Skip to main content
SpringerLink
Log in

Dynamics of flexible mechanical systems with contact-impact and plastic deformations

  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

A computer based formulation for the analysis of mechanical systems is investigated as a feasible method to predict the impact response of complex structural systems. A general methodology for the dynamic analysis of rigid-flexible multibody systems using a number of redundant Cartesian coordinates and the method of the Lagrange multipliers is presented. The component mode synthesis is then used to reduce the number of flexible degrees of freedom. In many impact situations, the individual structural members are overloaded giving rise to plastic deformations in highly localized regions, called plastic hinges. This concept is used by associating revolute nonlinear actuators with constitutive relations corresponding to the collapse behavior of the structural components. The contact of the system components is described using a continuous force model based on the Hertz contact law with hysteresis damping. The effect and importance of structural damping schemes in flexible bodies are also addressed here. Finally, the validity of this methodology is assessed by comparing the results of the proposed models with those obtained in different experimental tests where: a beam collides transversally with a rigid block; a torque box impacts a rigid barrier.

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

Access this article

Log in via an institution

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

References

  1. Halquist, J. O., Theoretical Manual for DYNA-3D, University of California, Lawrence Livermore Laboratory, Livermore, CA, 1983.

    Google Scholar 

  2. Haug, E., and Ulrich, D., ‘The PAM-CRASH code as an efficient tool for crashworthiness simulation and design’, in Proceedings of the 2nd European Cars/Trucks Simulation Symposium, M., Heller, Ed., Springer Verlag, Berlin, 1989, 74–87.

    Google Scholar 

  3. ABAQUS, User's Manual, Version 5.2, Hibbit, Karlsson and Sorensen, Inc., 1992.

  4. Kamal, M. M., ‘Analysis and simulation of vehicle to barrier impact’, SAE Transactions 79, 1970, 1453–1467.

    Google Scholar 

  5. Song, J. O., ‘An optimization method for crashworthiness design’, in Proceedings of the Sixth International SAE Conference on Vehicle Structural Mechanics, Detroit, MI, 1986, 39–46.

  6. Nikravesh, P. E. and Chung, I. S., ‘Structural collapse and vehicular crash simulation using hinge technique’, Journal of Structural Mechanics 12–3, 1984, 371–400.

    Google Scholar 

  7. Pereira, M. S., Nikravesh, P., Gim, G., and Ambrósio, J., ‘Dynamic analysis of roll-over and impact of vehicles’, XVIII Bus and Coach Experts Meeting, Budapest, Hungary, 1987.

  8. Ambrósio, J., Nikravesh, P., and Pereira, M. S., ‘Crashworthiness analysis of a truck’, Journal of Mathematical Computer Modelling 14, 1990, 959–964.

    Google Scholar 

  9. Ambrósio, J. and Pereira, M. S., ‘Multibody dynamics in impact and crashworthiness’, in Proceedings of the NATO-ASI Conference on Computer Aided Analysis of Rigid and Flexible Mechanical Systems, I, Tróia, Portugal, 1993, 425–460.

  10. Dias, J. and Pereira, M. S., ‘Design for vehicle crashworthiness using multibody dynamics’, International Journal of Vehicle Design, to appear.

  11. Deck, J. F. and Dubowsky, S., ‘On the limitations of predictions of dynamic response of machines with clearance connections’, in Flexible Mechanisms, Dynamics and Analysis, G., Kinzel, Ed., ASME DE-Vol. 47, The American Society of Mechanical Engineers, New York, 1992, 461–469.

    Google Scholar 

  12. Huang, R. C., Haug, E. J., and Andrews, J. G., ‘Sensitivity analysis and optimal design of a mechanical system with intermittent motion’, ASME Journal of Mechanical Design 100, 1978, 492–499.

    Google Scholar 

  13. Wehage, R. A. and Haug, E. J., ‘Dynamic analysis of mechanical systems with intermittent motion’, ASME Journal of Mechanical Design 104, 1982, 778–784.

    Google Scholar 

  14. Khulief, Y. A. and Shabana, A. A., ‘Dynamic analysis of constrained mechanical systems of rigid and flexible bodies with intermittent motion’, ASME Journal of Mechanical Design 108, 1986, 778–784.

    Google Scholar 

  15. Yigit, A. S., Ulsoy, A. G., and Scott, R. A., ‘Dynamics of a radially rotating beam with impact: Part 1: theoretical and computational model’, ASME Journal of Vibrations and Acoustics 112, 1990, 65–70.

    Google Scholar 

  16. Yigit, A. S., Ulsoy, A. G., and Scott, R. A., ‘Dynamics of a radially rotating beam with impact: Part 2: experimental and simulation results’, ASME Journal of Vibrations and Acoustics 112, 1990, 71–77.

    Google Scholar 

  17. Pereira, M. S. and Nikravesh, P., ‘Impact dynamics of multibody mechanical systems with frictional contact using joint coordinates and canonical equations of motion’, in Proceedings of the NATO-ASI Conference on Computer Aided Analysis of Rigid and Flexible Mechanical Systems, I, Tróia, Portugal, 1993, 505–526.

