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


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.


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



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dominik Schillinger
    • 1
    • 2
  • Quanji Cai
    • 1
  • Ralf-Peter Mundani
    • 1
  • Ernst Rank
    • 1
  1. 1.Lehrstuhl für Computation in Engineering, Department of Civil Engineering and SurveyingTechnische Universität MünchenMünchenGermany
  2. 2.Institute for Computational Engineering and SciencesThe University of Texas at AustinAustinUSA

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