Research Article Open Access

Mixed Formulation for a Signorini Problem

Tedjani Hadj Ammar1 and Benabderrahmane Benyattou2
  • 1 Ouargla University, Algeria
  • 2 Laghouat University, Algeria

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.

Journal of Mathematics and Statistics
Volume 8 No. 2, 2012, 216-220

DOI: https://doi.org/10.3844/jmssp.2012.216.220

Submitted On: 7 February 2012 Published On: 23 April 2012

How to Cite: Ammar, T. H. & Benyattou, B. (2012). Mixed Formulation for a Signorini Problem. Journal of Mathematics and Statistics, 8(2), 216-220. https://doi.org/10.3844/jmssp.2012.216.220

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Keywords

  • Signorini conditions
  • unilateral contact
  • mixed formulation
  • variational inequality