Schillinger, D., Ruess, M. , Düster, A. and Rank, E. (2011) The Finite Cell Method for large deformation analysis. PAMM: Proceedings in Applied Mathematics and Mechanics, 11(1), pp. 271-272. (doi: 10.1002/pamm.201110127)
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Abstract
The Finite Cell Method (FCM) combines the fictitious domain approach with high-order finite elements and adaptive integration. For linear elastic problems with smooth solution, FCM has been shown to achieve exponential rates of convergence in energy norm, while its structured cell grid guarantees simple mesh generation irrespective of the geometric complexity involved. In this contribution, the FCM idea is combined with standard finite element technology for the solution of geometrically nonlinear problems. In particular, a modified FCM formulation is introduced, which resets the deformed configuration of the fictitious domain to the deformation-free reference configuration after each Newton iteration. Numerical experiments show that this intervention allows for stable nonlinear FCM analysis with very small values of the penalty parameter, while the accuracy of the geometrically nonlinear solution within the physical domain remains unaffected.
| Item Type: | Articles |
|---|---|
| Additional Information: | 82nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Granz, Austria, April 18 - 21, 2011. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Ruess, Dr Martin |
| Authors: | Schillinger, D., Ruess, M., Düster, A., and Rank, E. |
| College/School: | College of Science and Engineering > School of Engineering > Infrastructure and Environment |
| Journal Name: | PAMM: Proceedings in Applied Mathematics and Mechanics |
| Publisher: | Wiley |
| ISSN: | 1617-7061 |
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