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Distributed Deformation: a Finite Element Method

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Advanced Design of Mechanical Systems: From Analysis to Optimization

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

Abstract

The finite element method has been established as the most important computational procedure to describe deformations of structural systems. But, the limitation of the finite element method to describe large deformations accurately is also well known. The use of multibody dynamics is the most general and accurate computational methodology to describe the large relative rotations of the systems components. The use of the finite element method in the framework of multibody dynamics leads to the ability to model flexible multibody systems that not only describe the large gross motion of the system components but also their deformations, as those shown in Figure 17.1. Finite element based approaches to describe flexible multibody systems, experiencing small and large deformations and the formulation of kinematic joints are discussed here. Several examples are introduced to be used, later, in optimization of flexible multibody systems.

Selected systems in which the flexibility plays important roles (a) Robot; (b) Road vehicle; (c) Train pantograph

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References

  • Ambrósio, J. Elastic-Plastic Large Deformations of Flexible Multibody Systems In Crash Analysis. Ph.D. Dissertation, University of Arizona, Tucson, Arizona, 1991.

    Google Scholar 

  • Ambrósio, J., and Nikravesh, P. Elastic-plastic deformations in multibody dynamics, Nonlinear Dynamics, 3, 85–104, 1992.

    Article  Google Scholar 

  • Ambrósio, J., and Pereira, M. Flexibility in Multibody Dynamics with Applications to Crashworthiness, In: Computer Aided Analysis of Rigid and Flexible Multibody Systems. Pereira, M., and Ambrósio, J. (Eds.), Kluwer Academic Publisher, Dordrecht, The Netherlands, 199–232, 1994.

    Google Scholar 

  • Ambrósio, J. Dynamics of structures undergoing gross motion and nonlinear deformations: a multibody approach. Computer & Structures, 59(6), 1001–1012, 1996.

    Article  MATH  Google Scholar 

  • Ambrósio, J., and Gonçalves, J. Complex flexible multibody systems with application to vehicle dynamics. Multibody Systems Dynamics, 6(2), 163–182, 2001.

    Article  MATH  Google Scholar 

  • Ambrósio, J. Efficient kinematic joints descriptions for flexible multibody systems experienceing linear and non-linear deformations. Int J Nume Meths in Engng, 56, 1771–1793, 2003.

    Article  MATH  Google Scholar 

  • Anantharaman, M., and Hiller, M. Numerical simulation of mechanical systems using methods for differential-algebraic equations. Int J Nume Methods in Engng, 32, 1531–1542, 1991.

    Article  MATH  Google Scholar 

  • Banerjee, A.K., and Nagarajan, S. Efficient simulation of large overall motion of nonlinearly elastic beams. In. Proc. of ESA Int. Workshop on Advanced Mathematical Methods in the Dynamics of Flexible Bodies. ESA, Noordwijk, The Netherlands, June 3–5, 3–23, 1996.

    Google Scholar 

  • Bathe, K.-J., and Bolourchi, S. Large displacement analysis of three-dimensional beam structures. Int J Nume Methods in Engng, 14, 961–986, 1979.

    Article  MATH  Google Scholar 

  • Belytschko, T., and Hsieh, B.J. Nonlinear transient finite element analysis with convected coordinates. Int J Nume Methods in Engng, 7, 255–271, 1973.

    Article  MATH  Google Scholar 

  • Cardona, A., and Geradin, M. A beam finite element non linear theory with finite rotations. Int. J. Nume Methods in Engng, 26, 2403–2438, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  • Cavin, R.K., and Dusto, A.R. Hamilton’s principle: finite element methods and flexible body dynamics. AIAA Journal, 15(12), 1684–1690, 1977.

    Article  MATH  Google Scholar 

  • Chang, B., and Shabana, A., Nonlinear finite element formulation for large displacement analysis of plates. ASME J. Appl. Mech, 57, 707–718, 1990.

    Article  MATH  Google Scholar 

  • Chu, S.-C., and Pan, K.C. Dynamic response of a high-speed slider-crank mechanism with an elastic connecting rod. ASME J. Engineering for Industry, B97 542–550, 1975.

    Google Scholar 

  • Erdman, A., and Sandor, G. Kineto-elastodynamics — a review of the state of the art and trends. Mech. Mach. Theory, 7, 19–33, 1972.

    Article  Google Scholar 

  • Geradin, M., and Cardona, A. A modelling of superelements in mechanism analysis, Int. J. Nume Methods in Engng, 32, 1565–1594, 1991.

    Article  MATH  Google Scholar 

  • Geradin, M. Advanced methods in flexible multibody dynamics: review of element formulations and reduction methods. In: Proc. of ESA Int. Workshop on Adv. Math Methods in the Dynamics of Flexible Bodies. ESA, Noordwijk, Netherlands, June 3–5, 83–106, 1996.

    Google Scholar 

  • Gonçalves, J., and Ambrósio, J. Advanced modelling of flexible multibody systems using virtual bodies. In: Proceedings of the NATO-ARW on Computational Aspects of Nonlinear Structural Systems with Large Rigid Body Motion., Ambrósio, J., and Kleiber, M. (Eds.), Pultusk, Poland, July 2–7, 359–374, 2000.

