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

Research output: Chapter in Book/Report/Conference proceedingChapter

7 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 languageEnglish (US)
Title of host publicationLecture Notes in Computational Science and Engineering
PublisherSpringer Verlag
Pages1-23
Number of pages23
DOIs
StatePublished - 2013

Publication series

NameLecture Notes in Computational Science and Engineering
Volume93
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.

Keywords

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

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