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Multibody System Dynamics

, Volume 20, Issue 1, pp 1–28 | Cite as

Three-dimensional formulation of rigid-flexible multibody systems with flexible beam elements

  • D. García-Vallejo
  • J. Mayo
  • J. L. Escalona
  • J. Domínguez
Article

Abstract

Multibody systems generally contain solids with appreciable deformations and which decisively influence the dynamics of the system. These solids have to be modeled by means of special formulations for flexible solids. At the same time, other solids are of such a high stiffness that they may be considered rigid, which simplifies their modeling. For these reasons, for a rigid-flexible multibody system, two types of formulations coexist in the equations of the system. Among the different possibilities provided in the literature on the material, the formulation in natural coordinates and the formulation in absolute nodal coordinates are utilized in this paper to model the rigid and flexible solids, respectively. This paper contains a mixed formulation based on the possibility of sharing coordinates between a rigid solid and a flexible solid. The global mass matrix of the system is shown to be constant and, in addition, many of the constraint equations obtained upon utilizing these formulations are linear and can be eliminated.

Keywords

Rigid-flexible multibody dynamics Natural coordinates Absolute nodal coordinates 

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References

  1. 1.
    Paul, B., Krajcinovic, K.: Computer analysis of machines with planar motion, part 1: kinematics; part 2: dynamics. ASME J. Appl. Mech. 37, 697–712 (1970) Google Scholar
  2. 2.
    Haug, E.J.: Elements and methods of computational dynamics. In: Haug, E.J. (ed.) Computer Aided Analysis and Optimization of Mechanical System Dynamics, pp. 3–38. Springer, Heidelberg (1984) Google Scholar
  3. 3.
    García de Jalón, J., Unda, J., Avello, A., Jiménez, J.M.: Dynamic analysis of three-dimensional mechanisms in natural coordinates. ASME J. Mech. Transm. Autom. Des. 109, 460–465 (1987) Google Scholar
  4. 4.
    García de Jalón, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems–The Real-Time Challenge. Springer, New York (1993) Google Scholar
  5. 5.
    García de Jalón, J., Serna, M.A., Avilés, R.: Computer method for kinematic analysis of lower-pair mechanisms, I. Mech. Mach. Theory 16, 543–556 (1981) CrossRefGoogle Scholar
  6. 6.
    García de Jalón, J., Serna, M.A., Avilés, R.: Computer method for kinematic analysis of lower-pair mechanisms, II. Mech. Mach. Theory 16, 557–566 (1981) CrossRefGoogle Scholar
  7. 7.
    Shabana, A.A.: Computational Dynamics, 2nd edn. Wiley-Interscience, New York (2001) MATHGoogle Scholar
  8. 8.
    Unda, J., García de Jalón, J., Losantos, F., Enparantza, R.: A comparative study on some different formulations of the dynamic equations of constrained mechanical systems. ASME J. Mech. Transm. Autom. Des. 109, 566–474 (1987) Google Scholar
  9. 9.
    Shabana, A.A.: Flexible multibody dynamics: review of past and recent developments. Multibody Syst. Dyn. 1, 189–222 (1997) CrossRefMathSciNetMATHGoogle Scholar
  10. 10.
    Shabana, A.A.: Dynamics of Multibody Systems, 2nd edn. Cambridge University Press, New York (1998) MATHGoogle Scholar
  11. 11.
    Vukasovic, N., Celigueta, J.T., García de Jalón, J.: Flexible multibody dynamics based on a fully Cartesian system of support coordinates. ASME J. Mech. Des. 115, 294–299 (1993) CrossRefGoogle Scholar
  12. 12.
    Mayo, J., Domínguez, J.: Geometrically non-linear formulation of flexible multibody systems in terms of beam elements: geometric stiffness. Comput. Struct. 59, 1039–1050 (1996) CrossRefMATHGoogle Scholar
  13. 13.
    Belytschko, T., Hsieh, B.J.: Non-linear transient finite element analysis with convected co-ordinates. Int. J. Numer. Methods Eng. 7, 255–271 (1973) CrossRefMATHGoogle Scholar
  14. 14.
    Shabana, A.A.: Finite element incremental approach and exact rigid body inertia. ASME J. Mech. Des. 118, 171–178 (1996) CrossRefGoogle Scholar
  15. 15.
    Wasfy, T.M., Noor, A.K.: Computational strategies for flexible multibody systems. Appl. Mech. Rev. 56, 553–613 (2003) CrossRefGoogle Scholar
  16. 16.
    Simo, J.C.: A finite strain beam formulation. The three-dimensional dynamic problem, part I. Comput. Methods Appl. Mech. Eng. 49, 55–70 (1985) CrossRefMATHGoogle Scholar
  17. 17.
    Simo, J.C., Vu-Quoc, L.: A three-dimensional finite-strain rod model, part II: computational aspects. Comput. Methods Appl. Mech. Eng. 58, 79–116 (1986) CrossRefMATHGoogle Scholar
