Solution of a contact problem for a plate with a deformable insert

Contact problems with friction are solved for a rectangular plate with a circular hole into which a ring plate (insert) is placed with a small clearance. Two versions of contact boundary conditions are formulated. According to the proposed approximate formulation of the problem, the boundary conditions in both versions are satisfied not at the actual contact points but at specified pairs of points. Therefore, it is sufficient to determine attachment, slip, contact, and contact-free regions on just one of the contacting contours. The finite-element method and the Boussinesq principle are used to solve the problem. One of the versions of boundary conditions, compared to the other, gives smaller values for the strain energies of the plate and insert, the stress-concentration coefficient, and the lengths of attachment and contact regions.