EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 48 / No 4 (July-August 2014) ESAIM: M2AN, 48 4 (2014) 1147-1169 References
Free Access
Issue
ESAIM: M2AN
Volume 48, Number 4, July-August 2014
Page(s) 1147 - 1169
DOI https://doi.org/10.1051/m2an/2013133
Published online 08 July 2014
  1. P. Alart and A. Curnier, A generalized Newton method for contact problems with friction. J. Mech. Theor. Appl. 7 (1988) 67–82. [Google Scholar]
  2. F. Armero and E. Petocz, Formulation and analysis of conserving algorithms for frictionless dynamic contact/impact problems. Comput. Methods Appl. Mech. Engrg. 158 (1998) 269–300. [CrossRef] [MathSciNet] [Google Scholar]
  3. J.P. Aubin, Approximation of elliptic boundary-value problems. Pure and Applied Mathematics, Vol. XXVI. Wiley-Interscience (1972). [Google Scholar]
  4. J.M. Ball, Strongly continuous semigroups, weak solutions, and the variation of constants formula. Proc. Amer. Math. Soc. 63 (1977) 370–373. [MathSciNet] [Google Scholar]
  5. D. Bárcenas, The fundamental theorem of calculus for Lebesgue integral. Divulg. Mat. 8 (2000) 75–85. [MathSciNet] [Google Scholar]
  6. H. Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Mathematics Studies, No. 5. Notas de Matemática (50). North-Holland Publishing Co., Amsterdam (1973). [Google Scholar]
  7. M. Crouzeix and A.L. Mignot, Analyse numérique des équations différentielles. Collection Mathématiques Appliquées pour la Maîtrise. Masson, Paris (1984). [Google Scholar]
  8. R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Vol. 8. INSTN: Collection Enseignement. Masson, Paris (1988). [Google Scholar]
  9. K. Deimling, Multivalued differential equations. Vol. 1 of de Gruyter Series in Nonlinear Analysis and Applications. Walter de Gruyter & Co., Berlin (1992). [Google Scholar]
  10. D. Doyen and A. Ern, Convergence of a space semi-discrete modified mass method for the dynamic Signorini problem. Commun. Math. Sci. 7 (2009) 1063–1072. [CrossRef] [MathSciNet] [Google Scholar]
  11. D. Doyen, A. Ern and S. Piperno, Time-integration schemes for the finite element dynamic Signorini problem. SIAM J. Sci. Comput. (2011) 223–249. [Google Scholar]
  12. A. Ern and J.L. Guermond, Theory and practice of finite elements. Appl. Math. Sci., vol. 159. Springer-Verlag, New York (2004). [Google Scholar]
  13. C. Hager and B.I. Wohlmuth, Analysis of a space-time discretization for dynamic elasticity problems based on mass-free surface elements. SIAM J. Num. Anal. 47 (2009) 1863–1885. [CrossRef] [Google Scholar]
  14. P. Hauret, Mixed interpretation and extensions of the equivalent mass matrix approach for elastodynamics with contact. Comput. Methods Appl. Mech. Engrg. 199 (2010) 2941–2957. [Google Scholar]
  15. T.J.R. Hugues, R.L. Taylor, J.L. Sackman, A. Curnier and W. Kano Knukulchai, A finite method for a class of contact-impact problems. Comput. Methods Appl. Mech. Engrg. 8 (1976) 249–276. [CrossRef] [Google Scholar]
  16. H.B. Khenous, P. Laborde and Y. Renard, Mass redistribution method for finite element contact problems in elastodynamics. Eur. J. Mech. A Solids 27 (2008) 918–932. [Google Scholar]
  17. S. Krenk, Energy conservation in Newmark based time integration algorithms. Comput. Methods Appl. Mech. Engrg. 195 (2006) 6110–6124. [CrossRef] [MathSciNet] [Google Scholar]
  18. N. Kikuchi and J.T. Oden, Contact problems in elasticity: a study of variational inequalities and finite element methods. SIAM Studies Appl. Math. SIAM, Philadelphia, Pa (1988). [Google Scholar]
  19. J.U. Kim, A boundary thin obstacle problem for a wave equation. Commun. Partial Differential Eqs. 14 (1989) 1011–1026. [Google Scholar]
  20. T.A. Laursen and V. Chawla, Design of energy conserving algorithms for frictionless dynamic contact problems. Int. J. Numer. Methods Engrg. 40 (1997) 863–886. [Google Scholar]
  21. T.A. Laursen and G.R. Love, Improved implicit integrators for transient impact problems-geometric admissibility within the conserving framework. Int. J. Numer. Methods Engrg. 53 (2002) 245–274. [Google Scholar]
  22. G. Lebeau and M. Schatzman, A wave problem in a half-space with a unilateral constraint at the boundary. J. Differ. Eqs. 53 (1984) 309–361. [Google Scholar]
  23. J.-J. Moreau, Liaisons unilatérales sans frottement et chocs inélastiques. C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 296 (1983) 1473–1476. [Google Scholar]
  24. J.-J. Moreau and P.D. Panagiotopoulos, Nonsmooth mechanics and applications. Vol. 302 of CISM Courses Lect. Springer-Verlag, Vienna (1988). [Google Scholar]
  25. L. Paoli, Time discretization of vibro-impact. R. Soc. London Philos. Trans. Ser. A Math. Phys. Eng. Sci. 359 (2001) 2405–2428. [Google Scholar]
  26. L. Paoli and M. Schatzman, A numerical scheme for impact problem I. SIAM J. Numer. Anal. 40 (2002) 702–733. [CrossRef] [MathSciNet] [Google Scholar]
  27. L. Paoli and M. Schatzman, Approximation et existence en vibro-impact. C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 1003–1007. [CrossRef] [MathSciNet] [Google Scholar]
  28. Y. Renard, Generalized Newton’s methods for the approximation and resolution of frictional contact problems in elasticity. Comput. Meth. Appl. Mech. Engng. 256 (2013) 38–55. [Google Scholar]
  29. Y. Renard and J. Pommier, Getfem++. An Open Source generic C++ library for finite element methods. http://home.gna.org/getfem. [Google Scholar]
  30. W. Rudin, Real and complex analysis. McGraw-Hill Series in Higher Mathematics. McGraw-Hill Book Co., New York, 2nd edn (1974). [Google Scholar]
  31. M. Schatzman, A hyperbolic problem of second order with unilateral constraints: the vibrating string with a concave obstacle. J. Math. Anal. Appl. 73 (1980) 138–191. [CrossRef] [MathSciNet] [Google Scholar]
  32. M. Schatzman and M. Bercovier, Numerical approximation of a wave equation with unilateral constraints. Math. Comput. 53 (1989) 55–79. [CrossRef] [MathSciNet] [Google Scholar]
  33. K. Schweizerhof, J.O. Hallquist and D. Stillman, Efficiency refinements of contact strategies and algorithms in explicit finite element programming. Compt. Plasticity. Edited by Owen, Onate, Hinton, Pineridge (1992) 457–482. [Google Scholar]
  34. J. Simon, Compact sets in the space Lp(0,T;B). Ann. Mat. Pura Appl. 146 (1987) 65–96. [Google Scholar]
  35. P. Wriggers, Computational contact mechanics. John Wiley and Sons Ltd. (2002). [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