The axisymmetric contact problem of thermoelasticity in the presence of an internal heat source

The problem investigated in the article concerns that of indentation of a semi-infinite elastic solid by a circular cylinder with a flat base on the assumption that there are heat sources distributed in the interior of the solid. With the thermo-mechanical coupling as well as the frictional forces between the punch and the solid disregarded, the problem is reduced, by means of potential methods, to an integral equation. Closed-form solution to the integral equation is deduced in terms of the intensity of the heat sources. This permits the contact stresses and the total indenting force to be expressed in explicit form in terms of the heat source function. The case of a point heat source is worked out in details. In particular, it is found that the action of the concentrated heat source becomes most pronounced when it is located on the axis of symmetry at a distance of approximately half of the radius of the contact patch from the origin.