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Stable algorithm for the stress field around a multiply branched crack
Author(s) -
Englund Jonas
Publication year - 2005
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.1311
Subject(s) - mathematics , computation , fredholm integral equation , regularization (linguistics) , stress intensity factor , stress field , integral equation , mathematical analysis , algorithm , fracture mechanics , computer science , finite element method , structural engineering , engineering , artificial intelligence
We present an algorithm for the computation of the stress field around a branched crack. The algorithm is based on an integral equation with good numerical properties. Our equation is obtained through a left regularization of an integral equation of Fredholm's first kind. Complex valued functions involving repeated products of square roots appear in the regularization. A new and effective scheme for correct evaluation of these functions is described. For validation, mode I and II stress intensity factors are computed for simple branched geometries. The relative errors in the stress intensity factors are typically as low as 10 −12 . A large scale example is also presented, where a crack with 176 branching points is studied. Copyright © 2005 John Wiley & Sons, Ltd.