Journal of Mathematics and Statistics

Mixed Formulation for a Signorini Problem

Tedjani Hadj Ammar and Benabderrahmane Benyattou

DOI : 10.3844/jmssp.2012.216.220

Journal of Mathematics and Statistics

Volume 8, Issue 2

Pages 216-220

Abstract

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 P1, P2, of the considered problem, where P1 depends on the displacement field and P2 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 P1 and P2 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.

Copyright

© 2012 Tedjani Hadj Ammar and Benabderrahmane Benyattou. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.