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Composite rigid body formalism for flexible multibody systems

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Abstract

The paper describes the extension of the composite rigid body formalism for the flexible multibody systems. The extension has been done in such a way that all advantages of the formalism with respect to the coordinates of large motion of rigid bodies are extended to the flexible degrees of freedom, e.g. the same recursive treatment of both coordinates and no appearance of O(n 3) computational complexity terms due to the flexibility. This extension has been derived for both open loop and closed loop systems of flexible bodies. The comparison of the computational complexity of this formalism with other known approaches has shown that the described formalism of composite rigid body and the residual algorithm based on it are more efficient formalisms for small number of bodies in the chains and deformation modes than the usual recursive formalism of articulated body inertia.

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References

  1. Ambrosio, J.A.C.: Geometric and material nonlinear deformations in flexible multibody systems. In: Ambrosio, J.A.C., Kleiber, M. (eds.) Computational Aspects of Nonlinear Structural Systems With Large Rigid Body Motion, pp. 3–28. IOS Press, Amsterdam (2001)

    Google Scholar 

  2. Andrzejewki, T., Bock, H.G., Eich, E., Schwerin, R.: Recent Advances in the Numerical Integration of Multibody Systems. Kluwer Academic, Dordrecht (1993)

    Google Scholar 

  3. Bae, D.S., Haug, E.J.: A recursive formulation for constrained mechanical system dynamics, part I: open loop systems. Mech. Struct. Mach. 15(3), 359–382 (1987)

    Article  Google Scholar 

  4. Bae, D.S., Haug, E.J.: A recursive formulation for constrained mechanical system dynamics, part II: closed loop systems. Mech. Struct. Mach. 15(4), 481–506 (1987)

    Article  Google Scholar 

  5. Bathe, K.J., Wilson, E.L.: Numerical Methods in Finite Element Analysis. Prentice-Hall, New York (1976)

    MATH  Google Scholar 

  6. Eichberger, A., Fuhrer, C., Schwertassek, R.: The Benefits of Parallel Multibody Simulation and Its Application to Vehicle Dynamics. Kluwer Academic, New York (1993)

    Google Scholar 

  7. Featherstone, R.: Robot Dynamics Algorithms. Kluwer Academic, Dodrecht (1993)

    Google Scholar 

  8. Friberg, O.: A method for selecting deformation modes in flexible multibody dynamics. Int. J. Numer. Methods Eng. 32, 1637–1655 (1991)

    Article  Google Scholar 

  9. García de Jalón, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems. Springer, Berlin (1994)

    Google Scholar 

  10. Gerstmayr, J., Schoberl, J.: A 3D finite element method for flexible multibody systems. Multibody Syst. Dyn. 15(4), 305–320 (2006)

    Article  MathSciNet  Google Scholar 

  11. Kim, S.S., Shabana, A.A., Haug, E.J.: Automated vehicle dynamic analysis with flexible components. Trans. ASME 106, 126–132 (1984)

    Google Scholar 

  12. Kim, S.S., Haug, E.J.: A recursive formulation for flexible multibody dynamics, part I: open-loop systems. Comput. Methods Appl. Mech. Eng. 71, 293–314 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kim, S.S., Haug, E.J.: A recursive formulation for flexible multibody dynamics, part II: closed-loop systems. Comput. Methods Appl. Mech. Eng. 74, 251–269 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  14. Rulka, W.: Effiziente Simulation der Dynamik mechatronischer Systeme für industrielle Anwendungen. PhD thesis TU Vienna, DLR-IB 532-01-06, 350 S (1998)

  15. Shabana, A.A., Wehage, R.A.: A coordinate reduction technique for dynamic analysis of spatial substructures with large angular rotations. J. Struct. Mech. 11, 401–431 (1983)

    Google Scholar 

  16. Shabana, A.A., Wehage, R.A.: Spatial transient analysis of inertia-variant flexible mechanical systems. Trans. ASME 106, 172–178 (1984)

    Google Scholar 

  17. Shabana, A.A.: Dynamics of Multibody Systems. Wiley, New York (2005)

    MATH  Google Scholar 

  18. Shabana, A.A.: Constrained motion of deformable bodies. Int. J. Numer. Methods Eng. 32, 1813–1831 (1991)

    Article  MATH  Google Scholar 

  19. Stejskal, V., Valasek, M.: Kinematics and Dynamics of Machinery. Dekker, New York (1996)

    Google Scholar 

  20. Schwertassek, R., Wallrapp, O.: Dynamik Flexibler Mehrkörpersysteme. Vieweg, Wiesbaden (1999)

    Google Scholar 

  21. Sunada, W., Dubowsky, S.: The application of finite element methods to the dynamic analysis of flexible spatial and co-planar kinkage systems. ASME J. Mech. Des. 103(3), 643–651 (1981)

    Google Scholar 

  22. Unda, J., Garcia de Jalon, J., Losantos, F., Enparantza, R.: A comparative study on some different formulations of the dynamic equations of constrained mechanical systems. J. Mech. Transm. Autom. Des. 109, 466–474 (1987)

    Google Scholar 

  23. Usoro, P.B., Nadira, R., Mahil, S.S.: A finite element-Lagrange approach to modeling lightweight flexible manipulators. Trans. ASME 108, 198–205 (1986)

    Article  MATH  Google Scholar 

  24. Valášek, M., Stejskal, V.: The complete equivalence of Newton–Euler equations of motion and Lagrange’s equations of mixed type. ACTA Technica ČSAV, No. 5, pp. 607–624

  25. Valášek, M.: On the efficient implementation of multibody systems formalism. Research Report IB-17, Institute B of Mechanics, University of Stuttgart, Stuttgart (1990)

  26. Vampola, T.: Efficient algorithm for assembly of equations of motion of multibody systems with consideration of flexibility. PhD thesis, FME CTU in Prague, Prague (1996)

  27. Wehage, R.A., Haug, E.J.: Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems. J. Mech. Des. 104, 247–255 (1982)

    Article  Google Scholar 

  28. Wittbrodt, E., Adamec-Wójcik, I., Wojciech, S.: Dynamics of Flexible Multibody Systems, Rigid Finite Element Method. Springer, Berlin (2006)

    MATH  Google Scholar 

  29. Wu, S.C., Haug, E.J., Kim, S.S.: A variational approach to dynamics of flexible multibody system. Mech. Struct. Mach. 17(1), 3–32 (1989)

    Article  MathSciNet  Google Scholar 

  30. Xie, M.: Flexible Multibody System Dynamics-Theory and Application. Taylor and Francis, London (1994)

    MATH  Google Scholar 

  31. Yoo, W.S., Haug, E.J.: Dynamics of flexible mechanical systems using finite element lumped mass approximation and static correction modes. T.R. 85-7, Center for Computer Aided Design, The University of Iowa, Iowa City (1985)

  32. Znamenáček, J., Valasek, M.: An efficient implementation of the recursive approach to flexible multibody dynamics. Multibody Syst. Dyn. 2, 227–252 (1998)

    Article  MathSciNet  MATH  Google Scholar 

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  1. Department of Mechanics, Biomechanics and Mechatronics, Faculty of Mechanical Engineering, Czech Technical University, Prague, Czech Republic

    T. Vampola & M. Valasek

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  1. T. Vampola
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  2. M. Valasek
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Vampola, T., Valasek, M. Composite rigid body formalism for flexible multibody systems. Multibody Syst Dyn 18, 413–433 (2007). https://doi.org/10.1007/s11044-007-9089-8

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  • DOI: https://doi.org/10.1007/s11044-007-9089-8

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