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Multibody System Dynamics

, Volume 43, Issue 1, pp 1–19 | Cite as

Interface reduction of linear mechanical systems with a modular setup

  • Philip Holzwarth
  • Nadine Walker
  • Peter Eberhard
Article
  • 165 Downloads

Abstract

The modular design of technical products offers many advantages. For example, development costs can be reduced if single problem-solving components can be reused in various settings. Taking the same approach in a simulative environment leads to substructured models, such as in elastic multibody systems or substructured finite-element models. To reduce simulation times, model order reduction is applied to each component of the system. The goal is to store reduced models that may be reused in various settings in a common database. The more precise the information about acting forces on the models is, the more modern model order reduction schemes, like moment matching with Krylov subspace methods, can make use of their inherent advantages. If the separate components are connected at many points, then the straightforward application of block Krylov methods leads to large reduced systems. Therefore, the “exact” information about the interfaces, that is, all admissible directions of force application, must be reduced to the most important ones. The novel contribution in this paper is a unifying framework for interface reduction techniques applied to substructured systems. The presented reduction technique is able to provide models for a database and can be automatized. Besides the theoretical derivation of the method, a numerical benchmark model is evaluated, and benefits and drawbacks are discussed.

Keywords

Model order reduction Substructured systems Krylov subspace methods Interface reduction 

Notes

Acknowledgements

The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Collaborative Research Centre SFB 1244 B1 at the University of Stuttgart. A previous version of this paper was presented at the IMSD conference 2016 in Montreal [28]. The authors want to thank the organizers for inviting this extended and revised paper for this journal.

