Free Access
Volume 50, Number 6, November-December 2016
Page(s) 1585 - 1613
Published online 05 October 2016
  1. R.A. Adams, Sobolev spaces. Academic Press (1975). [Google Scholar]
  2. J. Ahn and D.E. Stewart, An Euler-Bernoulli beam with dynamic contact: Discretization, convergence and numerical results. SIAM J. Numer. Anal. 43 (2005) 1455–1480. [CrossRef] [MathSciNet] [Google Scholar]
  3. P. Alart and A. Curnier, A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput. Methods Appl. Mech. Eng. 92 (1991) 353–375. [Google Scholar]
  4. B. Brogliato, Nonsmooth Mechanics, edited by E.D. Sontag, M. Thoma. Springer, London (1999). [Google Scholar]
  5. N.J. Carpenter, Lagrange constraints for transient finite element surface contact. Int. J. Numer. Methods Eng. 32 (1991) 103–128. [CrossRef] [Google Scholar]
  6. P.G. Ciarlet, The finite element method for elliptic problems. North-Holland (1978). [Google Scholar]
  7. P.G. Ciarlet, Basic error estimates for elliptic problems, in Vol. II of Handbook of Numerical Analysis. North-Holland (1991) 17–351. [Google Scholar]
  8. F. Dabaghi, A. Petrov, J. Pousin and Y. Renard, Convergence of mass redistribution method for the wave equation with a unilateral constraint at the boundary ESAIM: M2AN 48 (2014) 1147–1169. [CrossRef] [EDP Sciences] [Google Scholar]
  9. P. Deuflhard, R. Krause and S. Ertel, A contact-stabilized Newmark method for dynamical contact problems. Int. J. Numer. Methods Eng. 73 (2007) 1274–1290. [CrossRef] [Google Scholar]
  10. Y. Dumont and L. Paoli, Vibrations of a beam between obstacles: Convergence of a fully discretized approximation. ESAIM: M2AN 40 (2006) 705–734. [CrossRef] [EDP Sciences] [Google Scholar]
  11. Y. Dumont and L. Paoli, Numerical simulation of a model of vibrations with joint clearance. Int. J. Comput. Appl. Technol. 33 (2008) 41–53. [CrossRef] [Google Scholar]
  12. D. Doyen, Méthodes numériques pour des problèmes dynamiques de contact et de fissuration. Thèse de l’Université Paris-Est (2010). [Google Scholar]
  13. Y. Renard and J. Pommier, An open source generic C++ library for finite element methods. Available at (2016). [Google Scholar]
  14. C. Hager, S. Hüeber and B. Wohlmuth, A stable energy conserving approach for frictional contact problems based on quadrature formulas. Int. J. Numer. Methods Eng. 73 (2008) 205–225. [CrossRef] [Google Scholar]
  15. P. Hauret, and P. Le Tallec, Energy controlling time integration methods for nonlinear elastodynamics and low-velocity impact. Comput. Methods Appl. Mech. Eng. 195 (2006) 4890–4916. [CrossRef] [MathSciNet] [Google Scholar]
  16. P. Hauret, Mixed Interpretation and Extensions of the Equivalent Mass Matrix Approach for Elastodynamics with Contact. Comput. Methods Appl. Mech. Eng. 199 (2010) 2941–2957. [CrossRef] [MathSciNet] [Google Scholar]
  17. R.A. Ibrahim, V.I. Babitsky and M. Okuma, Vibro-Impact Dynamics of Ocean Systems and Related Problems. Vol. 44 of Lect. Notes Appl. Comput. Mech. Springer (2009). [Google Scholar]
  18. 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]
  19. K. Kuttler and M. Shillor, Vibrations of a beam between two stops, Dynamics of Continuous, Discrete and Impulsive Systems. Ser. B, Appl. Algorithms 8 (2001) 93–110. [Google Scholar]
  20. T.A. Laursen and V. Chawla, Design of energy conserving algorithms for frictionless dynamic contact problems. Int. J. Numer. Methods Eng. 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 Eng. 53 (2002) 245–274. [Google Scholar]
  22. L. Paoli, Time discretization of vibro-impact. Philos. Trans. R. Soc. Lond., A 359 (2001) 2405–2428. [CrossRef] [MathSciNet] [Google Scholar]
  23. L. Paoli and M. Schatzman, A numerical scheme for impact problems. I. The one-dimensional case. SIAM J. Numer. Anal. 40 (2002) 702–733. [CrossRef] [MathSciNet] [Google Scholar]
  24. L. Paoli and M. Schatzman, Numerical simulation of the dynamics of an impacting bar. Comput. Methods Appl. Mech. Eng. 196 (2007) 2839–2851. [CrossRef] [Google Scholar]
  25. A. Petrov, and M. Schatzman, Viscoélastodynamique monodimensionnelle avec conditions de Signorini. C. R. Acad. Sci. Paris, I 334 (2002) 983–988. [Google Scholar]
  26. A. Petrov and M. Schatzman, A pseudodifferential linear complementarity problem related to a one dimensional viscoelastic model with Signorini condition. Archive for Rational Mechanics and Analysis. Springer (2009). [Google Scholar]
  27. C. Pozzolini and M. Salaün, Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles. ESAIM: M2AN 45 (2011) 1163–1192. [CrossRef] [EDP Sciences] [Google Scholar]
  28. C. Pozzolini, Y. Renard and M. Salaün, Vibro-Impact of a plate on rigid obstacles: existence theorem, convergence of a scheme and numerical simulations. IMA J. Numer. Anal. 33 (2013) 261–294. [CrossRef] [MathSciNet] [Google Scholar]
  29. Y. Renard, The singular dynamic method for constrained second order hyperbolic equations. Application to dynamic contact problems. J. Comput. Appl. Math. 234 (2010) 906–923. [CrossRef] [MathSciNet] [Google Scholar]
  30. R.L. Taylor and P. Papadopoulos, On a finite element method for dynamic contact-impact problems. Int. J. Numer. Methods Eng. 36 (1993) 2123–2140. [CrossRef] [Google Scholar]
  31. Y. Mochida, Bounded Eigenvalues of Fully Clamped and Completely Free Rectangular Plates. Master thesis of the University of Waikato Hamilton, New Zealand (2007). [Google Scholar]

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