is a thermal conductor. The problem is formulated in terms of two governing integral equations with unknown pressure and temperature at the interface. These equations are solved numerically. The effect of thermal distortion on the temperature profile under the punches and size of the contact region is investigated.