Periodic Contact Problems for a Wedge with Friction Forces

Periodic contact problems for a three-dimensional elastic wedge (a dihedral angle, a half-space and a quarter of space are particular cases), taking into account the Coulomb friction forces in unknown contact areas are considered. One face of the wedge is rigidly fixed, and the other face interacts with an infinite rectilinear chain of identical rigid dies, the axis of the chain is parallel to the edge of the wedge. Friction forces perpendicular or parallel to the edge of the wedge are taken into account. Integral equations are derived in which the series generated by the Cerruti components of the contribution of friction forces are summed exactly. Problems are solved using the method of nonlinear integral equations, which makes it possible to simultaneously determine the contact area and contact pressures. The mechanical characteristics are calculated, the transition from a discrete to a continuous contact area of infinite length is studied.