| Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework |
| English |
| 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 >] |
| 2010 |
| International Journal for Numerical Methods in Engineering |
| 83 |
| 3 |
| 269-294 |
| Yes (verified by ORBilu) |
| International |
| 00295981 |
| [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. |
| Researchers ; Professionals ; Students |
| http://hdl.handle.net/10993/11873 |
| 10.1002/nme.2798 |
