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On the use of modal derivatives for nonlinear model order reduction

Weeger, Oliver ; Wever, Utz ; Simeon, Bernd (2021):
On the use of modal derivatives for nonlinear model order reduction. (Postprint)
In: International Journal for Numerical Methods in Engineering, 108 (13), Wiley, ISSN 0029-5981, e-ISSN 1097-0207,
DOI: 10.26083/tuprints-00019820,
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Item Type: Article
Origin: Secondary publication service
Status: Postprint
Title: On the use of modal derivatives for nonlinear model order reduction
Language: English
Abstract:

Modal derivative is an approach to compute a reduced basis for model order reduction of large-scale nonlinear systems that typically stem from the discretization of partial differential equations. In this way, a complex nonlinear simulation model can be integrated into an optimization problem or the design of a controller, based on the resulting small-scale state-space model. We investigate the approximation properties of modal derivatives analytically and thus lay a theoretical foundation of their use in model order reduction, which has been missing so far. Concentrating on the application field of structural mechanics and structural dynamics, we show that the concept of modal derivatives can also be applied as nonlinear extension of the Craig–Bampton family of methods for substructuring. We furthermore generalize the approach from a pure projection scheme to a novel reduced-order modeling method that replaces all nonlinear terms by quadratic expressions in the reduced state variables. This complexity reduction leads to a frequency-preserving nonlinear quadratic state-space model. Numerical examples with carefully chosen nonlinear model problems and three-dimensional nonlinear elasticity confirm the analytical properties of the modal derivative reduction and show the potential of the proposed novel complexity reduction methods, along with the current limitations.

Journal or Publication Title: International Journal for Numerical Methods in Engineering
Journal volume: 108
Number: 13
Publisher: Wiley
Collation: 25 Seiten
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 600 Technik
600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 16 Department of Mechanical Engineering > Cyber-Physical Simulation (CPS)
Date Deposited: 15 Dec 2021 10:47
Last Modified: 15 Dec 2021 10:47
DOI: 10.26083/tuprints-00019820
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-198209
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19820
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