References

  1. 1.
    Volkswagen AG: Das ist der MQB—Mehr Effizienz in jeder Hinsicht. Viavision 2, 2 (2012) (in German) Google Scholar
  2. 2.
    Lehner, M.: Modellreduktion in elastischen Mehrkörpersystemen. Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, vol. 10. Shaker Verlag, Aachen (2007) (in German) Google Scholar
  3. 3.
    Salimbahrami, S.B.: Structure preserving order reduction of large scale second order models. Doctoral thesis, Technische Universität München (2005) Google Scholar
  4. 4.
    Holzwarth, P., Eberhard, P.: SVD-based improvements for component mode synthesis in elastic multibody systems. Eur. J. Mech. A, Solids 49, 408–418 (2015) MathSciNetCrossRefGoogle Scholar
  5. 5.
    Holzwarth, P., Eberhard, P.: Interface reduction for CMS methods and alternative model order reduction. In: Proceedings of the MATHMOD 2015—8th Vienna International Conference on Mathematical Modelling, Vienna, Austria (2015) Google Scholar
  6. 6.
    Siemens AG NX: NX Nastran 11: Quick Reference Guide. Siemens Product Lifecycle Management Software Inc., Plano (2016) Google Scholar
  7. 7.
    Ansys: ANSYS, Academic Research, Release 17.0, Ansys Help System. ANSYS, Inc., Canonsburg (2015) Google Scholar
  8. 8.
    Benner, P., Schneider, A.: Model order and terminal reduction approaches via matrix decomposition and low rank approximation. In: Roos, J., Costa, L. (eds.) Scientific Computing in Electrical Engineering (SCEE 2008). Mathematics in Industry, pp. 523–530. Springer, Berlin (2009) Google Scholar
  9. 9.
    Lutowska, A.: Model order reduction for coupled systems using low-rank approximations. Ph.D. thesis, Eindhoven University of Technology (2012) Google Scholar
  10. 10.
    Fischer, M., Eberhard, P.: Linear model reduction of large scale industrial models in elastic multibody dynamics. Multibody Syst. Dyn. 31(1), 27–46 (2014) MathSciNetCrossRefGoogle Scholar
  11. 11.
    Shabana, A.A.: Dynamics of Multibody Systems, 3rd edn. Cambridge University Press, New York (2005) CrossRefzbMATHGoogle Scholar
  12. 12.
    Craig, R.: Coupling of substructures for dynamic analyses: an overview. In: Proceedings of the AIAA Dynamics Specialists Conference, Atlanta, April 5, 2000, Paper-ID 2000-1573 Google Scholar
  13. 13.
    Benner, P., Saak, J.: Efficient balancing-based MOR for second order systems arising in control of machine tools. In: Troch, I., Breitenecker, F. (eds.) Proceedings of the MATHMOD 2009. ARGESIM Reports, vol. 35, pp. 1232–1243 (2009) Google Scholar
  14. 14.
    Fehr, J., Fischer, M., Haasdonk, B., Eberhard, P.: Greedy-based approximation of frequency-weighted Gramian matrices for model reduction in multibody dynamics. Z. Angew. Math. Mech. 93(8), 501–519 (2012) MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Fischer, M., Eberhard, P.: Simulation of moving loads in elastic multibody systems with parametric model reduction techniques. Arch. Mech. Eng. 61(2), 209–226 (2014) CrossRefGoogle Scholar
  16. 16.
    Grimme, E.: Krylov projection methods for model reduction. Ph.D. thesis, University of Illinois at Urbana-Champaign (1997) Google Scholar
  17. 17.
    Bai, Z., Su, Y.: Dimension reduction of large-scale second-order dynamical systems via a second-order Arnoldi method. SIAM J. Sci. Comput. 26(5), 1692–1709 (2005) MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Chu, C.C., Tsai, H.C., Lai, M.H.: Structure preserving model-order reductions of MIMO second-order systems using Arnoldi methods. Math. Comput. Model. 51(7–8), 956–973 (2010) MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Holzwarth, P., Eberhard, P.: Interpolation and truncation model reduction techniques in coupled elastic multibody systems. In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics, Barcelona, Spain (2015) Google Scholar
  20. 20.
    Donders, S., Pluymers, B., Ragnarsson, P., Hadjit, R., Desmet, W.: The wave-based substructuring approach for the efficient description of interface dynamics in substructuring. J. Sound Vib. 329(8), 1062–1080 (2010) CrossRefGoogle Scholar
  21. 21.
    Nowakowski, C., Fehr, J., Eberhard, P.: Einfluss von Schnittstellenmodellierungen bei der Reduktion elastischer Mehrkörpersysteme. Automatisierungstechnik 59(8), 512–519 (2011) (in German) CrossRefGoogle Scholar
  22. 22.
    Fehr, J., Holzwarth, P., Eberhard, P.: Interface and model reduction for efficient explicit simulations—a case study with nonlinear vehicle crash models. Math. Comput. Model. Dyn. Syst. 22, 380–396 (2016) MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Schurr, D., Holzwarth, P., Ziegler, P., Eberhard, P.: Computational vibration analysis of elastic gears in vehicles using different reduction methods and nodal contact calculation. In: 22nd International Congress on Sound and Vibration, Florence, Italy (2015) Google Scholar
  24. 24.
    Hanss, M., Willner, K., Guidati, S.: On applying fuzzy arithmetic to finite element problems. In: Proc. of the 17th International Conference of the North American Fuzzy Information Processing Society (NAFIPS 98), Pensacola Beach, USA, pp. 365–369 (1998). Google Scholar
  25. 25.
    Walz, N., Fischer, M., Hanss, M., Eberhard, P.: Uncertainties in multibody systems—potentials and challenges. In: 4th International Conference on Uncertainty in Structural Dynamics (USD), Leuven, Belgium (2012) Google Scholar
  26. 26.
    Golub, G.H., van Loan, C.F.: Matrix Computations, 4th edn. The Johns Hopkins University Press, Baltimore (2013) zbMATHGoogle Scholar
  27. 27.
    Allemang, R.: The modal assurance criterion—20 years of use and abuse. In: Proceedings of the 20th International Modal Analysis Conference, Los Angeles, USA, pp. 14–21 (2002) Google Scholar
  28. 28.
    Holzwarth, P., Eberhard, P.: Interface reduction of substructured mechanical systems. In: Proceedings International Conference on Multibody System Dynamics, Montreal, Canada (2016) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

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

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