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Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law

Published online by Cambridge University Press:  27 March 2008

Guy Bayada ,
Jalila Sabil  and
Taoufik Sassi
Guy Bayada
Affiliation:
INSA-LYON, CNRS UMR 5208, UMR 5514 Bâtiment Léonard de Vinci, 21 Av. J. Capelle, 69621 Villeurbanne Cedex, France. [email protected]
Jalila Sabil
Affiliation:
Université Henri Poincaré, UFR STMP, Faculté des Sciences et Techniques, Laboratoire LEMTA B.P. 239, 54506 Vandœuvre-les-Nancy Cedex, France. [email protected]
Taoufik Sassi
Affiliation:
Laboratoire de Mathématiques Nicolas Oresme, LMNO CNRS UMR 6139, Université de Caen, Bd. Maréchal Juin, 14032 Caen Cedex, France. [email protected]
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Abstract

In this paper, the convergence of a Neumann-Dirichlet algorithm to approximateCoulomb's contact problem between two elastic bodies is proved in a continuous setting. In this algorithm, the natural interface between the two bodies is retained as a decomposition zone.

Keywords

Domain decomposition methodscontact problemsconvergence.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 2 , March 2008 , pp. 243 - 262
Copyright
© EDP Sciences, SMAI, 2008

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References

Alart, P., Barboteu, M., Le Tallec, P. and Vidrascu, M., Méthode de Schwarz additive avec solveur grossier pour problèmes non symétriques. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 399–404. CrossRef
Baillet, L. and Sassi, T., Simulations numériques de différentes méthodes d'éléments finis pour les problèmes contact avec frottement. C. R. Acad. Sci. Paris Sér. II B 331 (2003) 789–796.
Baillet, L. and Sassi, T., Mixed finite element method for the Signorini problem with friction. Numer. Methods Partial Differential Equations 22 (2006) 1489–1508. CrossRef
Bayada, G., Sabil, J. and Sassi, T., Algorithme de Neumann-Dirichlet pour des problèmes de contact unilatéral: résultat de convergence. C. R. Math. Acad. Sci. Paris 335 (2002) 381–386. CrossRef
Chandhary, A.B. and Bathe, K.J., A solution method for static and dynamic analysis of three-dimensional contact problems with friction. Comput. Struc. 24 (1986) 855–873. CrossRef
Christensen, P.W., Klarbring, A., Pang, J.S. and Strömberg, N., Formulation and comparison of algorithms for frictional contact problems. Internat. J. Numer. Methods Engrg. 42 (1998) 145–173. 3.0.CO;2-L>CrossRef
G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique, Travaux et Recherches Mathématiques 21. Dunod, Paris (1972).
Eck, C. and Wohlmuth, B., Convergence of a contact-Neumann iteration for the solution of two-body contact problems. Math. Models Methods Appl. Sci. 13 (2003) 1103–1118. CrossRef
Farhat, C. and Roux, F.X., Implicit parallel processing in structural mechanics. Computational Mechanics Advances 1 (1994) 1–124.
R. Glowinski, J.-L. Lions and R. Trémolières, Numerical analysis of variational inequalities, Studies in Mathematics and its Applications 8. North-Holland Publishing Co., Amsterdam (1981). Translated from the French.
Haslinger, J., Dostál, Z. and Kučera, R., On a splitting type algorithm for the numerical realization of contact problems with Coulomb friction. Comput. Methods Appl. Mech. Engrg. 191 (2002) 2261–2281. CrossRef
N. Kikuchi and J.T. Oden, Contact problems in elasticity: a study of variational inequalities and finite element methods, SIAM Studies in Applied Mathematics 8. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1988).
Kornhuber, R. and Krause, R., Adaptive multigrid methods for Signorini's problem in linear elasticity. Comput. Vis. Sci. 4 (2001) 9–20. CrossRef
R.H. Krause, Monotone multigrid methods for Signorini's problem with friction. Ph.D. thesis, University of Berlin, Germany (2001).
Krause, R.H. and Wohlmuth, B.I., Nonconforming domain decomposition techniques for linear elasticity. East-West J. Numer. Math. 8 (2000) 177–206.
Krause, R.H. and Wohlmuth, B.I., Dirichlet-Neumann, A type algorithm for contact problems with friction. Comput. Vis. Sci. 5 (2002) 139–148. CrossRef
Le Tallec, P., Domain decomposition methods in computational mechanics. Comput. Mech. Adv. 1 (1994) 121–220.
L. Lusternik and V. Sobolev, Précis d'analyse fonctionnelle. MIR, Moscow (1989).
B.F. Smith, P.E. Bjørstad and W.D. Gropp, Domain decomposition, Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, Cambridge (1996).
Zavarise, G. and Wriggers, P., A superlinear convergent augmented Lagrangian procedure for contact problems. Engrg. Comput. 16 (1999) 88–119. CrossRef