Schéma dissipatif HHT d’intégration temporelle pour un modèle de poutre en grandes rotations

Authors

  • Saïd Mamouri Université de Technologie de Compiègne Dept. GSM, Lab. Roberval, bp-20529 60205 Compiègne, France
  • Adnan Ibrahimbegovic Ecole Normale Supérieure de Cachan LMT/ 61, av du Président Wilson 94235 Cachan, France

Keywords:

dynamics, time integration, dissipative HHT scheme

Abstract

In this work we present au extension of HHT dissipative numerical integration scheme for the dynamics of structures undergoing large rotations. The problem used to illustrate the proposed modification pertains to so-called ’geometrically exact’ three-dimensional beam theory. Among different possibilities to parameterize the finite rotations, we choose a material representation of the rotation vector, which simplified the construction of time-integration schemes. We also present the essential details of the finite element implementation.

Downloads

Download data is not yet available.

References

[ALM 97] ALMIKDAD M., IBRAHIMBEGOVIC A., (( Dynamique et schémas d’intégration

pour modèles de poutres géométriquement exacts )), Revue Euro. Elém. Finis, vol. 6 No

, 1997, p. 471-502.

[AUB 95] AUBRY D., VAILHEN C., DRESSLER B., LUCAS D., (( Nonlinear dynamic analysis

of frictional contact between shell structures )), 9th DYMAT Tech. Conf. Mat. and Struc.

Modelling in collision reasearch, TU-Munich, vol. I, 1995.

[BAR 98] BARRACO A., GILBERT M., (( Quasi exact solutions for some elastodynamics problems

)), Fourth World Congress on Computational Mechanics (IV WCCM), vol. CD,

[BAU 95] BAUCHAU O., DAMILANO G., THERON J., (( Numerical integration of non-linear

elastic multibody systems )), Int. J. Numer. Methods Eng., vol. 38, 1995, p. 2727-2751.

[BOT 98] BOTTASSO C. L., BORRI M., (( Integrating finte rotations )), Comput. Methods

Appl. Mech. Eng., in press, vol. 164, 1998, p. 307-331.

[CAR 88] CARDONA A., GERADIN M., (( A beam finite element non-linear theory with finite

rotations )), Int. J. Numer. Methods Eng., vol. 26, 1988, p. 2403-2438.

[CAR 89] CARDONA A., GERADIN M., (( Time integration of the equations of motion in

mechanism analysis )), Comput. Struc, vol. 33, 1989, p. 801-820.

[HIL 77] HILBER H., HUGHES T., TAYLOR R., (( Improved numerical dissipation for time

integration algorithms in structural dynamics )), Earthq. Eng. Struc. Dynam., vol. 5, 1977,

p. 283-292.

[IBR 95a] IBRAHIMBEGOVIC A., (( On finite element implementation of geometrically nonlinear

Reissner’s beam theory: three dimensional curved beam element )), Comput. Methods

Appl. Mech. Eng., vol. 112, 1995, p. 11-26.

[IBR 95b] IBRAHIMBEGOVIC A., FREY F., KOZAR I., (( Computational aspect of vector-like

parameterization of three dimensional finite rotations )), Int. J. Numer. Methods. Eng.,

vol. 38, 1995, p. 3653-3673.

[IBR 97] IBRAHIMBEGOVIC A., (( On the choice of finite rotation parameters )), Comput.

Methods Appl. Mech. Eng., vol. 149, 1997, p. 49-71.

[IBR 98] IBRAHIMBEGOVIC A., ALMIKDAD M., (( Finite rotations in dynamics of beams and

implicit time-stepping schemes )), Int. J. Numer. Methods. Eng., vol. 41, 1998, p. 781-814.

[IBR 99] IBRAHIMBEGOVIC A., MAMOURI S., (( Nonlinear dynamics of flexible beams in

planar motion:formulation and time-stepping schemes for stiff problems )), Comput. Struc.,

vol. 70, 1999, p. 1-22.

[IDE 89] IDER S., AMIROUCHE F., (( Nonlinear modeling of flexible multibody systems dynamics

subjected to variable constraints )), J. Appl. Mech., vol. 56, 1989, p. 444-450.

[JEL 96] JELENIC G., CRISFIELD M., (( Non-linear ’master-slave’ relationship for joints in

D beams with large rotations )), Comput. Methods. Appl. Mech. Eng., vol. 135, 1996,

p. 211-228.

[JEL 98] JELENIC G., CRISFIELD M., (( Interpolation of rotational variables in nonlinear dynamics

of 3d beams )), Int. J. Numer. Methods Eng., vol. 43, 1998, p. 1193-1222.

[KAN 85] KANE T. R., LEVINSON D., Dynamics Theory and Applications, Mc-Graw Hill,

New York, 1985.

[KUH 98] KUHL D., CRISFIELD M. A., (( Energy-conserving and decaying algorithms in

nonlinear structural dynamics )), Int. J. Numer. Methods Eng., vol. 45, 1998, p. 569-599.

[MAR 83] MARSDEN J. E., HUGHES T., Mathematical foundations of elasticity, Prentice-

Hall, Englewoods Cliffs, N.J., 1983.

[SIM 86] SIMO J., VU-QUOC L., (( On the dynamics of flexible beams under large overall

motions the plane case, Part 1 and 2 )), ASME J. Appl. Mech., vol. 53, 1986, p. 849-863.

[SIM 95] SIMO J., TARNOW N., DOBLARE M., (( Nonlinear dynamics of three-dimensional

rods: Exact energy and momentum conserving algorithm )), Int. J. Numer. Methods Eng.,

vol. 38, 1995, p. 1431-1473.

[VEU 76] FRAEIJS DE VEUBEKE B., (( The dynamics of flexible bodies )), Int. J. Engng.

Science, vol. 14, 1976, p. 895-913.

Downloads

Published

2001-06-13

How to Cite

Mamouri, S. ., & Ibrahimbegovic, A. (2001). Schéma dissipatif HHT d’intégration temporelle pour un modèle de poutre en grandes rotations. European Journal of Computational Mechanics, 10(5), 607–623. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/2707

Issue

Section

Original Article