Mixed Formulation for a Signorini Problem
P. · Journal of Mathematics and Statistics · 2012
Problem statement: This study deals with the study of a Signorini Problem (SP) of unilateral contact between two a linear or non linear elastic bodies.Approach: We present two variational formulations noted P 1 , P 2 , of the considered problem, where P 1 depends on the displacement field and P 2 depends on the stress field.In the linear case, under assumptions, then the considered problem was equivalent to a mixed variational formulation problem, where the unknowns are the displacement field and the normal constraint stress on the contact area.Results: Problems P 1 and P 2 were formally equivalent to the Signorini Problem (SP) and using Lions-Stampachia Theorem, we shown the existence and uniqueness result.Conclusion: The Signorini problem (PS) has a unique variational solution.