    Google Scholar 

  • Gonçalves, J., and Ambrósio, J. Advanced modeling of flexible multibody dynamics using virtual bodies. Comp. Assisted Mechanics and Engng Sciences, 9(3), 373–390, 2002.

    MATH  Google Scholar 

  • Kane, T., Ryan, R., and Banerjee, A. Dynamics of cantilever beam attached to a moving base. AIAA J of Guidance Control and Dynamics, 10, 139–151, 1987.

    Article  Google Scholar 

  • Lowen, G., and Chassapis, C. Elastic behavior of linkages: an update. Mech. Mach. Theory, 21, 33–42, 1986.

    Article  Google Scholar 

  • Meijaard, J.P. Validation of flexible beam elements in dynamics programs. Nonlinear Dynamics, 9, 21–36, 1996.

    Article  Google Scholar 

  • Meirovitch, L., and Nelson, H. On the high-spin motion of a satellite containing elastic parts. Journal of Spacecrafts and Rockets, 3, 1597–1602, 1966.

    Article  Google Scholar 

  • Melzer, F. Symbolisch-numerische Modellierung Elastischer Mehrkorpersysteme mit Answendung auf Rechnerische Lebensdauervorhrsagen. PhD. Thesis, University of Stuttgart, Stuttgart, Germany, 1994.

    Google Scholar 

  • Melzer, F. Symbolic computations in flexible multibody systems. Nonlinear Dynamics, 9, 147–163, 1996.

    Article  Google Scholar 

  • Modi, V.J., Suleman, A., and Ng, A.C. An approach to dynamics and control of orbiting flexible structures. Int J Nume Methods in Engng, 32, 1727–1748, 1991.

    Article  MATH  Google Scholar 

  • Nikravesh, P., and Lin, Y.-S. Body reference frames in deformable multibody systems. Int. J. for Multiscale Computational Engineering, 1, 1615–1683, 2003.

    Google Scholar 

  • Pereira, M., and Proença, P. Dynamic analysis of spatial flexible multibody systems using joint co-ordinates. Int J Nume Methods in Engng, 32, 1799–1812, 1991.

    Article  MATH  Google Scholar 

  • Shabana, A. Dynamic Analysis of Large Scale Inertia Variant Flexible Mechanisms. Ph.D. Thesis, Iowa City, Iowa: University of Iowa, 1982.

    Google Scholar 

  • Shabana, A. Dynamics of Multibody Systems. John Wiley & New York, New York, 1989.

    Google Scholar 

  • Shabana, A., and Wehage, R. A coordinate reduction technique for transient amalysis os spatial structures with large angular rotations. J. of Struct. Mech., 11, 401–431, 1989.

    Google Scholar 

  • Shabana, A. Definition of the slopes and the finite element absolute nodal coordinate formulation. Multibody System Dynamics, 1, 339–348, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  • Simo, J.C., and Vu-Quoc, L. On the dynamics in space of rods undergoing large motions — a geometrically exact approach. Comp. Methods Appl. Mech. Eng, 66, 125–161, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  • Song, J., and Haug, E.J. Dynamic analysis of planar flexible mechanisms. Computer Methods in Applied Mechanics and Engineering, 24, 359–381, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  • Spanos, J. and Tsuha, W., Selection of component modes for flexible multibody simulation, J. Guidance, Control and Dynamics, 14, 278–286, 1991.

    Article  Google Scholar 

  • Thompson, B., and Sung, G. Survey of finite element techniques for mechanism design. Mech. Mach. Theory, 21, 351–359, 1986.

    Article  Google Scholar 

  • Yoo, W.S., and Haug, E.J. Dynamics of flexible mechanical systems using vibration and static correction modes. ASME J. of Mech, Trans and Autom in Design, 108, 315–322, 1986.

    Google Scholar 

  • Wallrapp, O., and Schwertassek, R. Representation of Geometric stiffening in multibody system simulation. Int. J. Nume. Methods Engng, 32, 1833–1850, 1991.

    Article  MATH  Google Scholar 

  • Wu, S.C., and Haug, E.J. A Substructure Methods for the Dynamic Simulation of Flexible Mechanical Systems with Geometric Nonlinearities. CCAD Technical Report 87–7, Center for Computer Aided Design, University of Iowa, Iowa City, Iowa, 1987.

    Google Scholar 

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Author information

Authors and Affiliations

  1. IDMEC, Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal

    Jorge Ambrósio

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  1. Jorge Ambrósio
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Editors and Affiliations

  1. Idmec, Instituto Superior Técnico, Technical University of Lisbon, Portugal

    Jorge A. C. Ambrósio

  2. Institute of Engineering and Computational Mechanics, University of Stuttgart, Germany

    Peter Eberhard

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Ambrósio, J. (2009). Distributed Deformation: a Finite Element Method. In: Ambrósio, J.A.C., Eberhard, P. (eds) Advanced Design of Mechanical Systems: From Analysis to Optimization. CISM International Centre for Mechanical Sciences, vol 511. Springer, Vienna. https://doi.org/10.1007/978-3-211-99461-0_17

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  • DOI: https://doi.org/10.1007/978-3-211-99461-0_17

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-99460-3

  • Online ISBN: 978-3-211-99461-0

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