Keywords :
Conformal mapping; Extended finite element method; Generalized finite element method; Numerical integration; Open-source MATLAB code; Partition of unity finite element method; Quadrature; Schwarz christoffel; Strong discontinuities; Weak discontinuities; Generalized finite element methods; Matlab code; Numerical integrations; Open-source; Partition of unity finite element methods; Schwarz; Strong discontinuity; Weak discontinuity; Brittle fracture; Concrete beams and girders; Crack propagation; Integration; Plates (structural components); Stiffness matrix; Finite element method
Abstract :
[en] Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. J. Numer. Meth. Engng. 1999; 45:601-620). 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 (Int. J. Numer. Meth. Engng 2009; 80(1):103-134. DOI: 10.1002/nme.2589) 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. © 2010 John Wiley & Sons, Ltd.
Natarajan, S.; Cardiff School of Engineering Theoretical, Applied and Computational Mechanics, Cardiff University, Wales, United Kingdom
Roy Mahapatra, D.; Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
Bordas, Stéphane ;
University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
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