Advertisement

Multibody System Dynamics

, Volume 12, Issue 4, pp 385–405 | Cite as

Flexible Multibody Systems Models Using Composite Materials Components

  • Maria Augusta Neto
  • Jorge A. C. Ambr’osioEmail author
  • Rog’erio Pereira Leal
Article

Abstract

The use of a multibody methodology to describe the large motion of complex systems that experience structural deformations enables to represent the complete system motion, the relative kinematics between the components involved, the deformation of the structural members and the inertia coupling between the large rigid body motion and the system elastodynamics. In this work, the flexible multibody dynamics formulations of complex models are extended to include elastic components made of composite materials, which may be laminated and anisotropic. The deformation of any structural member must be elastic and linear, when described in a coordinate frame fixed to one or more material points of its domain, regardless of the complexity of its geometry. To achieve the proposed flexible multibody formulation, a finite element model for each flexible body is used. For the beam composite material elements, the sections properties are found using an asymptotic procedure that involves a two-dimensional finite element analysis of their cross-section. The equations of motion of the flexible multibody system are solved using an augmented Lagrangian formulation and the accelerations and velocities are integrated in time using a multi-step multi-order integration algorithm based on the Gear method.

key words

composite material flexible multibody systems elastic coupling mode component synthesis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Shabana, A., ‘Dynamic analysis of large-scale inertia variant flexible systems’, Ph.D. Thesis, University of Iowa, Iowa City, Iowa, 1982.Google Scholar
  2. 2.
    Ambrósio, J. and J. Gonçalves ‘Complex flexible multibody systems with application to vehicle dynamics’, Multibody System Dynamics 6(2), 2001, 163–182.Google Scholar
  3. 3.
    Nikravesh, P., Computer-Aided Analysis of Mechanical Systems, Prentice Hall, Englewood-Cliffs, New Jersey, 1988.Google Scholar
  4. 4.
    Haug, E., Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon, Boston, Massachussetts, 1989.Google Scholar
  5. 5.
    de Jalón, J. and E. Bayo Kinematic and Dynamic Simulation of Multibody Systems : The Real-Time Challenge, Springer-Verlag, New York, 1994.Google Scholar
  6. 6.
    Gonçalves, J. and Ambrósio, J., ‘Advanced modeling of flexible multibody dynamics using virtual bodies’, Computer Assisted Mechanics and Engineering Sciences 93, 2002, 373–390.Google Scholar
  7. 7.
    Bauchau, O. and D. Hodges ‘Analysis of nonlinear multibody systems with elastic couplings’, Multibody System Dynamics 3, 1999, 163–188.Google Scholar
  8. 8.
    Cesnik, C. and Hodges, D., ‘VABS: A new concept for composite rotor blade cross-sectional modeling’, Journal of the American Helicopter Society 42 1, 1997, 27–38.Google Scholar
  9. 9.
    Yoo, W.S. and Haug, E., ‘Dynamics of flexible mechanical systems using vibration and static correction modes’, Journal of Mechanisms, Transmissions and Automation in Design 108, 1986, 315–322.Google Scholar
  10. 10.
    Pereira, M. and Proença, P., ‘Dynamic analysis of spatial flexible multibody systems using joint coordinates’, International Journal for Numerical Methods in Engineering 32, 1991, 1799–1812.Google Scholar
  11. 11.
    Cavin, R. and Dusto, A., ‘Hamilton’s principle: Finite element method and flexible body dynamics’, AIAA Journal 15(12), 1977, 1684–1690.Google Scholar
  12. 12.
    Hodges, D., ‘A review of composite rotor blade modeling’, AIAA Journal 28(3), 1990, 561–565.Google Scholar
  13. 13.
    Reddy, J., Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, Boca Raton, 1997.Google Scholar
  14. 14.
    Batoz, J. and Lardeur, P., ‘Adiscrete shear triangular nine d.o.f. element for the analysis of thick to very thin plates’, International Journal for Numerical Methods in Engineering 28, 1989, 533–560.Google Scholar
  15. 15.
    Lardeur, P., Development e evaluation de Deux elements finits de plaque e coques composites avec influence du cisalhement transversal Ph.D. Thesis, Université de Technologie de Compiègne, France, 1990.Google Scholar
  16. 16.
    Ochoa, O. and Reddy, J., Finite Element Analysis of Composite Laminates, Kluwer AcademicPublishers, Dordrecht, The Netherlands, 1992.Google Scholar
  17. 17.
    Oñate, E., Cálculo de Estruturas por el Método de Elementos Finitos, Segunda Edicion, Centro International de Métodos Numéricos en Ingenierìa, Barcelona, Spain, 1995.Google Scholar
  18. 18.
    Cook, R., Concepts and Applications of Finite Element Analysis, 2nd edn. Wiley and Sons, New York, 1987.Google Scholar
  19. 19.
    Yu, W. and Hodges, D., ‘On Timoshenko-like modeling of initially curved and twisted composite beams’, International Journal of Solids and Structures 39, 2002, 5101–5121.Google Scholar
  20. 20.
    Popescu, B. and Hodges, D. ‘On asymptotically correct Timoshenko-like anisotropic beam theory’, International Journal of Solids and Structures 37, 2000, 535–558.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Maria Augusta Neto
    • 1
  • Jorge A. C. Ambr’osio
    • 2
    Email author
  • Rog’erio Pereira Leal
    • 1
  1. 1.Departamento de Engenharia MecânicaFaculdade de Ciência e Tecnologia da Universidade de Coimbra (Polo II)Coimbra
  2. 2.Instituto de Engenharia MecânicaInstituto Superior TécnicoLisboa

Personalised recommendations