Multibody System Dynamics

, Volume 25, Issue 4, pp 377–393 | Cite as

Stress recovery with Krylov-subspaces in reduced elastic multibody systems

  • Christoph Tobias
  • Peter Eberhard


A method for the recovery of stresses in reduced elastic multibody systems is presented. Elastic coordinates of a flexible body belonging to a reduced elastic multibody system are therefore premultiplied with a matrix of shape functions for stresses. Whereas the classic procedures for stress recovery in elastic multibody systems use shape functions for stresses that belong to eigenmodes and particular modes, this work also investigates shape functions for stresses that are derived from a Krylov-subspace projection. The presented method for stress recovery is implemented in a process chain containing different software tools and allows the evaluation of stresses during the runtime of the elastic multibody simulation. Accordingly, the performance of the developed process is examined with the help of a simple example. Results show that the usage of shape functions for stresses that are derived from a Krylov-subspace projection can improve the approximation of stresses in a user-defined frequency range.


Reduced elastic multibody systems SID file Stress recovery Stress modes Krylov-subspaces 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arczewski, K., Fraczek, J.: Friction models and stress recovery methods in vehicle dynamics modelling. Multibody Syst. Dyn. 14(3), 205–224 (2005) MATHCrossRefGoogle Scholar
  2. 2.
    Melzer, F.: Symbolisch-numerische Modellierung elastischer Mehrkörpersysteme mit Anwendung auf rechnerische Lebensdauervorhersagen (in German). VDI Fortschritt-Berichte, Reihe 11, Nr. 214. VDI Verlag, Düsseldorf (1994) Google Scholar
  3. 3.
    Dietz, S.: Vibration and fatigue analysis of vehicle systems using component modes. VDI Fortschritt-Berichte, Reihe 12, Nr. 401. VDI Verlag, Düsseldorf (1999) Google Scholar
  4. 4.
    Fischer, P., Witteveen, W., Schabasser, M.: Integrated MBS-FE-durability analysis of truck frame components by modal stresses. In: Proceedings of the 15th European ADAMS Users’ Conference, Rome, Italy (2000) Google Scholar
  5. 5.
    Claus, H.: A deformation approach to stress distribution in flexible multibody systems. Multibody Syst. Dyn. 6(2), 143–161 (2001) MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Lehner, M., Eberhard, P.: A two-step approach for model reduction in flexible multibody dynamics. Multibody Syst. Dyn. 17(2), 157–176 (2007) MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Koutsovasilis, P., Beitelschmidt, M.: Comparison of model reduction techniques for large mechanical systems. Multibody Syst. Dyn. 20(2), 111–128 (2008) MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Schwertassek, R., Wallrapp, O.: Dynamik flexibler Mehrkörpersysteme. Vieweg, Braunschweig (1999) Google Scholar
  9. 9.
    Lehner, M.: Modellreduktion in elastischen Mehrkörpersystemen (in German). Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, vol. 10. Shaker Verlag, Aachen (2007) Google Scholar
  10. 10.
    Dietz, S., Knothe, K.: Reduktion der Anzahl der Freiheitsgrade in Finite-Element-Substrukturen (in German). Bericht aus dem Institut für Luft- und Raumfahrttechnik der Technischen Universität Berlin, ILR-Mitteilung 315, Technische Universität Berlin, Institut für Luft- und Raumfahrttechnik (1997) Google Scholar
  11. 11.
    Intec GmbH: SIMPACK FEMBS, Reference Guide, SIMPACK Version 8.901b. Wessling (2009) Google Scholar
  12. 12.
    Lohmann, B., Salimbahrami, B.: Ordnungsreduktion mittels Krylov-Unterraummethoden. at-Automatisierungstechnik 52, 30–38 (2004) CrossRefGoogle Scholar
  13. 13.
    Bai, Z.: Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Appl. Numer. Math. 43, 9–44 (2002) MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Salimbahrami, B.: Structure preserving order reduction of large scale second order models. Dissertation, Technische Universität München (2005) Google Scholar
  15. 15.
    Craig, R.: Coupling of substructures for dynamic analysis: an overview. AIAA Paper, 2000-1573 (2005) Google Scholar
  16. 16.
    Craig, R., Kurdila, A.: Fundamentals of Structural Dynamics. Wiley, New York (2006) MATHGoogle Scholar
  17. 17.
    Koutsovasilis, P.: Model order reduction in structural mechanics. VDI Fortschritt-Berichte, Reihe 12, Nr. 712. VDI Verlag, Düsseldorf (2009) Google Scholar
  18. 18.
    Bathe, K.-J.: Finite Element Procedures. Prentice-Hall, Upper Saddle River (1996) Google Scholar
  19. 19.
    Knothe, K., Wessels, H.: Finite Elemente: Eine Einführung für Ingenieure. Springer, Berlin (1999) MATHGoogle Scholar
  20. 20.
    Fehr, J., Eberhard, P.: Simulation process of flexible multibody dynamics by advanced model order reduction techniques. In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2009, Jume 29–July 2, Warsaw, Poland (2009) Google Scholar
  21. 21.
    Wallrapp, O.: Standardization of flexible body modeling in multibody system codes. Part I: definition of standard input data. Mech. Struct. Mach. 22(3), 283–304 (1994) CrossRefMathSciNetGoogle Scholar
  22. 22.
    Intes GmbH: PERMAS, User’s Reference Manual, PERMAS Version 11.00.445, INTES Publication No. 450. Stuttgart (2006) Google Scholar
  23. 23.
    Siemens PLM Software: NX Nastran, User’s Guide, NX Nastran Version 6.0. Plano (2008) Google Scholar
  24. 24.
    Intec GmbH: SIMPACK, Reference Guide, SIMPACK Version 8.901b. Wessling (2009) Google Scholar
  25. 25.
    Kurz, T., Eberhard, P., Henninger, C., Schiehlen, W.: From Neweul to Neweul-M2: Symbolical equations of motion for multibody system analysis and synthesis. Multibody Syst. Dyn. 24(1), 25–41 (2010) MATHCrossRefGoogle Scholar
  26. 26.
    Eichberger, A., Dietz, S.: Fatigue analysis on a virtual test rig based on multibody simulation. In: Rahnejat, H., Rothberg, S. (eds.) Multi-body Dynamics – Monitoring and Simulation Techniques – III, pp. 73–82. Wiley, New York (2004) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institute of Engineering and Computational MechanicsUniversity of StuttgartStuttgartGermany

Personalised recommendations