Abstract
In this contribution, coupled, parameterized second order systems are considered where the coupled, parameterized system is derived from the assembly of several parameterized component models. Two approaches for the Parametric Model Order Reduction of such coupled systems are presented and compared in a reduced order shape optimization example. In the first approach, the coupled, parameterized system is derived by coupling the parameterized, full order component models. Then, Parametric Model Order Reduction is executed for the coupled system. In the second approach, the parameterized, component models are first reduced independently of their actual mounting situation. Afterwards, the parameterized, reduced order component models are coupled to derive the parameterized, reduced order system model. It is shown that the first approach yields smaller parameterized, reduced order system models. However, the second approach allows to reuse and to recombine the parameterized, reduced order component models arbitrarily. It therefore introduces more flexibility in the modeling process, enabling for example a toolbox based optimization with parameterized, reduced order models.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bai, Z., Su, Y.: Dimension reduction of large-scale second-order dynamical systems via a second-order Arnoldi method. SIAM J. Sci. Comput. 16, 1692–1709 (2005)
Baur, U., Beattie, C., Benner, P., Gugercin, S.: Interpolatory projection methods for parameterized model reduction. SIAM J. Sci. Comput. 33(5), 2489–2518 (2011)
Feng, L.H., Rudnyi, E.B., Korvink, J.G.: Preserving the film coefficient as a parameter in the compact thermal model for fast electrothermal simulation. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 24(12), 1838–1847 (2005)
Fröhlich, B., Gade, J., Geiger, F., Bischoff, M., Eberhard, P.: Geometric element parameterization and parametric model order reduction in finite element based shape optimization. Comput. Mech. 63(5), 853–868 (2019). Springer, Berlin, Heidelberg
Heirmann, G.H.K., Desmet, W.: Interface reduction of flexible bodies for efficient modeling of body flexibility in multibody dynamics. Multibody Syst. Dyn. 24(2), 219–234 (2010)
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, pp. 366–378 (2015)
Lutowska, A.: Model order reduction for coupled systems using low-rank approximations. Doctoral Thesis, Eindhoven University of Technology, Netherlands (2012)
McKay, M.D., Beckman, R.J., Conover, W.J.: Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–245 (1979)
Nastran: Reference Manual. MSC Software Corporation, Newport Beach (2016)
Schilders, W.H.A., Lutowska A.: A novel approach to model order reduction for coupled multiphysics problems. In: Quarteroni, A., Rozza, G., (ed.), Reduced Order Methods for Modeling and Computational Reduction, pp. 1–49. Springer, Berlin (2014)
Walker, N., Fröhlich, B., Eberhard, P.: Model order reduction for parameter dependent substructured systems using Krylov subspaces. In: Proceedings of the 9th Vienna International Conference on Mathematical Modelling, Vienna (2018)
Woodbury, M.A.: In: Kuntzmann, J. (ed.) Inverting Modified Matrices. No. 42 in Statistical Research Group Memorandum Reports. Princeton University, Princeton (1950)
Acknowledgements
The authors gratefully thank the German Research Foundation (DFG) for the support of this research work within the collaborative research centre SFB/CRC 1244, “Adaptive Skins and Structures for the Built Environment of Tomorrow” with the projects B01 and A04.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Fröhlich, B., Geiger, F., Gade, J., Bischoff, M., Eberhard, P. (2020). Model Order Reduction of Coupled, Parameterized Elastic Bodies for Shape Optimization. In: Fehr, J., Haasdonk, B. (eds) IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018. IUTAM Bookseries, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-030-21013-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-21013-7_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21012-0
Online ISBN: 978-3-030-21013-7
eBook Packages: EngineeringEngineering (R0)