Solution of the contact problem for a pin-loaded plate

The problem of tension on an elastic rectangular plate with a circular hole in which, with a small clearance c, a rigid immovable pin of circular cross section is inserted without friction is solved via the finite element method. Two boundary conditions variants are imposed on the hole contour Γ, one of which is formulated for projections of displacements and forces onto the normal and the tangent to Γ and the other by linearizing the impenetration condition. The second variant yields a more precise solution in the sense that it yields a smaller strain energy of the plate, maximum stresses, and length l of the contact region. With the growth of c, the maximum l decreases almost linearly with c in the second variant, while it is constant in the first.