Skip to main content
Log in

Finite Element Method in Dynamics of Flexible Multibody Systems: Modeling of Holonomic Constraints and Energy Conserving Integration Schemes

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

In this work we discuss an application of the finite elementmethod to modeling of flexible multibody systems employing geometricallyexact structural elements. Two different approaches to handleconstraints, one based on the Lagrange multiplier procedure and anotherbased on the use of release degrees of freedom, are examined in detail.The energy conserving time stepping scheme, which is proved to be wellsuited for integrating stiff differential equations, gouverning themotion of a single flexible link is appropriately modified and extendedto nonlinear dynamics of multibody systems.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Argyris, J.H., ‘Excursion into large rotations’, Comput. Appl. Mech. Engrg. 32, 1982, 85-155.

    Google Scholar 

  2. Bauchau, O.A., Damilano, G. and Theron, J., ‘Numerical integration of non-linear elastic multibody systems’, Internat. J. Numer. Methods Engrg. 38, 1995, 2727-2751.

    Google Scholar 

  3. Bottasso, C.L. and Borri, M., ‘Energy preserving/decaying schemes for non-linear beam dynamics using helicoidal approximation’, Comput. Methods Appl. Mech. Engrg. 143, 1997, 393-415.

    Google Scholar 

  4. Cardona, A. and Geradin, M., ‘A beam finite element non-linear theory with finite rotations’, Internat. J. Numer. Methods Engrg. 26, 1988, 2403-2438.

    Google Scholar 

  5. Cardona, A. and Geradin, M., ‘Time integration of the equations of motion in mechanism analysis’, Comput. & Structures 33, 1989, 801-820.

    Google Scholar 

  6. Cardona, A., Geradin, M. and Doan, D.B., ‘Rigid and flexible joint modelling in multibody dynamics using finite elements’, Comput. Methods Appl. Mech. Engrg. 89, 1991, 395-418.

    Google Scholar 

  7. Chen, A.J., ‘Energy-momentum conserving methods for three dimensional dynamic nonlinear multibody systems’, Ph.D. Thesis, Stanford University (also SUDMC Report 98-01), 1998.

  8. Fraeijs de Veubeke, B.N., ‘The dynamics of flexible bodies’, Internat. J. Engrg. Sci. 14, 1976, 895-913.

    Google Scholar 

  9. Geradin, M. and Rixen, D., ‘Parametrization of finite rotations in computational dynamics’, European J. Finite Element 5, 1995, 497-554.

    Google Scholar 

  10. Hairier, E. and Wanner, G., Solving Ordinary Differential Equations: Stiff and Differential-Algebraic Problems, Springer-Verlag, Berlin, 1991.

    Google Scholar 

  11. Hughes, T.J.R., ‘Stablity, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics’,Comput. & Structures 6, 1976, 313-324.

    Google Scholar 

  12. Hughes, T.J.R., Caughey,T.K. and Liu, W.K., ‘Finite element methods for nonlinear elastodynamics which conserve energy’, ASME J. Appl. Mech. 45, 1978, 366-370.

    Google Scholar 

  13. Ibrahimbegovi?, A., ‘Stress resultant geometrically nonlinear shell theory with drilling rotations. Part 1: A consistent formulation’, Comput. Methods Appl. Mech. Engrg. 118, 1994, 265-284.

    Google Scholar 

  14. Ibrahimbegovi?, A., ‘Finite elastic deformation and finite rotation of 3d continumum with independent rotation field’, European J. Finite Element 4, 1995, 555-576.

    Google Scholar 

  15. Ibrahimbegovi?, A., ‘On finite element implementation of geometrically nonlinear Reissner's beam theory: Three dimensional curved beam element’, Comput. Methods Appl. Mech. Engrg. 112, 1995, 11-26.

    Google Scholar 

  16. Ibrahimbegovi?, A., ‘On the choice of finite rotation parameters’, Comput. Methods Appl. Mech. Engrg. 149, 1997, 49-71.

    Google Scholar 

  17. Ibrahimbegovi?, A., Frey F. and Kozar, I., ‘Computational aspect of vector-like parameterization of three dimensional finite rotations’, Internat. J. Numer. Methods. Engrg. 38, 1995, 3653-3673.

    Google Scholar 

  18. Ibrahimbegovi?, A. and Almikdad, M., ‘Finite rotations in dynamics of beams and implicit time-stepping schemes’, Internat. J. Numer. Methods Engrg. 41, 1998, 781-814.

    Google Scholar 

  19. Ibrahimbegovi?, A. and Mamouri, S., ‘On rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3d geometrically exact beam model’, Comput. Methods Appl. Mech. Engrg., 1998, in press.

  20. Ider, S.K. and Amirouche, F.M.L., ‘Nonlinear modeling of flexible multibody system dynamics subjected to variable constraints’, J. Appl. Mech. 56, 1989, 444-450.

    Google Scholar 

  21. Kane, T.R. and Levinson, D.A., Dynamics Theory and Applications, Mc-Graw Hill, New York, 1985.

    Google Scholar 

  22. Kane, T.R. and Levinson, D.A., ‘Simulation of large motions of nonuniform beams in orbit, Parts I and II’, Internat. J. Astro. Sci. 29, 1981, 213-276.

    Google Scholar 

  23. Kuhl, D. and Ramm, E., ‘Constraint energy-momentum algorithm and its application to nonlinear dynamics of shells’, Comput. Methods Appl. Mech. Engrg. 136, 1996, 293-315.

    Google Scholar 

  24. Love, E.H., A Treatise of the Mathematical Theory of Elasticity, Dover, New York, 1940.

    Google Scholar 

  25. Marsden, J.E., Lectures on Mechanics, Cambridge university Press, Cambridge, 1991.

    Google Scholar 

  26. Reissner, E., ‘On one dimensional large-displacement finite strain beam theory’, Structural Appl. Math. 52, 1973, 87-95.

    Google Scholar 

  27. Simo, J.C., ‘A finite strain beam formulation. Part 1’, Comput. Methods Appl. Mech. Engrg. 49, 1981, 53-70.

    Google Scholar 

  28. Simo, J.C., Tarnow, N. and Doblare, M., ‘Nonlinear dynamics of three-dimensional rods: Exact energy and momentum conserving algorithm’, Internat. J. Numer. Methods Engrg. 38, 1995, 1431-1473.

    Google Scholar 

  29. Simo, J.C. and Vu-Quoc, L., ‘A three dimensional finite strain rod model' Part 2: Computational aspect’, Comput. Methods Appl. Mech. Engrg. 58, 1986, 79-116.

    Google Scholar 

  30. Simo, J.C. and Vu-Quoc, L., ‘On the dynamics in space of rods undergoing large motions-A geometrically exact approach’, Comput. Methods Appl. Mech. Engrg. 66, 1988, 125-161.

    Google Scholar 

  31. Taylor, R.L. and Chen, A.J., ‘Analysis of rigid flexible structural components’, IACM Expressions 4, 1997, 8-11.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ibrahimbegović, A., Mamouri, S., Taylor, R.L. et al. Finite Element Method in Dynamics of Flexible Multibody Systems: Modeling of Holonomic Constraints and Energy Conserving Integration Schemes. Multibody System Dynamics 4, 195–223 (2000). https://doi.org/10.1023/A:1009867627506

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009867627506

Navigation