Premium
On the elimination of quadrature subcells for discontinuous functions in the eXtended Finite‐Element Method
Author(s) -
Ventura G.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1570
Subject(s) - classification of discontinuities , discontinuity (linguistics) , quadrature (astronomy) , finite element method , stiffness matrix , extended finite element method , mathematical analysis , gauss–kronrod quadrature formula , stiffness , mathematics , structural engineering , geometry , physics , nyström method , engineering , integral equation , optics
The introduction of discontinuous/non‐differentiable functions in the eXtended Finite‐Element Method allows to model discontinuities independent of the mesh structure. 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 line is commonly adopted. In the paper, it is shown how standard Gauss quadrature can be used in the elements containing the discontinuity without splitting the elements into subcells or introducing any additional approximation. The technique is illustrated and developed in one, two and three dimensions for crack and material discontinuity problems. Copyright © 2005 John Wiley & Sons, Ltd.