Skip to main content
SpringerLink
Log in

Modeling intermittent contact for flexible multibody systems

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper consists of two parts. The first part presents a complementarity based recursive scheme to model intermittent contact for flexible multibody systems. A recursive divide-and-conquer framework is used to explicitly impose the bilateral constraints in the entire system. The presented approach is an extension of the hybrid scheme for rigid multibody systems to allow for small deformations in form of local mode shapes. The normal contact and frictional complementarity conditions are formulated at position and velocity level, respectively, for each body in the system. The recursive scheme preserves the essential characteristics of the contact model and formulates a minimal size linear complementarity problem at logarithmic cost for parallel implementation.

For a certain class of contact problems in flexible multibody systems, the complementarity based time-stepping scheme requires prohibitively small time-steps to retain accuracy. Modeling intermittent contact for this class of contact problems motivated the development of an iterative scheme. The second part of the paper describes this iterative scheme to model unilateral constraints for a multibody system with relatively fewer contacts. The iterative scheme does not require a traditional complementarity formulation and allows the use of any higher order integration methods. A comparison is then made between the traditional complementarity formulation and the presented iterative scheme via numerical examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Wriggers, P.: Finite element algorithms for contact problems. Arch. Comput. Methods Eng. 2(3), 1–49 (1995)

    Article  MathSciNet  Google Scholar 

  2. Hunt, K., Crossley, F.: Coefficient of restitution interpreted as damping in vibroimpact. ASME J. Appl. Mech. 42, 440–445 (1995)

    Google Scholar 

  3. Pereira, M.S., Nikravesh, P.: Impact dynamics of multibody systems with frictional contact using joint coordinates and canonical equations of motion. Nonlinear Dyn. 9, 53–71 (1996)

    Article  Google Scholar 

  4. Pfeiffer, F.: The idea of complementarity in multibody dynamics. Arch. Appl. Mech. 72(11–12), 807–816 (2003)

    MATH  Google Scholar 

  5. Trinkle, J., Zeng, D., Sudarsky, S., Lo, G.: On dynamic multi-rigid-body contact problems with Coulomb friction. Z. Angew. Math. Mech. 77(4), 267–279 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Barhorst, A.A.: On modelling variable structure dynamics of hybrid parameter multibody systems. J. Sound Vib. 209(4), 571–592 (1998)

    Article  Google Scholar 

  7. Pfeiffer, F.B., Glocker, C.: Multibody Dynamics with Unilateral Contacts. Wiley Series in Nonlinear Sciences. Wiley, New York (1996)

    Book  MATH  Google Scholar 

  8. Foerg, M., Pfeiffer, F., Ulbrich, H.: Simulation of unilateral constrained systems with many bodies. Multibody Syst. Dyn. 14, 137–154 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ebrahimi, S.: A contribution to computational contact procedures in flexible multibody systems. Ph.D. thesis, University of Stuttgart (2007)

  10. Ebrahimi, S., Eberhard, P.: On the use of linear complementarity problems for contact of planar flexible bodies. In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics, Madrid, Spain (2005)

  11. Bhalerao, K.D., Anderson, K.S., Trinkle, J.C.: A recursive hybrid time-stepping scheme for intermittent contact in multi-rigid-body dynamics. J. Comput. Nonlinear Dyn. 4(4), 041010 (2009)

    Article  Google Scholar 

  12. Shabana, A.: Flexible multibody dynamics: Review of past and recent developments. Multibody Syst. Dyn. 1(2), 189–222 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Schwertassek, R., Wallrapp, O., Shabana, A.: Flexible multibody simulation and choice of shape functions. Nonlinear Dyn. 20(4), 361–380 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mukherjee, R., Anderson, K.S.: A logarithmic complexity divide-and-conquer algorithm for multi-flexible articulated body systems. Comput. Nonlinear Dyn. 2(1), 10–21 (2007)

    Article  MathSciNet  Google Scholar 

  15. Featherstone, R.: A divide-and-conquer articulated body algorithm for parallel O(log (n)) calculation of rigid body dynamics. Part 1: Basic algorithm. Int. J. Robotics Res. 18(9), 867–875 (1999)

    Article  Google Scholar 

  16. Featherstone, R.: A divide-and-conquer articulated body algorithm for parallel O(log (n)) calculation of rigid body dynamics. Part 2: Trees, loops, and accuracy. Int. J. Robotics Res. 18(9), 876–892 (1999)

    Article  Google Scholar 

  17. Mukherjee, R., Anderson, K.S.: An orthogonal complement based divide-and-conquer algorithm for constrained multibody systems. Nonlinear Dyn. 48(1–2), 199–215 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kane, T.R., Levinson, D.A.: Dynamics: Theory and Application. McGraw-Hill, New York (1985)

    Google Scholar 

  19. Stewart, D.E., Trinkle, J.C.: An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and coulomb friction. Int. J. Numer. Methods Eng. 39, 2673–2691 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  20. Escalona, J., Mayo, J., Dominguez, J.: A critical study of the use of the generalized impulse-momentum balance equations in flexible multibody systems. J. Sound Vib. 217(3), 523–545 (1998)

    Article  Google Scholar 

  21. Escalona, J., Sany, J., Shabana, A.: On the use of the restitution condition in flexible body dynamics. Nonlinear Dyn. 30, 71–86 (2002)

    Article  MATH  Google Scholar 

  22. Ebrahimi, S., Eberhard, P.: A linear complementarity formulation on position level for frictionless impact of planar deformable bodies. Z. Angew. Math. Mech. 86(10), 808–817 (2006)

    Article  MathSciNet  Google Scholar 

  23. Mukherjee, R.M., Anderson, K.S.: Efficient methodology for multibody simulations with discontinuous changes in system definition. Multibody Syst. Dyn. 18, 145–168 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  24. Mukherjee, R.M., Anderson, K.S.: A generalized momentum method for multi-flexible body systems for model resolution change. In: Proceedings of the 12th Conference on Nonlinear Vibrations, Dynamics, and Multibody Systems. Blacksburg, VA (2008)

  25. Botz, M., Hagedorn, P.: Dynamic simulation of multibody systems including planar elastic beams using autolev. Eng. Comput. 14(4), 456–479 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  26. Claus, H.: A deformation approach to stress distribution in flexible multibody systems. Multibody Syst. Dyn. 6, 143–161 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  27. Shabana, A.A., Yakoub, R.Y.: Three dimensional absolute nodal coordinate formulation for beam elements: Theory. J. Mech. Des. 123(4), 606–613 (2001)

    Article  Google Scholar 

  28. Yakoub, R.Y., Shabana, A.A.: Three dimensional absolute nodal coordinate formulation for beam elements: Implementation and applications. J. Mech. Des. 123(4), 614–621 (2001)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Troy, NY, 12180, USA

    Kishor D. Bhalerao & Kurt S. Anderson

Authors
  1. Kishor D. Bhalerao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kurt S. Anderson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kishor D. Bhalerao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bhalerao, K.D., Anderson, K.S. Modeling intermittent contact for flexible multibody systems. Nonlinear Dyn 60, 63–79 (2010). https://doi.org/10.1007/s11071-009-9580-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-009-9580-2

Keywords

Search

Navigation