Skip to main content
Springer Nature Link
Log in

Modeling elastic beams using dynamic splines

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

In this paper, the authors present the description and an application of the theory of dynamic splines for the modeling of very flexible beams in multibody systems. The use of spline formalism reveals an alternative method for the description of continuum flexibility by using discrete parameters. The proposed approach is discussed in general terms and a specific example is presented and compared to nonlinear finite element simulation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Shabana, A.A.: Flexible multibody dynamics: review of past and recent developments. Multibody Syst. Dyn. 1(2), 189–222 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Valembrois, R.E., Fisette, P., Samin, J.C.: Comparison of various techniques for modeling flexible beams in multibody dynamics. Nonlinear Dyn. 12, 367–397 (1997)

    Article  Google Scholar 

  3. Shabana, A.A.: Dynamics of Multibody Systems, 2nd edn. Wiley, New York (1998)

    MATH  Google Scholar 

  4. Shabana, A.A.: Dynamic analysis of large scale inertia-variant flexible systems. PhD thesis, The University of Iowa (1982)

  5. Cardona, A.: Superelements modeling in flexible multibody dynamics. Multibody Syst. Dyn. 4, 245–266 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Oliviers, M., Campion, G., Samin, J.C.: Nonlinear dynamic model of a system of flexible bodies using augmented bodies. Multibody Syst. Dyn. 2, 25–48 (1998)

    Article  MATH  Google Scholar 

  7. Kim, S., Haug, E.: Selection of deformation modes for flexible multibody dynamics. Mech. Struct. Mach. 18, 565–586 (1990)

    Article  Google Scholar 

  8. Theodore, R., Ghosal, A.: Comparison of the assumed modes and finite element models for flexible multilink manipulators. Int. J. Robot. Res. 14(2), 91–111 (1995)

    Article  Google Scholar 

  9. Géradin, M., Cardona, A.: Flexible Multibody Dynamics—A Finite Element Approach. Wiley, New York (2001)

    Google Scholar 

  10. Gerstmayr, J., Schöberl, J.: A 3D finite element method for flexible multibody systems. Multibody Syst. Dyn. 15, 309–324 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Von Dombrowski, S.: Analysis of large flexible body deformation in multibody systems using absolute coordinates. Multibody Syst. Dyn. 8, 409–432 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  12. Shabana, A.A.: Definition of the slopes and the finite element absolute nodal coordinate formulation. Multibody Syst. Dyn. 1(3), 339–348 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kübler, L., Eberhard, P., Geisler, J.: Flexible multibody systems with large deformations and nonlinear structural damping using absolute nodal coordinates. Nonlinear Dyn. 34, 31–52 (2003)

    Article  MATH  Google Scholar 

  14. Berzeri, M., Shabana, A.: Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation. J. Sound Vib. 235(4), 539–565 (2000)

    Article  Google Scholar 

  15. Sanborn, G.G., Shabana, A.A.: On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation. Multibody Syst. Dyn. 22, 181–197 (2009)

    Article  MATH  Google Scholar 

  16. Liu, Z.Y., Hong, J.Z., Liu, J.Y.: Finite element formulation for dynamics of planar flexible multi-beam system. Multibody Syst. Dyn. 22, 1–26 (2009)

    Article  MathSciNet  Google Scholar 

  17. Mayo, J.M., Garçia-Vallejo, D., Dominguez, J.: Study of the geometric stiffening effect: comparison of different formulations. Multibody Syst. Dyn. 11(4), 321–341 (2004)

    Article  MATH  Google Scholar 

  18. Simo, J.C., Vu-Quoc, L.: On the dynamics of flexible beams under large overall motions—the plane case. J. Appl. Mech. 53, 849–863 (1986)

    Article  MATH  Google Scholar 

  19. Ambrósio, J.A.C.: Geometric and material nonlinear deformations in flexible multibody systems. In: Ambrosio, J.A.C. Kleiber, M. (eds.) Computational Aspects of Nonlinear Structural Systems with Large Rigid Body Motion, Nato Science Series. Iowa State University Press, Ames (2001)

    Google Scholar 

  20. Hsiao, K.M., Yang, R.T.: A co-rotational formulation for nonlinear dynamic analysis of curved Euler beam. Comput. Struct. 54, 1091–1097 (1995)

    Article  MATH  Google Scholar 

  21. Wu, S.C., Haug, E.J.: Geometric non-linear substructuring for dynamics of flexible mechanical systems. Int. J. Numer. Methods Eng. 26, 2211–2276 (1988)

    Article  MATH  Google Scholar 

  22. Chen, Z.Q., Agar, T.J.A.: Geometric nonlinear analysis of flexible spatial beams structures. Comput. Struct. 49, 1083–1094 (1993)

    Article  MATH  Google Scholar 

  23. Sharf, I.: Geometrical non-linear beam element for dynamics simulation of multibody systems. Int. J. Numer. Methods Eng. 39, 763–786 (1996)

    Article  MATH  Google Scholar 

  24. Farin, G.: Curves and Surfaces for CAGD, 5th edn. Morgan Kaufmann, San Francisco (2002)

    Google Scholar 

  25. Qin, H., Terzopoulos, D.: D-NURBS: a physics-based framework for geometric design. IEEE Trans. Vis. Comput. Graph. 2(1), 85–96 (1996)

    Article  Google Scholar 

  26. Lenoir, J., Cotin, S., Duriez, C., Neumann, P.: Interactive physically-based simulation of catheter and guidewire. Computer and Graphics 30(3), 417–423 (2006)

    Article  Google Scholar 

  27. Lenoir, J., Grisoni, L., Meseure, P., Chaillou, C.: Adaptive resolution of 1D mechanical B-spline. In: Graphite. Dunedin (New Zealand), pp. 395–403 (2005)

    Chapter  Google Scholar 

  28. Theetten, A., Grisoni, L., Andriot, C., Barsky, B.: Geometrically exact dynamic splines. Comput. Aided Des. 40, 35–48 (2008)

    Article  Google Scholar 

  29. Gerstmayr, J., Irschik, H.: On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach. J. Sound Vib. 318, 461–487 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Rome “Tor Vergata”, Via del Politecnico, 1-00133, Rome, Italy

    Pier Paolo Valentini & Ettore Pennestrì

Authors
  1. Pier Paolo Valentini
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Ettore Pennestrì
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Pier Paolo Valentini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Valentini, P.P., Pennestrì, E. Modeling elastic beams using dynamic splines. Multibody Syst Dyn 25, 271–284 (2011). https://doi.org/10.1007/s11044-010-9232-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-010-9232-9

Keywords