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A Review of the Finite Cell Method for Nonlinear Structural Analysis of Complex CAD and Image-Based Geometric Models

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Advanced Computing

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 93))

Abstract

The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions. For the analysis of complex geometries, it circumvents expensive and potentially error-prone meshing procedures, while maintaining high rates of convergence. The present contribution provides an overview of recent accomplishments in the FCM with applications in structural mechanics. First, we review the basic components of the technology using the p- and B-spline versions of the FCM. Second, we illustrate the typical solution behavior for linear elasticity in 1D. Third, we show that it is straightforward to extend the FCM to nonlinear elasticity. We also outline that the FCM can be extended to applications beyond structural mechanics, such as transport processes in porous media. Finally, we demonstrate the benefits of the FCM with two application examples, i.e. the vibration analysis of a ship propeller described by T-spline CAD surfaces and the nonlinear compression test of a CT-based metal foam.

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Notes

  1. 1.

    It is worthwhile to note that high-order basis functions are significantly more stable than low-order functions for flow problems moderately dominated by convection [8].

  2. 2.

    Using eight threads on two interconnected Intel(R) Xeon(R) W5590 @ 3.33 GHz.

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Acknowledgements

D. Schillinger, Q. Cai and R.-P. Mundani gratefully acknowledge support from the Munich Centre of Advanced Computing (MAC) and the International Graduate School of Science and Engineering (IGSSE) at the Technische Universität München. D. Schillinger gratefully acknowledges support from the German National Science Foundation (Deutsche Forschungsgemeinschaft DFG) under grant number SCHI 1249/1-1. The authors thank T.J.R. Hughes, M. Ruess and M.A. Scott for their help with the analysis of the ship propeller.

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Authors and Affiliations

  1. Lehrstuhl für Computation in Engineering, Department of Civil Engineering and Surveying, Technische Universität München, Arcisstr, 21, 80333, München, Germany

    Dominik Schillinger, Quanji Cai, Ralf-Peter Mundani & Ernst Rank

  2. Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, Austin, TX, 78712, USA

    Dominik Schillinger

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  1. Dominik Schillinger
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Correspondence to Dominik Schillinger .

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Editors and Affiliations

  1. Department of Informatics, Technische Universität München, Munich, Germany

    Michael Bader

  2. Department of Informatics, Technische Universität München, Munich, Germany

    Hans-Joachim Bungartz

  3. Department of Informatics, Technische Universität München, Munich, Germany

    Tobias Weinzierl

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Schillinger, D., Cai, Q., Mundani, RP., Rank, E. (2013). A Review of the Finite Cell Method for Nonlinear Structural Analysis of Complex CAD and Image-Based Geometric Models. In: Bader, M., Bungartz, HJ., Weinzierl, T. (eds) Advanced Computing. Lecture Notes in Computational Science and Engineering, vol 93. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38762-3_1

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