  18. Wu, S. C., Yang, S. M., and Haug, E. J., ‘Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion’, Mechanism and Machine Theory 21–5, 1986, 401–425.

    Google Scholar 

  19. Wu, S. C. and Haug, E. J., ‘A substructure technique for dynamics of flexible mechanical systems with contact-impact’, ASME Journal of Applied Mechanics 112, 1990, 390–398.

    Google Scholar 

  20. Goldsmith, W., Impact, Edward Arnold Publishers Ltd., London, 1960.

    Google Scholar 

  21. Khulief, Y. A. and Shabana, A. A., ‘A continuous force model for the impact analysis of flexible multibody systems’, Mechanism and Machine Theory 22–3, 1987, 213–224.

    Google Scholar 

  22. Hunt, K. H. and Grossley, F. R., ‘Coefficient of restitution interpreted as damping in vibroimpact’, ASME Journal of Applied Mechanics 97, Series E, 440–445.

  23. Lankarani, H. M. and Nikravesh, P. E., ‘A contact force model with hysteresis damping for impact analysis of multibody systems’, ASME Journal of Mechanical Design 112, 1990, 369–376.

    Google Scholar 

  24. Lankarini, H. M., Canonical Equations of Motion and Estimation of Parameters in the Analysis of Impact Problems, Ph. D. Dissertation, Dept. of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona, 1988.

  25. Trabia, M., ‘A continuous force model for elastic-plastic impact of solids’, in Advances in Design Automation, B. J., Gilmore, Ed., ASME DE-Vol. 65–1, The American Society of Mechanical Engineers, New York, 1993, 687–692.

    Google Scholar 

  26. Peng, K. C. and Liou, F. W., ‘A survey of the experimental studies on flexible fechanisms’, in Flexible Mechanism, Dynamics and Robot Trajectories, S., Derby, Ed., ASME DE-Vol. 24, The American Society of Mechanical Engineers, New York, 1990, 161–168.

    Google Scholar 

  27. Karkoub, M. and Erdman, A. G., ‘Experimental structural damping analysis in high speed elastic mechanisms’, in Flexible Mechanism, Dynamics and Robot Trajectories, S., Derby, Ed., ASME DE-Vol. 24, The American Society of Mechanical Engineers, New York, 1990, 251–258.

    Google Scholar 

  28. Cook, R. D., Malkus, D. S., and Plesha, M. E., Concepts and Applications of Finite Elements Analysis, Wiley, New York, 1989.

    Google Scholar 

  29. Bathe, K. J., Finite Element Procedures in Engineering Analysis, Prentice-Hall, New Jersey, 1982.

    Google Scholar 

  30. Plesha, M. E., ‘Mixed time integration for the transient analysis of jointed media’, International Journal of Numerical Analysis Methods in Geomechanics 10–1, 1986, 91–110.

    Google Scholar 

  31. Shabana, A. A., Dynamics of Multibody Systems, Wiley, New York, 1989.

    Google Scholar 

  32. Benfield, W. A. and Hruda, R. F., ‘Vibration analysis of structures by component mode synthesis’, AIAA Journal 9–7, 1971, 1255–1261.

    Google Scholar 

  33. Shampine, L. F. and Gordon, M. K., Computer Solutions of Differential Ordinary Equations, Prentice Hall, New Jersey, 1975.

    Google Scholar 

  34. Wierzbicki, T. and Akerström, T., ‘Dynamic crushing of strain rate sensitive box columns’, SAE Paper No. 770592, 1977.

  35. Drazetic, P. and Ravalard, Y., Impact d'un Barreau Contre un Massif Rigide, Rapport d`Essai, Laboratoire de Génie Mécanique, Université de Valenciennes, Valenciennes, France, 1991.

    Google Scholar 

  36. Anceau, J. H., Drazetic, P., and Ravalard, Y., ‘Plastic hinges behavior in multibody systems’, Mécanique Matérieux Électricité 44, France, 1992.

  37. Mason, H. L., ‘Impact on beams’, Transactions of the ASME 58, 1935, A55-A61.

    Google Scholar 

  38. Ni, C. M., ‘Impact response of curved box beam-columns with large global and local deformations’, AIAA Paper No. 73-401, 1973.

  39. Anderson, W. J., McIvor, I. K., and Kimball, B. S., ‘Modular program development for vehicle crash simulation, Vol. 2; plastic hinge experiments’, Technical Report DOT-HS-802-531, 1977.

Download references

Author information

Authors and Affiliations

  1. IDMEC-Instituto de Mecânica, Instituto Superior Técnico, Av. Rovisco Pais, 1096, Lisboa CODEX, PORTUGAL

    J. P. Dias & M. S. Pereira

Authors
  1. J. P. Dias
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. S. Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dias, J.P., Pereira, M.S. Dynamics of flexible mechanical systems with contact-impact and plastic deformations. Nonlinear Dyn 8, 491–512 (1995). https://doi.org/10.1007/BF00045710

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00045710

Key words

Search

Navigation