Reference : Integrating strong and weak discontinuities without integration subcells and example ...
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Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework
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 mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
International Journal for Numerical Methods in Engineering
Yes (verified by ORBilu)
[en] 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
[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.
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