Quasistatic periodic contact problem for a viscoelastic layer, a cylinder, and a space with a cylindrical cavity

This paper considers the contact problem of interaction of a rigid die, a rigid band, and a rigid insert with a viscoelastic layer, a viscoelastic cylinder, and viscoelastic space with a cylindrical cavity, respectively. It is assumed that the die, band, and insert move at a constant velocity along the boundaries of the viscoelastic bodies. In the first stage, the displacement of the boundaries of the above-mentioned bodies is determined as a function of the applied normal loads ignoring friction in the contact area. In the second stage, integral equations are derived to determine contact pressure in the contact problems. In the third stage, approximate solutions of the integral equations are constructed using a modified Multhopp–Kalandia method.