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.
Mots clés : domain decomposition methods, contact problems, convergence
@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: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {243--262}, publisher = {EDP-Sciences}, volume = {42}, number = {2}, year = {2008}, doi = {10.1051/m2an:2008003}, mrnumber = {2405147}, zbl = {1133.74042}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2008003/} }
TY - JOUR AU - Bayada, Guy AU - Sabil, Jalila AU - Sassi, Taoufik TI - Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 243 EP - 262 VL - 42 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008003/ DO - 10.1051/m2an:2008003 LA - en ID - M2AN_2008__42_2_243_0 ER -
%0 Journal Article %A Bayada, Guy %A Sabil, Jalila %A Sassi, Taoufik %T Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 243-262 %V 42 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008003/ %R 10.1051/m2an:2008003 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 2, pp. 243-262. doi : 10.1051/m2an:2008003. http://www.numdam.org/articles/10.1051/m2an:2008003/
[1] Méthode de Schwarz additive avec solveur grossier pour problèmes non symétriques. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 399-404. | MR | Zbl
, , and ,[2] 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
and ,[3] Mixed finite element method for the Signorini problem with friction. Numer. Methods Partial Differential Equations 22 (2006) 1489-1508. | MR | Zbl
and ,[4] Algorithme de Neumann-Dirichlet pour des problèmes de contact unilatéral: résultat de convergence. C. R. Math. Acad. Sci. Paris 335 (2002) 381-386. | MR | Zbl
, and ,[5] A solution method for static and dynamic analysis of three-dimensional contact problems with friction. Comput. Struc. 24 (1986) 855-873. | Zbl
and ,[6] Formulation and comparison of algorithms for frictional contact problems. Internat. J. Numer. Methods Engrg. 42 (1998) 145-173. | MR | Zbl
, , and ,[7] Les inéquations en mécanique et en physique, Travaux et Recherches Mathématiques 21. Dunod, Paris (1972). | MR | Zbl
and ,[8] Convergence of a contact-Neumann iteration for the solution of two-body contact problems. Math. Models Methods Appl. Sci. 13 (2003) 1103-1118. | MR | Zbl
and ,[9] Implicit parallel processing in structural mechanics. Computational Mechanics Advances 1 (1994) 1-124. | MR | Zbl
and ,[10] Numerical analysis of variational inequalities, Studies in Mathematics and its Applications 8. North-Holland Publishing Co., Amsterdam (1981). Translated from the French. | MR | Zbl
, and ,[11] 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 | Zbl
, and ,[12] 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 | Zbl
and ,[13] Adaptive multigrid methods for Signorini's problem in linear elasticity. Comput. Vis. Sci. 4 (2001) 9-20. | MR | Zbl
and ,[14] Monotone multigrid methods for Signorini's problem with friction. Ph.D. thesis, University of Berlin, Germany (2001).
,[15] Nonconforming domain decomposition techniques for linear elasticity. East-West J. Numer. Math. 8 (2000) 177-206. | MR | Zbl
and ,[16] A Dirichlet-Neumann type algorithm for contact problems with friction. Comput. Vis. Sci. 5 (2002) 139-148. | MR | Zbl
and ,[17] Domain decomposition methods in computational mechanics. Comput. Mech. Adv. 1 (1994) 121-220. | MR | Zbl
,[18] Précis d'analyse fonctionnelle. MIR, Moscow (1989).
and ,[19] Domain decomposition, Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, Cambridge (1996). | MR | Zbl
, and ,[20] A superlinear convergent augmented Lagrangian procedure for contact problems. Engrg. Comput. 16 (1999) 88-119. | Zbl
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