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

Dominik Schillinger; Quanji Cai; Ralf Peter Mundani; Ernst Rank

doi:10.1007/978-3-642-38762-3_1

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

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

Civil, Environmental, and Geo- Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter

12 Scopus citations

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.

Original language	English (US)
Title of host publication	Lecture Notes in Computational Science and Engineering
Publisher	Springer Verlag
Pages	1-23
Number of pages	23
DOIs	https://doi.org/10.1007/978-3-642-38762-3_1
State	Published - 2013

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	93
ISSN (Print)	1439-7358

Bibliographical note

Funding Information:
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 Forschungsge-meinschaft 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.

Publisher Copyright:
© 2013, Springer-Verlag Berlin Heidelberg.

Keywords

Embedded/fictitious domain methods
finite cell method
large deformation solid mechanics

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10.1007/978-3-642-38762-3_1

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Schillinger, D., Cai, Q., Mundani, R. P., & Rank, E. (2013). A Review of the Finite Cell Method for Nonlinear Structural Analysis of Complex CAD and Image-Based Geometric Models. In Lecture Notes in Computational Science and Engineering (pp. 1-23). (Lecture Notes in Computational Science and Engineering; Vol. 93). Springer Verlag. https://doi.org/10.1007/978-3-642-38762-3_1

A Review of the Finite Cell Method for Nonlinear Structural Analysis of Complex CAD and Image-Based Geometric Models. / Schillinger, Dominik; Cai, Quanji; Mundani, Ralf Peter et al.
Lecture Notes in Computational Science and Engineering. Springer Verlag, 2013. p. 1-23 (Lecture Notes in Computational Science and Engineering; Vol. 93).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

Abstract

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Keywords

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