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Derivation of Geometrically Parameterized Shell Elements in the Context of Shape Optimization

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Optimal Design and Control of Multibody Systems (IUTAM 2022)

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 42))

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Abstract

The goal of this contribution is to extend an existing workflow for shape optimization with geometrically parameterized finite elements by implementing a parameterized shell element. The challenge is to find an element technology that is free of locking and hourglass-modes on the one hand, but its implementation must be simple enough so that it can contain the geometric parameters on the other hand. The derived element is used in a numerical optimization example. Therefore, a ribbed plate is used to show the whole workflow including the preparation of the system matrices depending on global design parameters, parametric model order reduction and shape optimization. A final validation is done using a commercial finite element software to compare the results.

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References

  1. Allemang, R.: The modal assurance criterion - 20 years of use and abuse. In Proceedings of the 20th International Modal Analysis Conference, Los Angeles, USA, pp. 14–21 (2002)

    Google Scholar 

  2. Ansys: Documentation for Ansys, Release 18.2. Ansys, Inc. (2018)

    Google Scholar 

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

    Google Scholar 

  4. Bathe, K.J.: Finite Element Procedures. Prentice Hall, Upper Saddle River (2014)

    Google Scholar 

  5. Bathe, K.J., Dvorkin, E.N.: A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation. Int. J. Numer. Meth. Eng. 21(2), 367–383 (1985)

    Article  Google Scholar 

  6. Benner, P., Ohlberger, M., Cohen, A., Willcox, K.: Model Reduction and Approximation. SIAM, Theory and Algorithms (2017)

    Google Scholar 

  7. 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 

  8. Neto, M.A., Amaro, A., Roseiro, L., Cirne, J., Leal, R.: Finite element method for plates/shells. In: Engineering Computation of Structures: The Finite Element Method, pp. 195–232. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-17710-6_6

    Chapter  Google Scholar 

  9. DIN Standards Commitee Building and Civil Engineering: In Eurocode 2: Design of Concrete Structures - Part 1–1: General Rules - Rules for Buildings. Beuth Verlag, Bridges and Civil Engineering Structures; Berlin (2021)

    Google Scholar 

  10. 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 

  11. 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)

    Article  MathSciNet  Google Scholar 

  12. Fröhlich, B.; Wagner, J.; Böhm, M.; Sawodny, O.; Eberhard, P.: Combining Optimal control and shape optimization for an adaptive engineering structure with parameterized reduced order finite element models. In: Proceedings of the 9th ECCOMAS Thematic Conference on Smart Structures and Materials, Paris, France, pp. 43–54 (2019)

    Google Scholar 

  13. Ibrahimbegovic, A., Taylor, R.L., Wilson, E.L.: A robust quadrilateral membrane finite element with drilling degrees of freedom. Int. J. Numer. Meth. Eng. 30(3), 445–457 (1990)

    Article  Google Scholar 

  14. Liu, W.K., Ong, J.S.J., Uras, R.A.: Finite element stabilization matrices, a unification approach. Comput. Methods Appli. Mech. Eng. 53(1), 13–46 (1985)

    Article  MathSciNet  Google Scholar 

  15. Mathworks: Matlab, Product Help, Matlab Release 2020b. The MathWorks, Inc. (2020)

    Google Scholar 

  16. Panzer, H.K.F.: Model Order Reduction by Krylov Subspace Methods with Global Error Bounds and Automatic Choice of Parameters. Dissertation, Technische Universität München. München: Verlag Dr. Hut (2014)

    Google Scholar 

  17. Salimbahrami, S.B.: Structure Preserving Order Reduction of Large Scale Second Order Models. Dissertation, Technische Universität München. München (2005)

    Google Scholar 

  18. Simo, J.C., Rifai, M.S.: A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Meth. Eng. 29(8), 1595–1638 (1990)

    Article  MathSciNet  Google Scholar 

  19. Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method for Solid and Structural Mechanics. Butterworth-Heinemann, Oxford (2005)

    Google Scholar 

  20. Zienkiewicz, O.C., Taylor, R.L., Zhu, J.Z.: The Finite Element Method - Its Basis & Fundamentals. Butterworth-Heinemann, Oxford (2005)

    Google Scholar 

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Acknowledgements

This project is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project-ID 279064222 - SFB 1244, “Adaptive skins and structures for the built environment of tomorrow” with the project B01 (Characterization, modeling and model order reduction). This support is highly appreciated.

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Authors and Affiliations

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

    Manuel Vierneisel & Peter Eberhard

  2. Institute for Structural Mechanics, University of Stuttgart, Pfaffenwaldring 7, 70569, Stuttgart, Germany

    Florian Geiger & Manfred Bischoff

Authors
  1. Manuel Vierneisel
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  2. Florian Geiger
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  3. Manfred Bischoff
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  4. Peter Eberhard
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Corresponding author

Correspondence to Peter Eberhard .

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Editors and Affiliations

  1. Institute of Mechanics and Ocean Engineering, Hamburg University of Technology, Hamburg, Germany

    Karin Nachbagauer

  2. Technical University of Munich, Institute for Advanced Studies TUM–IAS, Garching, Germany

    Alexander Held

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Vierneisel, M., Geiger, F., Bischoff, M., Eberhard, P. (2024). Derivation of Geometrically Parameterized Shell Elements in the Context of Shape Optimization. In: Nachbagauer, K., Held, A. (eds) Optimal Design and Control of Multibody Systems. IUTAM 2022. IUTAM Bookseries, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-031-50000-8_6

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  • DOI: https://doi.org/10.1007/978-3-031-50000-8_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49999-9

  • Online ISBN: 978-3-031-50000-8

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