Skip to main content
SpringerLink
Log in

Morembs—A Model Order Reduction Package for Elastic Multibody Systems and Beyond

  • Chapter
  • First Online:
Reduced-Order Modeling (ROM) for Simulation and Optimization

Abstract

Many new promising model order reduction (MOR) methods and algorithms were developed during the last decade. Industry and academic research institutions intend to test, validate, compare, and use these new promising MOR techniques with their own models. Therefore, an MOR toolbox bridging the gap between theoretical, algorithmic, and numerical developments to an end-user-oriented program, usable by non-experts, was developed called ‘Model Order Reduction of Elastic Multibody Systems’ (Morembs). A C++ implementation as well as a Matlab implementation including an intuitive graphical user interface is available. Import from various FE programs is possible, and the reduced elastic bodies can be exported to a variety of programs to simulate the compact models. In the course of the various projects, many improvements on the algorithmic side were added. As we learned over the years, there is not one ‘optimal’ MOR method. ‘Optimal’ MOR depends on circumstances, like boundary conditions, excitation spectra, further model usage. The toolbox is now used, e.g., in solid mechanics, biomechanics, vehicle dynamics, control of flexible structures, or crash simulations. In all these use cases, the toolbox allows the user to facilitate their well-known modeling and simulation environment. Only the critical MOR process during preprocessing is performed with Morembs, which helps to compare the various MOR techniques to find the most suited one.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Tobias, C., Fehr, J., Eberhard, P.: Durability-based structural optimization with reduced elastic multibody systems. In: Proceedings of the 2nd International Conference on Engineering Optimization, Paper-ID 1119, Lisbon, Portugal, 6–9 Sept 2010

    Google Scholar 

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

    Book  Google Scholar 

  3. Benner, P., Mehrmann, V., Sorensen, D. (eds.): Dimension Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering, vol. 45. Springer, Berlin (2005)

    Google Scholar 

  4. Schilders, W., van der Vorst, H., Rommes, J. (eds.): Model Order Reduction: Theory, Research Aspects and Applications. Mathematics in Industry, vol. 13. Springer, Berlin (2008)

    MATH  Google Scholar 

  5. 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)

    Google Scholar 

  6. 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 

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

    Book  Google Scholar 

  8. Volzer, T., Eberhard, P.: Arch. Mech. Eng. 63(4) (2016)

    Google Scholar 

  9. 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 

  10. Tobias, C., Matha, D., Eberhard, P.: Durability-based data reduction for multibody system results and its applications. Euromech Newsl. 40, 15–24 (2011)

    Google Scholar 

  11. Tobias, C.: Schädigungsberechnung in elastischen Mehrkörpersystemen (in German). Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, vol. 24. Shaker Verlag, Aachen (2012)

    Google Scholar 

  12. Wengert, N.: Gekoppelte dynamisch-optische Simulation von Hochleistungsobjektiven (in German). Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, vol. 40. Shaker Verlag, Aachen (2015)

    Google Scholar 

  13. Hanss, M., Walz, N.P.: Software FAMOUS. Universität Stuttgart, Institut für Technische und Numerische Mechanik (2015). http://www.itm.uni-stuttgart.de/research/famous. Accessed 08 May 2017

  14. Iroz, I., Hanss, M., Eberhard, P.: Simulation of friction-induced vibrations using elastic multibody models. In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics, Barcelona, Spain (2015)

    Google Scholar 

  15. Antoulas, A.C.: On Pole Placement in Model Reduction, at -. Automatisierungstechnik 55(9), 443–448 (2007)

    Google Scholar 

  16. Fehr, J., Fischer, M., Haasdonk, B., Eberhard, P.: Greedy-based approximation of frequency-weighted gramian matrices for model reduction in multibody dynamics. Zeitschrift für Angewandte Math. Mech. 93(8), 501–519 (2012)

    Article  MathSciNet  Google Scholar 

  17. Gugercin, S., Antoulas, A.C., Beattie, C.A.: \(\cal{H}_2\) model reduction for large-scale linear dynamical systems. SIAM J. Matrix Anal. Appl. 30(2), 609–638 (2008)

    Article  MathSciNet  Google Scholar 

  18. Panzer, H.K.F.: Model order reduction by Krylov subspace methods with global error bounds and automatic choice of parameters. Dissertation, Technische Universität München. Verlag Dr. Hut, München (2014)

    Google Scholar 

  19. Craig, R.: Coupling of substructures for dynamic analyses: an overview. In: Proceedings of the AIAA Dynamics Specialists Conference, Atlanta (2000)

    Google Scholar 

  20. 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)

    Article  Google Scholar 

  21. 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  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  24. Baur, U., Beattie, C., Benner, P., Gugercin, S.: Interpolatory projection methods for parameterized model reduction. SIAM J. Sci. Comput. 33, 2489–2518 (2009)

    Article  MathSciNet  Google Scholar 

  25. Wyatt, S.: Issues in interpolatory model reduction: inexact solves, second-order systems and DAEs. Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, 2012

    Google Scholar 

  26. 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)

    Article  Google Scholar 

  27. Fischer, M., Eberhard, P.: Application of parametric model reduction with matrix interpolation for simulation of moving loads in elastic multibody systems. Adv. Comput. Math., 1–24 (2014)

