Skip to main content
SpringerLink
Log in

Interpolation-based parametric model order reduction for material removal in elastic multibody systems

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

One essential step in the simulation of elastic multibody systems is the model order reduction of the elastic degrees of freedom. For simulations of material removal, the system matrices can be described as parameter dependent. In this contribution, parametric model reduction methods based on interpolation are applied for this type of problem. Thereby, the interpolation of the reduced system matrices, interpolation of projection matrices, interpolation of subspaces and the interpolation of the transfer functions are investigated. The advantages and disadvantages of these techniques, especially for the application in elastic multibody systems are carved out and illustrated for the manufacturing of a T-shaped workpiece which varies in its thickness due to material removal. In this contribution, we focus on the investigation of the methods in the frequency domain.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Antoulas, A.: Approximation of Large-Scale Dynamical Systems. SIAM, Philadelphia (2005)

    Book  MATH  Google Scholar 

  2. Benner, P., Gugercin, S., Willcox, K.: A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Rev. 57(4), 483–531 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Amsallem, D., Farhat, C.: An interpolation method for adapting reduced-order models and application to aeroelasticity. AIAA J. 46, 1803–1813 (2008)

    Article  Google Scholar 

  4. Burgard, S., Farle, O., Klis, D., Dyczik-Edlinger, R.: Order-reduction of fields-level models with affine and non-affine parameters by interpolation of subspaces. In: 8th Vienna International Conference on Mathematical Modelling, pp. 170–175 (2015)

    Google Scholar 

  5. Panzer, H., Mohring, J., Eid, R., Lohmann, B.: Parametric model order reduction by matrix interpolation. Automatisierungstechnik 58(8), 475–484 (2010)

    Article  Google Scholar 

  6. Amsallem, D., Farhat, C.: An online method for interpolating linear parametric reduced-order models. SIAM J. Sci. Comput. 33, 2169–2198 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fischer, M., Eberhard, P.: Application of parametric model reduction with matrix interpolation for simulation of moving loads in elastic multibody systems. Adv. Comput. Math. 41(5), 1049–1072 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fischer, M., Eberhard, P.: Simulation of moving loads in elastic multibody systems with parametric model reduction techniques. Archive Mech. Eng. 61(2), 209–226 (2014)

    Article  Google Scholar 

  9. Baur, U., Benner, P.: Modellreduktion für parametrisierte Systeme durch balanciertes Abschneiden und Interpolation. Automatisierungstechnik 57(8), 411–419 (2009)

    Article  Google Scholar 

  10. Baumann, M.: Parametrische Modellreduktion in elastischen Mehrkörpersystemen. Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart (2016, submitted for publication) (in German)

  11. 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)

  12. Schwertassek, R., Wallrapp, O.: Dynamik flexibler Mehrkörpersysteme. Vieweg, Braunschweig (1999) (in German)

    Book  Google Scholar 

  13. Craig, R.: Coupling of substructures for dynamic analyses: an overview. In: Proceedings of the AIAA Dynamics Specialists Conference, Paper-ID 2000-1573, Atlanta, April 5 (2000)

    Google Scholar 

  14. Fehr, J.: Automated and error-controlled model reduction in elastic multibody systems. Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, vol. 21. Shaker Verlag, Aachen (2011)

  15. Baumann, M., Hamann, D., Eberhard, P.: Time-dependent parametric model order reduction for material-removal simulations. In: Proceedings of the MoRePaS 2015—Model Reduction of Parametrized Systems III (2015)

    Google Scholar 

Download references

Acknowledgements

Part of this research was supported by a grant of the German Research Foundation DFG under EB 195/11-1. This support is highly appreciated. A preliminary version of this paper was published at the ECCOMAS Multibody Conference in Barcelona, Spain and was in the accompanying proceedings. We are grateful to the organisers that they invited a submission of the conference paper in extended and revised form to this journal.

Author information

Authors and Affiliations

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

    Michael Baumann & Peter Eberhard

Authors
  1. Michael Baumann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Eberhard
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Eberhard.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Baumann, M., Eberhard, P. Interpolation-based parametric model order reduction for material removal in elastic multibody systems. Multibody Syst Dyn 39, 21–36 (2017). https://doi.org/10.1007/s11044-016-9516-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-016-9516-9

Keywords

Search

Navigation