Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework

Natarajan, Sundararajan and Mahapatra, Roy D and Bordas, Stephane PA (2010) Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework. In: International Journal for Numerical Methods in Engineering, 83 (3). pp. 269-294.

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Abstract

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. Nuttier 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. Copyright (C) 2010 John Wiley & Sons, Ltd.

Item Type:	Journal Article
Publication:	International Journal for Numerical Methods in Engineering
Publisher:	John Wiley and Sons
Additional Information:	Copyright of this article belongs to John Wiley and Sons.
Keywords:	Schwarz Christoffel;conformal mapping;numerical integration; extended finite element method;quadrature; generalized finite element method;partition of unity finite element method;strong discontinuities;weak discontinuities;open-source MATLAB code.
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	10 Aug 2010 05:26
Last Modified:	19 Sep 2010 06:13
URI:	http://eprints.iisc.ac.in/id/eprint/31216

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