Free Access
Volume 44, Number 2, March-April 2010
Page(s) 323 - 346
Published online 27 January 2010
  1. P. Alart and A. Curnier, A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput. Methods Appl. Mech. Engrg. 92 (1991) 353–375. [CrossRef] [MathSciNet] [Google Scholar]
  2. K.J. Bathe and F. Brezzi, Stability of finite element mixed interpolations for contact problems. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 12 (2001) 167–183. [MathSciNet] [Google Scholar]
  3. D.P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods. Athena Scientific (1982). [Google Scholar]
  4. D.P. Bertsekas, Nonlinear Programming. Athena Scientific (1999). [Google Scholar]
  5. B. Bourdin, G.A. Francfort and J.-J. Marigo, The variational approach to fracture. J. Elasticity 91 (2008) 5–148. [CrossRef] [MathSciNet] [Google Scholar]
  6. L. Champaney, J.-Y. Cognard and P. Ladevèze, Modular analysis of assemblages of three-dimensional structures with unilateral contact conditions. Comput. Struct. 73 (1999) 249–266. [CrossRef] [Google Scholar]
  7. Z. Chen, On the augmented Lagrangian approach to Signorini elastic contact problem. Numer. Math. 88 (2001) 641–659. [CrossRef] [MathSciNet] [Google Scholar]
  8. P.G. Ciarlet, Mathematical elasticity, Vol. I: Three-dimensional elasticity, Studies in Mathematics and its Applications 20. North-Holland Publishing Co., Amsterdam (1988). [Google Scholar]
  9. F.H. Clarke, Optimization and nonsmooth analysis, Classics in Applied Mathematics 5. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, USA, second edition (1990). [Google Scholar]
  10. Z. Denkowski, S. Migórski and N.S. Papageorgiou, An introduction to nonlinear analysis: applications. Kluwer Academic Publishers, Boston, USA (2003). [Google Scholar]
  11. I. Ekeland and R. Témam, Convex analysis and variational problems, Classics in Applied Mathematics. 28. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, USA (1999). [Google Scholar]
  12. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements, Applied Mathematical Sciences 159. Springer-Verlag, New York, USA (2004). [Google Scholar]
  13. M. Fortin and R. Glowinski, Augmented Lagrangian methods: Applications to the numerical solution of boundary value problems, Studies in Mathematics and its Applications 15. North-Holland Publishing Co., Amsterdam (1983). [Google Scholar]
  14. M. Frémond, Contact with adhesion, in Topics in nonsmooth mechanics, Birkhäuser, Basel, Switzerland (1988) 157–185. [Google Scholar]
  15. R. Glowinski and P. Le Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM Studies in Applied Mathematics 9. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, USA (1989). [Google Scholar]
  16. J. Haslinger, I. Hlaváček and J. Nečas, Numerical methods for unilateral problems in solid mechanics, in Handbook of numerical analysis IV, Amsterdam, North-Holland (1996) 313–485. [Google Scholar]
  17. P. Hauret and P. Le Tallec, A discontinuous stabilized mortar method for general 3d elastic problems. Comput. Methods Appl. Mech. Engrg. 196 (2007) 4881–4900. [CrossRef] [MathSciNet] [Google Scholar]
  18. P. Hild and P. Laborde, Quadratic finite element methods for unilateral contact problems. Appl. Numer. Math. 41 (2002) 401–421. [CrossRef] [MathSciNet] [Google Scholar]
  19. S. Hüeber and B.I. Wohlmuth, An optimal a priori error estimate for nonlinear multibody contact problems. SIAM J. Numer. Anal. 43 (2005) 156–173 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  20. 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, USA (1988). [Google Scholar]
  21. D. Kinderlehrer, Remarks about Signorini's problem in linear elasticity. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 8 (1981) 605–645. [MathSciNet] [Google Scholar]
  22. K. Kunisch and G. Stadler, Generalized Newton methods for the 2D-Signorini contact problem with friction in function space. ESAIM: M2AN 39 (2005) 827–854. [CrossRef] [EDP Sciences] [Google Scholar]
  23. P. Ladevèze, Nonlinear Computational Structural Mechanics – New Approaches and Non-Incremental Methods of Calculation. Springer-Verlag (1999). [Google Scholar]
  24. J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications I, Die Grundlehren der mathematischen Wissenschaften, Band 181. Springer-Verlag, New York, USA (1972). [Google Scholar]
  25. E. Lorentz, A mixed interface finite element for cohesive zone models. Comput. Methods Appl. Mech. Engrg. 198 (2008) 302–317. [CrossRef] [Google Scholar]
  26. M. Marcus and V.J. Mizel, Every superposition operator mapping one Sobolev space into another is continuous. J. Funct. Anal. 33 (1979) 217–229. [CrossRef] [MathSciNet] [Google Scholar]
  27. M. Moussaoui and K. Khodja, Régularité des solutions d'un problème mêlé Dirichlet-Signorini dans un domaine polygonal plan. Commun. Partial Differ. Equ. 17 (1992) 805–826. [CrossRef] [MathSciNet] [Google Scholar]
  28. L. Qi and J. Sun, A nonsmooth version of Newton's method. Math. Program. 58 (1993) 353–367. [CrossRef] [Google Scholar]
  29. L. Slimane, A. Bendali and P. Laborde, Mixed formulations for a class of variational inequalities. ESAIM: M2AN 38 (2004) 177–201. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you