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Publisher DOI: 10.1007/s00466-022-02140-7
Title: An eigenvalue stabilization technique to increase the robustness of the finite cell method for finite strain problems
Language: English
Authors: Garhuom, Wadhah  
Usman, Khuldoon 
Düster, Alexander 
Keywords: Finite cell method; Condition number; Eigenvalues; Stabilization; Large deformations
Issue Date: 30-Jan-2022
Publisher: Springer
Source: Computational Mecahnics 69 (5): 1225-1240 (2022)
Abstract (english): 
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.
DOI: 10.15480/882.4324
ISSN: 1432-0924
Journal: Computational Mechanics 
Institute: Konstruktion und Festigkeit von Schiffen M-10 
Document Type: Research Paper
Project: SPP 1748: Teilprojekt "High-Order Immersed-Boundary-Methoden in der Festkörpermechanik für generativ gefertigte Strukturen" 
Projekt DEAL 
Funded by: Deutsche Forschungsgemeinschaft (DFG) 
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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