Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Local uniqueness and continuation of solutions for the discrete Coulomb friction problem in elastostatics


Authors: Patrick Hild and Yves Renard
Journal: Quart. Appl. Math. 63 (2005), 553-573
MSC (2000): Primary 74M10, 74G20; Secondary 35A07, 35J85, 65N30.
DOI: https://doi.org/10.1090/S0033-569X-05-00974-0
Published electronically: July 11, 2005
MathSciNet review: 2169034
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Abstract | References | Similar Articles | Additional Information

Abstract: This work is concerned with the frictional contact problem governed by the Signorini contact model and the Coulomb friction law in static linear elasticity. We consider a general finite-dimensional setting and we study local uniqueness and smooth or nonsmooth continuation of solutions by using a generalized version of the implicit function theorem involving Clarke's gradient. We show that for any contact status there exists an eigenvalue problem and that the solutions are locally unique if the friction coefficient is not an eigenvalue. Finally we illustrate our general results with a simple example in which the bifurcation diagrams are exhibited and discussed.


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Additional Information

Patrick Hild
Affiliation: Laboratoire de Mathématiques de Besançon, CNRS UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France
Email: hild@math.univ-fcomte.fr

Yves Renard
Affiliation: MIP, CNRS UMR 5640, INSAT, Complexe scientifique de Rangueil, 31077 Toulouse, France
Email: renard@insa-toulouse.fr

DOI: https://doi.org/10.1090/S0033-569X-05-00974-0
Keywords: Coulomb friction, unilateral contact, local uniqueness, bifurcation, Clarke's gradient.
Received by editor(s): January 13, 2005
Published electronically: July 11, 2005
Dedicated: We dedicate this article to the memory of Jean-Claude Paumier.
Article copyright: © Copyright 2005 Brown University


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