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Stress recovery with Krylov-subspaces in reduced elastic multibody systems

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Abstract

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.

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References

  1. Arczewski, K., Fraczek, J.: Friction models and stress recovery methods in vehicle dynamics modelling. Multibody Syst. Dyn. 14(3), 205–224 (2005)

    Article  MATH  Google Scholar 

  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)

  3. Dietz, S.: Vibration and fatigue analysis of vehicle systems using component modes. VDI Fortschritt-Berichte, Reihe 12, Nr. 401. VDI Verlag, Düsseldorf (1999)

  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. Claus, H.: A deformation approach to stress distribution in flexible multibody systems. Multibody Syst. Dyn. 6(2), 143–161 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Lehner, M., Eberhard, P.: A two-step approach for model reduction in flexible multibody dynamics. Multibody Syst. Dyn. 17(2), 157–176 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Koutsovasilis, P., Beitelschmidt, M.: Comparison of model reduction techniques for large mechanical systems. Multibody Syst. Dyn. 20(2), 111–128 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Schwertassek, R., Wallrapp, O.: Dynamik flexibler Mehrkörpersysteme. Vieweg, Braunschweig (1999)

    Google Scholar 

  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)

  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)

  11. Intec GmbH: SIMPACK FEMBS, Reference Guide, SIMPACK Version 8.901b. Wessling (2009)

  12. Lohmann, B., Salimbahrami, B.: Ordnungsreduktion mittels Krylov-Unterraummethoden. at-Automatisierungstechnik 52, 30–38 (2004)

    Article  Google Scholar 

  13. Bai, Z.: Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Appl. Numer. Math. 43, 9–44 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Salimbahrami, B.: Structure preserving order reduction of large scale second order models. Dissertation, Technische Universität München (2005)

  15. Craig, R.: Coupling of substructures for dynamic analysis: an overview. AIAA Paper, 2000-1573 (2005)

  16. Craig, R., Kurdila, A.: Fundamentals of Structural Dynamics. Wiley, New York (2006)

    MATH  Google Scholar 

  17. Koutsovasilis, P.: Model order reduction in structural mechanics. VDI Fortschritt-Berichte, Reihe 12, Nr. 712. VDI Verlag, Düsseldorf (2009)

  18. Bathe, K.-J.: Finite Element Procedures. Prentice-Hall, Upper Saddle River (1996)

    Google Scholar 

  19. Knothe, K., Wessels, H.: Finite Elemente: Eine Einführung für Ingenieure. Springer, Berlin (1999)

    MATH  Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

  22. Intes GmbH: PERMAS, User’s Reference Manual, PERMAS Version 11.00.445, INTES Publication No. 450. Stuttgart (2006)

  23. Siemens PLM Software: NX Nastran, User’s Guide, NX Nastran Version 6.0. Plano (2008)

  24. Intec GmbH: SIMPACK, Reference Guide, SIMPACK Version 8.901b. Wessling (2009)

  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)

    Article  MATH  Google Scholar 

  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 

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Authors and Affiliations

  1. Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany

    Christoph Tobias & Peter Eberhard

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  1. Christoph Tobias
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  2. Peter Eberhard
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Correspondence to Peter Eberhard.

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Tobias, C., Eberhard, P. Stress recovery with Krylov-subspaces in reduced elastic multibody systems. Multibody Syst Dyn 25, 377–393 (2011). https://doi.org/10.1007/s11044-010-9239-2

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