Free Access
Math. Model. Nat. Phenom.
Volume 4, Number 1, 2009
Modelling and numerical methods in contact mechanics
Page(s) 1 - 20
Published online 27 January 2009
  1. J. Alberty, C. Carstensen, S. A. Funken, R. Klose. Matlab Implementation of the Finite Element Method in Elasticity. Berichtsreihe des Mathematischen Seminars Kiel, 00-21 (2000). [Google Scholar]
  2. D. N. Arnold, F. Brezzi, J. Douglas. PEERS: A new finite element for plane elasticity Japan J. Appl. Math., No. 1 (1984), 347–367. [Google Scholar]
  3. Z. Belhachmi, F. Ben Belgacem. Quadratic finite element for Signorini problem. Math. Comp., 72 (2003), No. 241, 83–104. [CrossRef] [MathSciNet] [Google Scholar]
  4. Z. Belhachmi, J.M. Sac-Epée, J. Sokolowski. Mixed finite element methods for a smooth domain formulation of a crack problem. SIAM J. Numer. Anal., 43 (2005), No. 3, 1295–1320. [CrossRef] [MathSciNet] [Google Scholar]
  5. F. Ben Belgacem. Numerical simulation of some variational inequalities arisen from unilateral contact problems by finite element method. Siam J. Numer. Anal, 37 (2000),No. 4, 1198–1216. [Google Scholar]
  6. F. Ben Belgacem, P. Hild, P. Laborde. Extension of the mortar finite element method to a variational inequality modelling unilateral contact. Math. Models Methods Appl. Sci., 9 (1999), No. 2, 287–303. [CrossRef] [MathSciNet] [Google Scholar]
  7. F. Ben Belgacem, Y. Renard. Hybrid finite element methods for the Signorini problem. Math. Comput., 72 (2003), No. 243, 1117–1145. [Google Scholar]
  8. C. Bernardi, V. Girault. A local regularization operator for triangular and quadrilateral finite elements. SIAM. J. Numer. Anal., 35 (1998), No. 5, 1893–1916. [Google Scholar]
  9. D. Braess, O. Klaas, R. Niekamp, E. Stein, F. Wobschal. Error Indicators For Mixed Finite Elements in 2-dimensional Linear Elasticity. Comput. Methods. Appl. Mech. Engrg., 127 (1995), No. 1-4, 345–356. [Google Scholar]
  10. F. Brezzi, J. Douglas Jr, L.D. Marini. Two families of mixed finite elements for second order elliptic problems. Numer. Math., 47 (1985), No. 2, 217–235. [CrossRef] [MathSciNet] [Google Scholar]
  11. F. Brezzi, M. Fortin. Mixed and hybrid finite element methods. Springer Verlag, New York, Springer Series in Computational Mathematics, 15, 1991. [Google Scholar]
  12. C. Carstensen, G. Dolzmann, S.A. Funken, D.S. Helm. Locking-free adaptive mixed finite element in linear elasticity. Comput. Methods. Appl.Mech. Engrg., 190 (2000), No. 13-14, 1701–1718. [CrossRef] [MathSciNet] [Google Scholar]
  13. P.G. Ciarlet. Basic Error Estimates for Elliptic Problems. In the Handbook of Numerical Analysis, Vol II, P.G. Ciarlet & J.-L. Lions eds, North-Holland, (1991), 17–351. [Google Scholar]
  14. P. Coorevits, P. Hild, K. Lhalouani, T. Sassi. Mixed finite element methods for unilateral problems: convergence analysis and numerical studies. Math. Comp., 71, (2001), No. 237, 1–25. [Google Scholar]
  15. G. Duvaut, J.-L. Lions. Les inéquations en mécanique et en physique. Dunod, 1972. [Google Scholar]
  16. V. Girault, P.-A. Raviart. Finite element methods for the Navier-Stokes equations, Theory and algorithms. Springer-Verlag 1986. [Google Scholar]
  17. R. Glowinski. Lectures on numerical methods for nonlinear variational problems. Springer, Berlin, 1980. [Google Scholar]
  18. J. Haslinger, I. Hlaváček. Contact between Elastic Bodies -2.Finite Element Analysis, Aplikace Matematiky, 26 (1981), 263–290. [Google Scholar]
  19. J. Haslinger, I. Hlaváček, J. Nečas. Numerical Methods for Unilateral Problems in Solid Mechanics, in the Handbook of Numerical Analysis, Vol IV, Part 2, P.G. Ciarlet & J.-L. Lions eds, North-Holland, 1996. [Google Scholar]
  20. F. Hecht, O. Pironneau. FreeFem++, [Google Scholar]
  21. P. Hild, Y. Renard. An error estimates for the Signorini problem with Coulomb friction approximated by finite elements. Siam J. Numer. Anal., 45 (2007), No. 5, 2012–2031. [Google Scholar]
  22. S. Hüeber, B.I. Wohlmuth. An optimal a priori error estimates for nonlinear multibody contact problems. SIAM J. Numer. Anal., 43 (2005), No. 1, 156–173 [Google Scholar]
  23. A.M. Khludnev, J. Sokolowski. Smooth domain method for crack problems. Quarterly of Applied Mathematics., 62 (2004), No. 3, 401–422. [MathSciNet] [Google Scholar]
  24. N. Kikuchi, J. Oden. Contact problems in elasticity: A study of variational inequalities and finite element methods. SIAM, 1988. [Google Scholar]
  25. D. Kinderlehrer, G. Stamppachia. An introduction to variational inequalities and their applications, Academic Press, 1980. [Google Scholar]
  26. K. Lhalouani, T. Sassi. Nonconforming mixed variational formulation and domain decomposition for unilateral problems. East-West J. Numer. Math., 7 (1999), No. 1, 23–30. [MathSciNet] [Google Scholar]
  27. L. Slimane, A. Bendali, P. Laborde. Mixed formulations for a class of variational inequalities. M2AN, 38 (2004), 1, 177–201. [Google Scholar]
  28. R. Stenberg. A family of mixed finite elements for the elasticity problem. Numer. Math., 53 (1988), 5, 513–538. [CrossRef] [MathSciNet] [Google Scholar]
  29. S. Tahir. Méthodes d'approximation par éléments finis et analyse a posteriori d'inéquations variationnelles modélisant des problèmes de fissures unilatérales en élasticité linéaire. Ph.D. Thesis, University of Metz, France (2006). [Google Scholar]
  30. S. Tahir, Z. Belhachmi. Mixed finite elements discretizations of some variational inequalities arising in elasticity problems in domains with cracks. Electron. J. Diff. Eqns., Conference 11 (2004), 33–40. [Google Scholar]
  31. Z.-H. Zhong. Finite Element Procedures for Contact-Impact Problems. Oxford. University. Press, Oxford 1993. [Google Scholar]

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