Dynamics of geometrically nonlinear rods: II. Numerical methods and computational examples

Nonlinear Dynamics

Volumn 30, Issue 4, 2002, Pages 383-415

  Weiss, H ^a  

^a GERMAN AEROSPACE CENTER DLR   (Germany)

Author keywords

Nonmaterial boundary conditions; Nonstationary motion; One dimensional continua; String pendulum; Underwater cables

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; CALCULATIONS; COMPUTER SIMULATION; EQUATIONS OF MOTION; FINITE ELEMENT METHOD; INITIAL VALUE PROBLEMS; INTEGRATION; INTERPOLATION; KINEMATICS; POLYNOMIALS;

EULER-BERNOULLI-BEAM; FIRST-ORDER HERMITIAN POLYNOMIAL; GEOMETRICALLY NONLINEAR ROD; INITIAL BOUNDARY VALUE PROBLEM; NEWMARK TYPE METHOD;

BEAMS AND GIRDERS;

EID: 0036922105     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021257410404     Document Type: Article

References (31)

1. Weiss, H., 'Dynamics of geometrically nonlinear rods: I. Mechanical models and equations of motion', Nonlinear Dynamics 30, 2002, 357-381.
2. Timoshenko, S., Young, D. H., and Weaver, W., Vibration Problems in Engineering, Wiley, New York, 1974.
3. Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley, New York, 1979.
4. Shabana, A. A., Vibration of Discrete and Continuous Systems, Springer, New York, 1997.
5. Simo, J. C., Tarnow, N., and Doblaré, M., 'Non-linear dynamics of three-dimensional rods: Exact energy and momentum conserving algorithms', International Journal for Numerical Methods in Engineering 38, 1995, 1431-1473.
6. Bauchau, O. A. and Theron, N. J., 'Energy decaying scheme for non-linear beam models', Computer Methods in Applied Mechanics and Engineering 134, 1996, 37-56.
7. Crisfield, M. A., Galvanetto, U., and Jelenić, G., 'Dynamics of 3-D co-rotational beams', Computational Mechanics 20, 1997, 507-519.
8. Ibrahimbegović, A. and Al Mikdad, M., 'Finite rotations in dynamics of beams and implicit time-stepping schemes', International Journal for Numerical Methods in Engineering 41, 1998, 781-814.
9. Burgess, J. J., 'Bending stiffness in a simulation of undersea cable deployment', International Journal of Offshore and Polar Engineering 3, 1993, 197-204.
10. Dichmann, D. J. and Maddocks, J. H., 'An impetus-striction simulation of the dynamics of an elastica', Journal of Nonlinear Science 6, 1996, 271-292.
11. Stelzle, W., Geometrisch-nichtlineare Modellierung elastischer Balken mit Helix-Elementen, Fortschritt-Berichte VDI Reihe, Vol. 18, Nr. 224, VDI Verlag, Düsseldorf, 1998.
12. Kuhn, A., Steiner, W., Zemann, J., Dinevski, D., and Troger, H., 'A comparison of various mathematical formulations and numerical solution methods for the large amplitude oscillations of a string pendulum', Applied Mathematics and Computation 67, 1995, 227-264.
13. Berger, R., Instationaere Bewegung und Stabilitaetsverhalten eindimensionaler Kontinua, Fortschritt-Berichte VDI Reihe, Vol. 18 Nr. 189, VDI Verlag, Düsseldorf, 1996.
14. Pedrazzi, C., 'Dog on lead mine-hunting underwater cable simulation', in Proceedings to the 12th European ADAMS Users' Conference, Marburg, Germany, November 18-19, 1997.
15. Zienkiewicz, O. C., The Finite Element Method, McGraw-Hill, New York, 1977.
16. Huebner, K. H. and Thornton, E. A., The Finite Element Method for Engineers, Wiley, New York, 1982.
17. Kuessner, M., 'Gemischte Finite-Elemente-Formulierungen für nichtlineare Probleme der Festkörpermechanik', Dissertation, Technische Hochschule Darmstadt, 1995.
18. Shabana, A. A., 'Definition of the slopes and the finite element absolute nodal coordinate formulation', Multibody System Dynamics 1, 1997, 339-348.
19. von Dombrowski, S. and Schwertassek, R., 'Analysis of large deformation problems in multibody systems using absolute coordinates', in Proceedings of the EUROMECH Colloquium 404 on Advances in Computational Multibody Dynamics, Lisbon, Portugal, September 20-23, 1999.
20. Berneck, P., 'Die Anwendung direkter Zeitintegrationsverfahren auf Probleme der Strukturmechanik', Dissertation, Technische Hochschule Darmstadt, 1996.
21. Belytschko, T. and Schoeberle, D. F., 'On the unconditional stability of an implicit algorithm for nonlinear structural dynamics', Journal of Applied Mechanics 42, 1975, 865-869.
22. Hughes, T. J. R., Caughty, T. K., and Liu, W. K., 'Finite-element-methods for nonlinear elastodynamics which conserve energy', Journal of Applied Mechanics 45, 1978, 366-370.
23. Kuhl, D. and Ramm, E., 'Constraint energy momentum algorithm and its application to nonlinear dynamics of shells', Computer Methods in Applied Mechanics and Engineering 136, 1996, 293-315.
24. Simo, J. C., Tarnow, N., and Wong, K. K., 'Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics', Computer Methods in Applied Mechanics and Engineering 100, 1992, 63-116.
25. Weiss, H., 'An exact energy and momentum conserving integration scheme for the nonlinear dynamics of geometrically exact threads', Zeitschrift fuer angewandte Mathematik und Mechanik 78, 1998, S805-S806.
26. La Budde, R. A. and Greenspan, D., 'Discrete mechanics - A general treatment', Journal of Computational Physics 15, 1974, 134-167.
27. Tarnow, N. and Simo, J. C., 'How to render second accurate time-stepping algorithms fourth order accurate while retaining the stability and conservation properties', Computer Methods in Applied Mechanics and Engineering 115, 1994, 233-252.
28. Schagerl, M., Steindl, A., and Troger, H., 'Dynamic analysis of the deployment process of tethered satellite systems', in IUTAM-IASS Symposium on Deployable Structures: Theory and Applications, S. Pellegrino and S.D. Guest (eds.), Solid Mechanics and Its Applications, Vol. 80, Kluwer, Dordrecht, 2000, pp. 345-354.
29. Krupa, M., Kuhn, A., Poth, W., Schagerl, M., Steiner, W., Steindl, A., Troger, H., and Wiedermann, G., 'Tethered satellite systems: A new concept of space flight', European Journal of Mechanics A/Solids 19, 2000, S149-S164.
30. Blevins, R. D., Applied Fluid Dynamics Handbook, Wiley, New York, 1980.
31. Nordell, W. J. and Meggit, D. J., 'Undersea suspended cable structures', ASCE Journal Structures Division 107, 1981, 1025-1040.