    Google Scholar 

  28. Baumann, M.: Parametrische Modellreduktion in elastischen Mehrkörpersystemen (in German). Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, vol. 43. Shaker Verlag, Aachen (2016)

    Google Scholar 

  29. Haasdonk, B., Ohlberger, M.: Efficient reduced models and a-posteriori error estimation for parametrized dynamical systems by offline/online decomposition. Math. Comput. Model. Dyn. Syst. 17(2), 145–161 (2011)

    Article  MathSciNet  Google Scholar 

  30. Ruiner, T., Fehr, J., Haasdonk, B., Eberhard, P.: A-posteriori error estimation for second order mechanical systems. Acta Mech. Sin. 28(3), 854–862 (2012)

    Article  MathSciNet  Google Scholar 

  31. Nowakowski, C.: Zur Modellierung und Reduktion elastischer Bauteile unter verteilten Lasten für die Mehrkörpersimulation (in German). Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, vol. 35. Shaker Verlag, Aachen (2014)

    Google Scholar 

  32. Nowakowski, C., Fehr, J., Eberhard, P.: Einfluss von Schnittstellenmodellierungen bei der Reduktion elastischer Mehrkörpersysteme (in German), at -. Automatisierungstechnik 59(8), 512–519 (2011)

    Article  Google Scholar 

  33. 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(4), 380–396 (2016)

    Article  MathSciNet  Google Scholar 

  34. Ihrle, S., Lauxmann, M., Eiber, A., Eberhard, P.: Nonlinear modelling of the middle ear as an elastic multibody system-applying model order reduction to acousto-structural coupled systems. J. Comput. Appl. Math. 246, 18–26 (2012)

    Article  MathSciNet  Google Scholar 

  35. Ihrle, S., Eiber, A., Eberhard, P.: Modeling of the incudo-malleolar joint within a biomechanical model of the human ear. Multibody Syst. Dyn. 39(4), 1–20 (2016)

    MATH  Google Scholar 

  36. Simpack, A.G.: Multibody simulation software (2017). http://www.simpack.com/. Accessed 08 May 2017

  37. FIRST, Simulationstool für elasto-hydrodynamisch gekoppelte Mehrkörpersysteme (in German). IST Ingenieurgesellschaft für Strukturanalyse und Tribologie mb. http://www.ist-aachen.de/first. Accessed 08 May 2017

  38. Nowakowski, C., Fehr, J., Eberhard, P.: Model reduction for a crankshaft used in coupled simulations of engines. In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2011, Brussels, Belgium (2011)

    Google Scholar 

  39. Shiiba, T., Fehr, J., Eberhard, P.: Flexible multibody simulation of automotive systems with non-modal model reduction techniques. Veh. Syst. Dyn. 50(12), 1905–1922 (2012)

    Article  Google Scholar 

  40. Grunert, D., Fehr, J.: Identification of nonlinear behavior with clustering techniques in car crash simulations for better model reduction. Adv. Model. Simul. Eng. Sci. 3(1), 1–19 (2016)

    Google Scholar 

  41. Bohn, B., Garcke, J., Iza-Teran, R., Paprotny, A., Peherstorfer, B., Schepsmeier, U., Thole, C.A.: Analysis of car crash simulation data with nonlinear machine learning methods. Procedia Comput. Sci. 18, 621–630 (2013)

    Article  Google Scholar 

  42. Holzwarth, P., Eberhard, P.: Input-output based model reduction for interconnected systems. Eur. J. Mech. A/Solids 49, 408–418 (2015)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart, the support of this research work within the project EB 195/11-1, FE 1583/2-1, Ei 231/6-1, the FVV (Forschungsvereinigung Verbrennungskraftmaschinen e.V.) with its working groups ‘Optimale FE Reduktion’ and the Automotive Simulation Center Stuttgart (ASCS) for providing partially the funding for this research.

Author information

Authors and Affiliations

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

    Jörg Fehr, Dennis Grunert, Philip Holzwarth, Benjamin Fröhlich, Nadine Walker & Peter Eberhard

Authors
  1. Jörg Fehr
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dennis Grunert
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Philip Holzwarth
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Benjamin Fröhlich
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Nadine Walker
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Peter Eberhard
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jörg Fehr .

Editor information

Editors and Affiliations

  1. Department of Corporate Research, Robert Bosch GmbH, Renningen, Germany

    Winfried Keiper

  2. Interdisciplinary Center for Scientific Computing, Heidelberg University, Heidelberg, Germany

    Anja Milde

  3. Fachbereich Mathematik, Universität Konstanz, Konstanz, Germany

    Stefan Volkwein

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Fehr, J., Grunert, D., Holzwarth, P., Fröhlich, B., Walker, N., Eberhard, P. (2018). Morembs—A Model Order Reduction Package for Elastic Multibody Systems and Beyond. In: Keiper, W., Milde, A., Volkwein, S. (eds) Reduced-Order Modeling (ROM) for Simulation and Optimization. Springer, Cham. https://doi.org/10.1007/978-3-319-75319-5_7

Download citation

Publish with us

Policies and ethics

Search

Navigation