In this paper, the convergence of a Neumann-Dirichlet algorithm to approximate Coulomb'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.
@article{M2AN_2008__42_2_243_0,
author = {Bayada, Guy and Sabil, Jalila and Sassi, Taoufik},
title = {Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {42},
year = {2008},
pages = {243-262},
doi = {10.1051/m2an:2008003},
mrnumber = {2405147},
zbl = {1133.74042},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2008__42_2_243_0}
}
Bayada, Guy; Sabil, Jalila; Sassi, Taoufik. Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008) pp. 243-262. doi : 10.1051/m2an:2008003. http://gdmltest.u-ga.fr/item/M2AN_2008__42_2_243_0/
[1] , , and , Méthode de Schwarz additive avec solveur grossier pour problèmes non symétriques. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 399-404. | MR 1784922 | Zbl 0961.65108
[2] and , 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. | Zbl 1134.74401
[3] and , Mixed finite element method for the Signorini problem with friction. Numer. Methods Partial Differential Equations 22 (2006) 1489-1508. | MR 2257645 | Zbl 1105.74041
[4] , and , Algorithme de Neumann-Dirichlet pour des problèmes de contact unilatéral: résultat de convergence. C. R. Math. Acad. Sci. Paris 335 (2002) 381-386. | MR 1931521 | Zbl 1044.74031
[5] and , A solution method for static and dynamic analysis of three-dimensional contact problems with friction. Comput. Struc. 24 (1986) 855-873. | Zbl 0604.73116
[6] , , and , Formulation and comparison of algorithms for frictional contact problems. Internat. J. Numer. Methods Engrg. 42 (1998) 145-173. | MR 1618014 | Zbl 0917.73063
[7] and , Les inéquations en mécanique et en physique, Travaux et Recherches Mathématiques 21. Dunod, Paris (1972). | MR 464857 | Zbl 0298.73001
[8] and , Convergence of a contact-Neumann iteration for the solution of two-body contact problems. Math. Models Methods Appl. Sci. 13 (2003) 1103-1118. | MR 1998817 | Zbl 1053.74044
[9] and , Implicit parallel processing in structural mechanics. Computational Mechanics Advances 1 (1994) 1-124. | MR 1280753 | Zbl 0805.73062
[10] , and , Numerical analysis of variational inequalities, Studies in Mathematics and its Applications 8. North-Holland Publishing Co., Amsterdam (1981). Translated from the French. | MR 635927 | Zbl 0463.65046
[11] , and , On a splitting type algorithm for the numerical realization of contact problems with Coulomb friction. Comput. Methods Appl. Mech. Engrg. 191 (2002) 2261-2281. | MR 1903144 | Zbl 1131.74344
[12] and , 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). | MR 961258 | Zbl 0685.73002
[13] and , Adaptive multigrid methods for Signorini's problem in linear elasticity. Comput. Vis. Sci. 4 (2001) 9-20. | MR 1936249 | Zbl 1051.74045
[14] , Monotone multigrid methods for Signorini's problem with friction. Ph.D. thesis, University of Berlin, Germany (2001).
[15] and , Nonconforming domain decomposition techniques for linear elasticity. East-West J. Numer. Math. 8 (2000) 177-206. | MR 1807260 | Zbl 1050.74046
[16] and , A Dirichlet-Neumann type algorithm for contact problems with friction. Comput. Vis. Sci. 5 (2002) 139-148. | MR 1950338 | Zbl 1099.74536
[17] , Domain decomposition methods in computational mechanics. Comput. Mech. Adv. 1 (1994) 121-220. | MR 1263805 | Zbl 0802.73079
[18] and , Précis d'analyse fonctionnelle. MIR, Moscow (1989).
[19] , and , Domain decomposition, Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, Cambridge (1996). | MR 1410757 | Zbl 0857.65126
[20] and , A superlinear convergent augmented Lagrangian procedure for contact problems. Engrg. Comput. 16 (1999) 88-119. | Zbl 0947.74079