Contact integration of a rigid die with elastic layer under friction heat formation

The mathematical statement and solution of the static thermoelasticity problem for a rigid punch on the surface of elastic layer pinched on the elastic layer base are given. In this problem the friction heat generation under Amonton's law is taken into account. With the assumption that the punch is an insulator, the problem is reduced to the system of two integral equations for contact pressure and function that is a linear combination of the temperature and the heat flow on a contact surface. The numerical algorithm of the solution of this system is presented. The effect of the diminishing of contact area which is caused by the stationary thermal heat generation during interaction of the layer and the punch with parabolic and semicylindrical base is investigated.