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  4. An eigenvalue stabilization technique to increase the robustness of the finite cell method for finite strain problems
 
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An eigenvalue stabilization technique to increase the robustness of the finite cell method for finite strain problems

Citation Link: https://doi.org/10.15480/882.4324
Publikationstyp
Research Report
Date Issued
2022-01-30
Sprache
English
Author(s)
Garhuom, Wadhah  orcid-logo
Usman, Khuldoon  
Düster, Alexander  
Institut
Konstruktion und Festigkeit von Schiffen M-10  
TORE-DOI
10.15480/882.4324
TORE-URI
http://hdl.handle.net/11420/11988
Journal
Computational Mechanics  
Volume
69
Issue
5
Start Page
1225
End Page
1240
Citation
Computational Mecahnics 69 (5): 1225-1240 (2022)
Publisher DOI
10.1007/s00466-022-02140-7
Scopus ID
2-s2.0-85123885174
Publisher
Springer
Broken cells in the finite cell method—especially those with a small volume fraction—lead to a high condition number of the global system of equations. To overcome this problem, in this paper, we apply and adapt an eigenvalue stabilization technique to improve the ill-conditioned matrices of the finite cells and to enhance the robustness for large deformation analysis. In this approach, the modes causing high condition numbers are identified for each cell, based on the eigenvalues of the cell stiffness matrix. Then, those modes are supported directly by adding extra stiffness to the cell stiffness matrix in order to improve the condition number. Furthermore, the same extra stiffness is considered on the right-hand side of the system—which leads to a stabilization scheme that does not modify the solution. The performance of the eigenvalue stabilization technique is demonstrated using different numerical examples.
Subjects
Finite cell method
Condition number
Eigenvalues
Stabilization
Large deformations
DDC Class
530: Physik
600: Technik
620: Ingenieurwissenschaften
Funding(s)
SPP 1748: Teilprojekt "High-Order Immersed-Boundary-Methoden in der Festkörpermechanik für generativ gefertigte Strukturen"  
Projekt DEAL  
Funding Organisations
Deutsche Forschungsgemeinschaft (DFG)  
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by/4.0/
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