On some results concerning the reciprocal formulation for the Signorini's problem

Abstract

In the paper the relationship between two formulations of the Signorini's Problem is investigated. The first one is based on the minimum-potential energy theorem, and is expressed in terms of displacements. In the second one, the so called “reciprocal formulation”, the unknown function appears to be a contact pressure. Based on Ekeland-Temam's results concerning the duality theory the equivalance of both formulations is shown. For the sake of some numerical experience the simple example of a beam supported on elastic supports is considered. Numerical results fully confirm the theoretical investigations.