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An extension of the finite cell method using boolean operations
Publikationstyp
Journal Article
Date Issued
2017-01-30
Sprache
English
Author(s)
TORE-URI
Journal
Volume
59
Issue
5
Start Page
877
End Page
886
Citation
Computational Mechanics 5 (59): 877-886 (2017)
Publisher DOI
Scopus ID
Publisher
Springer
In the finite cell method, the fictitious domain approach is combined with high-order finite elements. The geometry of the problem is taken into account by integrating the finite cell formulation over the physical domain to obtain the corresponding stiffness matrix and load vector. In this contribution, an extension of the FCM is presented wherein both the physical and fictitious domain of an element are simultaneously evaluated during the integration. In the proposed extension of the finite cell method, the contribution of the stiffness matrix over the fictitious domain is subtracted from the cell, resulting in the desired stiffness matrix which reflects the contribution of the physical domain only. This method results in an exponential rate of convergence for porous domain problems with a smooth solution and accurate integration. In addition, it reduces the computational cost, especially when applying adaptive integration schemes based on the quadtree/octree. Based on 2D and 3D problems of linear elastostatics, numerical examples serve to demonstrate the efficiency and accuracy of the proposed method.
Subjects
finite cell method
frictitious domain approach
void shape
quadtree
octree
DDC Class
620: Ingenieurwissenschaften
More Funding Information
Supported by the Alexander von Humboldt Foundation.