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Computational Mechanics

, Volume 63, Issue 5, pp 853–868 | Cite as

Geometric element parameterization and parametric model order reduction in finite element based shape optimization

  • Benjamin Fröhlich
  • Jan Gade
  • Florian Geiger
  • Manfred Bischoff
  • Peter EberhardEmail author
Original Paper
  • 401 Downloads

Abstract

This contribution proposes a new approach to derive geometrically parameterized, reduced order finite element models. An element formulation for geometrically parameterized finite elements is suggested. The parameterized elements are used to derive models with a parameterized geometry where the parameterized system matrices are expressed in an affine representation. Parametric model order reduction can then be efficiently used to reduce the full order parameterized model to a reduced order parameterized model. The approach shows two beneficial features. First, design studies and shape optimizations can be conducted with parameterized reduced order model of much lower dimension compared to the parameterized, full order model. Second, it is possible to compute sensitivities analytically, and therefore, to avoid the computation of finite differences gradients. The approach is illustrated with two numerical examples. The first example includes a detailed error analysis. The second example is a shape optimization example of an adaptive structure.

Keywords

Parametric model order reduction Shape optimization Reduced order modeling Moment matching 

Notes

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 A04 and B01 and as well as the project DFG EB 195/11-2 “Model Order Reduction for Elastic Multibody Systems with Moving Interactions”.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Engineering and Computational MechanicsUniversity of StuttgartStuttgartGermany
  2. 2.Institute for Structural MechanicsUniversity of StuttgartStuttgartGermany

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