  18. 18.
    Simo, J.C., Vu-Quoc, L.: On the dynamics of flexible beams under large overall motions–The plane case: part I and part II. ASME J. Appl. Mech. 53, 849–863 (1986) MATHCrossRefGoogle Scholar
  19. 19.
    Avello, A.: Dinámica de mecanismos flexibles con coordenadas cartesianas y teoría de grandes deformaciones, PhD thesis, Universidad de Navarra, San Sebastian, Spain (1990) Google Scholar
  20. 20.
    Shabana, A.A., Hussien, H., Escalona, J.L.: Application of the absolute nodal coordinate formulation to large rotation and large deformation problems. ASME J. Mech. Des. 120, 188–195 (1998) CrossRefGoogle Scholar
  21. 21.
    Shabana, A.A.: Computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics. Nonlinear Dyn. 16, 293–306 (1998) CrossRefMathSciNetMATHGoogle Scholar
  22. 22.
    Berzeri, M., Campanelli, M., Shabana, A.A.: Definition of the elastic forces in the finite-element absolute nodal coordinate formulation and the floating frame of reference formulation. Multibody Syst. Dyn. 5, 21–54 (2001) CrossRefMATHGoogle Scholar
  23. 23.
    Berzeri, M., Shabana, A.A.: Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation. J. Sound Vib. 235, 539–565 (2000) CrossRefGoogle Scholar
  24. 24.
    Omar, M., Shabana, A.A.: A two-dimensional shear deformable beam for large rotation and deformation problems. J. Sound Vib. 243, 565–573 (2001) CrossRefGoogle Scholar
  25. 25.
    Yakoub, R.Y., Shabana, A.A.: Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications. ASME J. Mech. Des. 123, 614–621 (2001) CrossRefGoogle Scholar
  26. 26.
    Shabana, A.A., Yakoub, R.Y.: Three-dimensional absolute nodal coordinate formulation for beam elements: theory. ASME J. Mech. Des. 123, 606–613 (2001) CrossRefGoogle Scholar
  27. 27.
    Mikkola, A.M., Shabana, A.A.: A non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications. Multibody Syst. Dyn. 9, 283–309 (2003) CrossRefMathSciNetMATHGoogle Scholar
  28. 28.
    Sopanen, J.T., Mikkola, A.M.: Description of elastic forces in absolute nodal coordinate formulation. Nonlinear Dyn. 34, 53–74 (2003) CrossRefMATHGoogle Scholar
  29. 29.
    Sopanen, J.T., Mikkola, A.M.: Studies on the stiffness properties of the absolute nodal coordinate formulation for three-dimensional beams. In: Proceedings of the ASME DETC&CIE Conference, Chicago, IL (2003). ISBN: 0-7918-3698-3 Google Scholar
  30. 30.
    Dufva, K., Sopanen, J., Mikkola, A.: A two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. J. Sound Vib. 280, 719–738 (2005) CrossRefGoogle Scholar
  31. 31.
    Dmitrochenko, O.N., Pogorelov, D.Yu.: Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody Syst. Dyn. 10, 17–43 (2003) CrossRefMATHGoogle Scholar
  32. 32.
    Dufva, K., Sopanen, J., Mikkola, A.: Three-dimensional beam element based on a cross-sectional coordinate system approach. Nonlinear Dyn. 43, 311–327 (2006) CrossRefMATHGoogle Scholar
  33. 33.
    García-Vallejo, D., Escalona, J.L., Mayo, J., Domínguez, J.: Describing rigid-flexible multibody systems using absolute coordinates. Nonlinear Dyn. 34, 75–94 (2003) CrossRefMATHGoogle Scholar
  34. 34.
    Escalona, J.L., Hussien, H.A., Shabana, A.A.: Application of the absolute nodal coordinate formulation to multibody system dynamic. J. Sound Vib. 214, 833–951 (1998) CrossRefGoogle Scholar
  35. 35.
    Schwab, A.L., Meijaard, J.P.: Comparison of three-dimensional flexible beam elements for dynamic analysis: finite element method and absolute nodal coordinate formulation. In: Proceedings of the ASME DETC Conference, Long Beach, CA (2005). ISBN: 0-7918-3766-1 Google Scholar
  36. 36.
    Sugiyama, H., Gerstmayer, J., Shabana, A.A.: Cross-section deformation in the absolute nodal coordinate formulation. In: Proceedings of the ASME DETC Conference, Long Beach, CA (2005). ISBN: 0-7918-3766-1 Google Scholar
  37. 37.
    García-Vallejo, D., Mayo, J., Escalona, J.L., Domínguez, J.: Efficient evaluation of the elastic forces and the Jacobian in the absolute nodal coordinate formulation. Nonlinear Dyn. 35, 313–329 (2004) CrossRefMATHGoogle Scholar
  38. 38.
    Sugiyama, H., Escalona, J.L., Shabana, A.A.: Formulation of three-dimensional joint constraint using the absolute nodal coordinates. Nonlinear Dyn. 31, 167–195 (2003) CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • D. García-Vallejo
    • 1
  • J. Mayo
    • 1
  • J. L. Escalona
    • 1
  • J. Domínguez
    • 1
  1. 1.Department of Mechanical and Materials EngineeringUniversity of SevilleSevilleSpain

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