EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 50 / No 6 (November-December 2016) ESAIM: M2AN, 50 6 (2016) 1585-1613 References
Free Access
Issue
ESAIM: M2AN
Volume 50, Number 6, November-December 2016
Page(s) 1585 - 1613
DOI https://doi.org/10.1051/m2an/2015094
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 http://home.gna.org/getfem/ (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]

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