Lumped Deformations: a Plastic Hinge Approach

  • Jorge Ambrósio
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 511)


The design requirements of advanced mechanical and structural systems exploit the ease of use of the powerful computational resources available today to create virtual prototyping environments. These advanced simulation facilities play a fundamental role in the study of systems that undergo large rigid body motion while their components experience material or geometric nonlinear deformations, such as vehicles, deployable structures, space satellites, machines operating at high speeds or flexible robot manipulators, some exemplified in Figure 16.1.
Figure 16.1.

Natural biological and artificial engineering systems for which multibody dynamics provide good modeling methodologies


Multibody System Plastic Hinge Vehicle Model Railway Vehicle Multibody Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. ABAQUS 6.5 Users Manual. ABAQUS, Inc. Providence, Richmond, 2004.Google Scholar
  2. Aird, T.J., and Rice, J.R. Systematic search in high dimensional sets. SIAM Journal on Numerical Analysis, 14, 296–312, 1977.zbMATHCrossRefMathSciNetGoogle Scholar
  3. Ambrósio, J., and Nikravesh, P. Elastic-plastic deformation in multibody dynamics. Nonlinear Dynamics, 3, 85–104, 1992.CrossRefGoogle Scholar
  4. Ambrósio, J., Pereira, M., and Dias, J. Distributed and discrete nonlinear deformations on multibody systems. Nonlinear Dynamics. 10(4), 359–379, 1996.CrossRefGoogle Scholar
  5. Ambrósio, J., and Pereira, M. Multibody dynamic tools for crashworthiness and impact. In: Crashworthiness Of Transportation Systems: Structural Impact And Occupant Protection, Ambrósio, J., Pereira, M., and Silva, F., (Eds.), NATO ASI Series E. Vol. 332, Kluwer Academic Publishers, Dordrecht, Netherland, 475–521, 1997.Google Scholar
  6. Ambrósio J. Multibody dynamics tools for structural and biomechanics crashworthiness, Part IV. In: Crashworthiness: Energy Management and Occupant Protection. Ambrósio, J., (Ed.), Springer-Verlag, Wien, Austria, 203–302, 2001.Google Scholar
  7. Ambrósio, J., Carvalho, M., Ruben, N., Veríssimo, P., and Sousa, L. Generic road vehicle model for crashworthiness. In Silva Gomes, J., ed., Proceedings of 5th International Conference on Mechanics and Materials in Design. Porto, Portugal, July 24–26, 2006.Google Scholar
  8. Anceau, J., Drazetic, P., and Ravalard, I. Plastic hinges behaviour in multibody systems, Mécanique Matériaux Électricité, 444, 1992.Google Scholar
  9. Dias, J.P., and Pereira, M.S. Design for vehicle crashworthiness using multibody dynamics. Int. J. of Vehicle Design, 15(6), 563–577, 1994.Google Scholar
  10. Flores, P., Ambrósio, J., Pimenta Claro, J., and Lankarani, H. Kinematics and Dynamics of Multibody Systems with Imperfect Joints: Models and Case Studies. Springer, Dordrecht, The Netherlands, 2008.zbMATHGoogle Scholar
  11. Gear, C.W. Numerical solution of differential-algebraic equations. IEEE Transactions on Circuit Theory, CT-18, 89–95, 1981.Google Scholar
  12. Gielen, A.W.J., Mooi, H.G., and Huibers, J.H.A.M. An optimization methodology for improving car-to-car compatibility. ImechE Transactions, C567/047/2000, 2000.Google Scholar
  13. Gonçalves, J., and Ambrósio, J. Complex flexible multibody systems with application to vehicle dynamics. Multibody System Dynamics, 6(2), 163–182, 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  14. Haug, E.J., and Arora, J.S. Applied Optimal Design. John Wiley and Sons, New York, New York, 1979.Google Scholar
  15. Hertz, H. Gesammelte Werk. Leipzig, Germany, 1895.Google Scholar
  16. Huston, R.L., and Wang, Y. Flexibility effects in multibody systems. In: Computer Aided Analysis Of Rigid And Flexible Mechanical Systems. Pereira, M., and Ambrósio, J., (Eds.), NATO ASI Series E. Vol. 268, Kluwer Academic Publishers, Dordrecht, Netherlands, 351–376, 1994.Google Scholar
  17. Kamal, M. M. Analysis and simulation of vehicle to barrier impact. SAE Paper No. 700414. Society of Automotive Engineers, Warrendale, Pennsylvania, 1970.Google Scholar
  18. Kecman, D. Bending collapse of rectangular and square section tubes. Int. J. of Mech. Sci., 25(9–10), 623–636, 1983.CrossRefGoogle Scholar
  19. Kindervater, C.M. Aircraft and helicopter crashworthiness: design and simulation. In: Crashworthiness Of Transportation Systems: Structural Impact And Occupant Protection, Ambrósio, J., Pereira, M., and Silva, F. (Eds.), NATO ASI Series E. Vol. 332, Kluwer Academic Publishers, Dordrecht, Netherland, 525–577, 1997.Google Scholar
  20. Lankarani, H., and Nikravesh, P. Continuous contact force models for impact analysis in multibody systems. Nonlinear Dynamics, 5, 193–207, 1994.Google Scholar
