Boundary variational formulations and numerical solution techniques for unilateral contact problems

In this paper the numerical solution of the elastic frictionless contact problem is obtained by means of boundary discretization techniques. Variational formulations in terms of boundary tractions are given in presence of both bilateral and unilateral constraints. The discretization of the boundary functional is examined from the point of view of the theory of approximation and it is proved that the coerciveness (but not the symmetry) of the continuum problem is preserved when standard B.E.Ms are employed. As a consequence, the contact problem can be cast as a L.C.P. having, as coefficient matrix, a generally non symmetric P matrix. A simple, but meaningful example is discussed in some detail.