Mathematics – Numerical Analysis
Scientific paper
2011-07-24
International Journal for Numerical Methods in Engineering, v83 (3), 269-294, 2010
Mathematics
Numerical Analysis
37 pages, 23 figures
Scientific paper
10.1002/nme.2798
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re-meshing, as the discontinuity evolves. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted. In this paper, we use a simple integration technique, proposed for polygonal domains [2] to suppress the need for element subdivision. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi-material problem, show that the proposed method yields accurate results. Owing to its simplicity, the proposed integration technique can be easily integrated in any existing code.
Bordas Stephane PA
Mahapatra Roy D.
Natarajan Sundararajan
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