Dynamics of geometrically nonlinear rods: I. Mechanical models and equations of motion

Nonlinear Dynamics

Volumn 30, Issue 4, 2002, Pages 357-381

  Weiss, H ^a  

^a GERMAN AEROSPACE CENTER DLR   (Germany)

Author keywords

Dynamics; Geometrically nonlinear rods; Nonmaterial boundary conditions; Nonstationary motion; One dimensional continua

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; CONTINUUM MECHANICS; EQUATIONS OF MOTION; KINEMATICS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NUMERICAL METHODS; SHEAR DEFORMATION; STIFFNESS; STRAIN;

EULER-BERNOULLI-BEAM EQUATION; EXTENSIBLE ROD; NONLINEAR ROD; NONSTATIONARY MOTION; ONE-DIMENSIONAL CONTINUUM; TORSIONAL STIFFNESS;

BEAMS AND GIRDERS;

EID: 0036922353     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021268325425     Document Type: Article

References (28)

1. Weiss, H., 'Dynamics of geometrically nonlinear rods: II. Numerical methods and computational examples', Nonlinear Dynamics 30, 2003, 383-415.
2. Plagge, F., 'Nichtlineares, inelastisches Verhalten von Spiralseilen', Dissertation, Technische Universität Braunschweig, 1997.
3. Szabo, I., Geschichte der mechanischen Prinzipien, Birkhäuser, Basel, 1979.
4. Truesdell, C. and Noll, W., The Nonlinear Field Theories of Mechanics, Springer, New York, 1965.
5. Wang, C.-C. and Truesdell, C., Introduction to Rational Elasticity, Noordhoff, Leiden, 1973.
6. Ciarlet, P.G., Mathematical Elasticity. Volume I: Three-Dimensional Elasticity, Elsevier, Amsterdam, 1987.
7. 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.
8. 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.
9. Schiehlen, W., Technische Dynamik, Teubner, Stuttgart, 1986.
10. Spong, M. W. and Vidyasagar, M., Robot Dynamics and Control, Wiley, New York, 1989.
11. Bremer, H., 'On the dynamics of elastic multibody systems', Applied Mechanics Reviews 54(9), 1999, 275-303.
12. Whitham, G. B., Linear and Nonlinear Waves, Wiley, New York, 1974.
13. Schnell, W., Gross, D., and Hauger, W., Technische Mechanik, Band 2: Elastostatik, Springer, Berlin, 1992.
14. Goeldner, H., Lehrbuch höhere Festigkeitslehre. Band I: Grundlagen der Elastizitätstheorie, Fachbuchverlag, Leipzig, 1991.
15. Franke, W., Ein Beitrag zur dynamischen räumlichen Elastizitästheorie II. Ordnung eines geraden Stabes unter dem besonderen Aspekt transienter axialer Einwirkung, Shaker, Aachen, 1997.
16. Trommer, G., 'Das Aufdrehmoment eines Garnes', Faserforschung und Textiltechnik 17(8), 1966, 355-362.
17. Buerger, W., 'Theorie einfacher Wellen und Anwendungen in der Kontinuumsmechanik', Habilitation, Technische Hochschule Darmstadt, 1971.
18. Weiss, H., 'Zur Dynamik geometrisch nichtlinearer Balken', Dissertation, Technische Universität Chemnitz, 1999.
19. Triantafyllou, M. S. and Howell, C. T., 'Dynamic response of cables under negative tension: An ill-posed problem', Journal of Sound and Vibration 173(4), 1994, 433-447.
20. Hamel, G., Theoretische Mechanik, Springer, Berlin, 1949.
21. Reissner, E., 'On one-dimensional large-displacement finite-strain beam theory', Studies in Applied Mathematics 52, 1973, 87-95.
22. Simo, J. C., 'A finite strain beam formulation. The three dimensional dynamic problem. Part I', Computer Methods in Applied Mechanics and Engineering 49, 1985, 55-70.
23. Simo, J. C. and Vu-Quoc, L., 'Three dimensional finite strain rod model. Part II: Computational aspects', Computer Methods in Applied Mechanics and Engineering 58, 1986, 79-116.
24. Svetlizkij, V. A., Mechanics of Rods, Vysshaya Shcola, Moscow, 1987 [in Russian].
25. Antman, S. S., Nonlinear Problems of Elasticity, Springer, New York, 1995.
26. Dichmann, D. J., Li, Y., and Maddocks, J. H., 'Hamiltonian formulations and symmetries in rod mechanics', in Mathematical Approaches to Biomolecular Structures, J. P. Mesirov, K. Shulten, and D. Sumners (eds.), IMA Volumes in Mathematics and Its Applications, Vol. 82, Springer, New York, 1996, pp. 71-113.
27. Berger, R., Instationäre Bewegung und Stabilitätsverhalten eindimensionaler Kontinua, Fortschritt-Berichte VDI Reihe, Vol. 18, Nr. 189, VDI Verlag, Düsseldorf, 1996.
28. Stelzle, W., Geometrisch-nichtlineare Modellierung elastischer Balken mit Helix-Elementen, Fortschritt-Berichte VDI Reihe, Vol. 18, Nr. 224, VDI Verlag, Düsseldorf, 1998.