Numerical simulation of the dynamics of an impacting bar

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 29-30, 2007, Pages 2839-2851

  Paoli, Laetitia ^a   Schatzman, Michelle ^b  

^a UNIVERSITÉ JEAN MONNET   (France)

^b UNIVERSITÉ LYON 1   (France)

Author keywords

Dynamics of discrete mechanical systems; Event driven scheme; Frictionless unilateral constraints; Microimpacts; Restitution coefficient; Time stepping scheme

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SIMULATION; DYNAMICS; IMPACT STRENGTH;

DISCRETE MECHANICAL SYSTEMS; EVENT-DRIVEN SCHEME; MICROIMPACTS; RESTITUTION COEFFICIENT; TIME-STEPPING SCHEME;

BARS (METAL);

BARS (METAL); COMPUTATIONAL METHODS; COMPUTER SIMULATION; DYNAMICS; IMPACT STRENGTH;

EID: 34247617166     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.11.024     Document Type: Article

References (22)

1. Paoli L., and Schatzman M. A numerical scheme for impact problems. I. The one-dimensional case. SIAM J. Numer. Anal. 40 2 (2002) 702-733 (electronic)
2. Paoli L., and Schatzman M. A numerical scheme for impact problems II. The multidimensional case. SIAM J. Numer. Anal. 40 2 (2002) 734-768 (electronic)
3. Stoianovici D., and Hurmuzlu Y. A critical study of the applicability of rigid body collision theory. ASME J. Appl. Mech. 63 (1996) 307-316
4. Hurmuzlu Y. An energy based coefficient of restitution for planar impacts of slender bars with massive external surfaces. ASME J. Appl. Mech. 65 (1998) 952-962
5. L. Paoli, M. Schatzman, Understanding impact through continuous medium vibrations, in: J. Martins, M. Monteiro-Marques (Eds.), Contact Mechanics, no. 103 in Solid Mechanics and its Applications, Kluwer, 2002.
6. Stronge W.J. Impact Mechanics (2000), Cambridge University Press
7. L. Paoli, M. Schatzman, Dynamics of an impacting bar, in: W. Wunderlich, (Ed.), Proceedings of European Conference on Computational Mechanics, Munich, 1999 (CD-ROM).
8. Schatzman M. A class of nonlinear differential equations of second order in time. Nonlinear Anal.: Theory, Methods Appl. 2 (1978) 355-373
9. L. Paoli, M. Schatzman, Mouvement à un nombre fini de degrés de liberté avec contraintes unilatérales: cas avec perte d'énergie, Modél. Math. Anal. Num. (M2AN).
10. Panet M., Paoli L., and Schatzman M. Theoretical and numerical study for a model of vibrations with unilateral constraints. In: Raous M., Jean M., and Moreau J.-J. (Eds). Contact Mechanics (1995), Plenum Press 457-464
11. Schatzman M. Penalty method for impact in generalized coordinates. Phil. Trans. R. Soc. Lond. 359 1789 (2001) 2429-2446
12. Paoli L.A. An existence result for vibrations with unilateral constraints: case of a nonsmooth set of constraints. Math. Models Methods Appl. Sci. 10 6 (2000) 815-831
13. L. Paoli, M. Schatzman, Ill-posedness in vibroimpact and its numerical consequences, in: Proceedings of European Congress on Computational Mechanics, 2000 (CD-ROM).
14. Ballard P. The dynamics of discrete mechanical systems with perfect unilateral constraints. Arch. Rat. Mech. Anal. 154 (2000) 199-274
15. J.-J. Moreau, Unilateral Problems in Structural Analysis, no. 288 in CISM Courses and Lectures, Springer, Ch. Standard Inelastic Shocks and the Dynamics of Unilateral Constraints, 1985.
16. J.-J. Moreau, Dynamique des systèmes à liaisons unlatérales avec frottement sec éventuel; essais numériques, Tech. Rep. 85, LMGC, Université des Sciences et Techniques du Languedoc, 1986.
17. Mabrouk M. A unified variational model for the dynamics of perfect unilateral constraints. Eur. J. Mech. A Solids 17 5 (1998) 819-842
18. Paoli L. Time-discretization of vibro-impact. Phil. Trans. Roy. Soc. 359 1789 (2001) 2405-2428
19. Paoli L., and Schatzman M. Approximation et existence en vibro-impact. C.R. Acad. Sci. Paris Série I 329 (1999) 1103-1107
20. Schatzman M. Un problème hyperbolique du 2ème ordre avec contrainte unilatérale: la corde vibrante avec obstacle ponctuel. J. Differ. Equat. 36 2 (1980) 295-334
21. Schatzman M., and Bercovier M. Numerical approximation of a wave equation with unilateral constraints. Math. Comp. 53 187 (1989) 55-79
22. Stewart D.E. Rigid-body dynamics with friction and impact. SIAM Rev. 42 1 (2000) 3-39 (electronic)