  21. Lankarani, H.M., Ma, D., and Menon, R. Impact dynamics of multibody mechanical systems and application to crash responses of aircraft occupant/structure. In: Computer Aided Analysis Of Rigid And Flexible Mechanical Systems. Pereira, M., and Ambrósio, J. (Eds.), NATO ASI Series E. Vol. 268, Kluwer Academic Publishers, Dordrecht, Netherlands, 239–265, 1995.Google Scholar
  22. MADYMO Madymo Manuals Version 6.2, TNO MADYMO BV, Delft, The Netherlands, 2004.Google Scholar
  23. Matolesy, M. Crashworthiness of bus structures and rollover protection. In: Crashworthiness Of Transportation Systems: Structural Impact And Occupant Protection, Ambrósio, J., Pereira, M., and Silva, F. (Eds.), NATO ASI Series E. Vol. 332, Kluwer Academic Publishers, Dordrecht, The Netherlands, 321–360, 1997.Google Scholar
  24. Milho, J., Ambrósio, J., and Pereira, M. A multibody methodology for the design of anti-climber devices for train crashworthiness simulation. International Journal of Crashworthiness, 7(1), 7–20, 2002.CrossRefGoogle Scholar
  25. Milho, J., Ambrósio, J., and Pereira, M. Validated multibody model for train crash analysis. International Journal of Crashworthiness, 8(4), 339–352, 2003.CrossRefGoogle Scholar
  26. Milho, J., Ambrósio, J., and Pereira, M. Design of train crash experimental tests by optimization procedures. International Journal of Crashworthiness, 9(5), 483–493, 2004.CrossRefGoogle Scholar
  27. Møller, H., and Lund, E. Shape sensitivity analysis of strongly coupled fluid-structure interaction problems. In: Proceedings of 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, California. AIAA Paper No 2000-4823, 2000.Google Scholar
  28. Møller, H., Lund, E., Ambrósio, J., and Gonçalves, J. Simulation of fluid loaded flexible multiple bodies. Multibody System Dynamics, 13(1), 113–128, 2005.CrossRefGoogle Scholar
  29. Mooi H.G., and Huibers J.H.A.M. Simple and effective lumped mass model for determining kinetics and dynamics of car-to-car crashes. In: Proceedings of the International Crashworthiness Conference. Chirwa, C., and Viano, D. (Eds.), Detroit, Michigan, September 9–11, 1998.Google Scholar
  30. Mooi H.G., Nastic T., and Huibers J.H.A.M. Modelling and optimization of car-to-car compatibility, In: VDI berichte Nr 1471. Delft, The Netherlands, 239–255, 1999.Google Scholar
  31. Murray, N.W. The static approach to plastic collapse and energy dissipation in some thin-walled steel structures, In: Structural Crashworthiness. Jones, N., and Wierzbicki, T. (Eds.), Butterworths, London, United Kingdom, 44–65, 1983.Google Scholar
  32. Nikravesh, P.E., Chung, I.S., and Benedict, R.L. Plastic hinge approach to vehicle simulation using a plastic hinge technique. Computers and Structures, 16, 385–400, 1983.CrossRefGoogle Scholar
  33. Pereira, M., and Dias, J. Analysis and Design for Train Crashworthiness Using Multibody Models, In Proceedings of the WCCMV, Vienna, Austria, July 7–12, 2002.Google Scholar
  34. Pfeiffer, F., and Glocker, C. Multibody Dynamics with Unilateral Contacts. John Wiley and Sons, New York, New York, 1996.zbMATHCrossRefGoogle Scholar
  35. Puppini, R., Diez, M., Avalle, M., Ciglaric, I., and Feist F. Generic Car (FE) Models for Categories Super Minis, Small Family Cars, Large Family Executive Cars, MPV and Heavy Vehicle, Technical Report APROSYS AP-SP7-0029-A, 2005.Google Scholar
  36. SAFETRAIN BRITE/EURAM Project no BE-3092 Mathematical Modelling. SAFETRAIN Technical Report T5.2-F, Gec-Alsthom, Valenciennes, France, 2001.Google Scholar
  37. SAFETRAIN BRITE/EURAM Project no BE-3092 Dynamic Tests, SAFETRAIN Technical Report T8.2-F. Deutsche Bann, Berlin, Germany, 2001.Google Scholar
  38. Shampine L., and Gordon, M. Computer Solution of Ordinary Differential Equations: The Initial Value Problem, San Francisco, California, Freeman, 1975.zbMATHGoogle Scholar
  39. Sousa, L., Veríssimo, P., and Ambrósio, J. Development of generic road vehicle models for crashworthiness. Multibody System Dynamics. 19(1), 135–158, 2008.CrossRefGoogle Scholar
  40. Valasek, M., and Šika, Z. Evaluation of dynamic capabilities of machines and robots. Multibody System Dynamics, 5, 183–202, 2001.CrossRefGoogle Scholar
  41. Wimmer, A. Einfluß der belastungsgeschwindigkeit auf das festigkeits-und verformungsverhalten am beispiel von kraftfarhzeugen. ATZ, 77(10), 281–286, 1977.Google Scholar
  42. Zweep, C.D., and Kellendonk, G. Evaluation of accident parameters in a numerical fleet for assessing Compatibility. Transactions Journal of Passenger Cars — Mechanical Systems. SAE Paper No. 2005-01-070, 2005.Google Scholar
  43. Zweep, C.D., Kellendonk, G., and Lemmen, P. Evaluation of fleet systems model for vehicle compatibility. International Journal of Crashworthiness, 10(5), 483–494, 2005.CrossRefGoogle Scholar

Copyright information

© CISM, Udine 2009

Authors and Affiliations

  • Jorge Ambrósio
    • 1
  1. 1.IDMEC, Instituto Superior TécnicoTechnical University of LisbonLisbonPortugal

Personalised recommendations