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Integration of crack singularities in XFEM with the generalized Duffy-distance transformation

May 22, 2018 – 10.00
Graduiertenschule MUSiC

Dr. Jiahe Lv

Associate Professor, China University of Geosciences, Wuhan, China


With the development of GFEM/XFEM for fracture problems, the accurate and efficient integration of singular enrichment functions has been an open issue, especially for 3D case. To our opinion, three difficulties should be concerned simultaneously as: a). the singularity with respect to local distance ; b). the near singularity caused by ill-shaped integral patches/cells; c). the near singularity during the iso-parametric transformation. Based on the generalized Duffy transformation, the near singularity caused by distorted integral patch/cell shape is discovered numerically and theoretically, and the Duffy-distance transformation is developed step by step for 2D and 3D vertex singularities. Meanwhile, the conformal preconditioning strategy for both 2D and 3D problems is constructed to eliminate the near singularity caused by element shape distortion during the iso-parametric transformation, which enables the Duffy-distance transformation to be applicable for arbitrary shaped elements. As a result, the near singularities can be fully or partly cancelled depending on the order of singularity. Implementation of the proposed scheme in existing codes is straightforward. Numerous numerical examples for arbitrary shaped triangles and tetrahedrons are presented to demonstrate its robustness and efficiency, along with comparisons to the generalized Duffy transformation.

 Location: Appelstr. 11A, Seminar room A 501, 5th floor