Local Sliding of Elastic Bodies in the Presence of Gas in the Intercontact Gap

We study the problem of contact of two elastic bodies made of the same material one of which has a gently sloping hollow with regard for gas pressure in the intercontact gap and the local friction sliding of the surfaces near the ends of the gap. The problem is reduced to a system of two singular integral equations for the height of the intercontact gap and the relative shift of the surfaces near the gap and in the sliding regions. The first of these equations is solved analytically, whereas the second equation is solved numerically. We also analyze the dependences of the length of sliding regions, contact stresses, and the relative shift of the surfaces on the applied loads.