Stable algorithm for the stress field around a multiply branched crack | Zendy

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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.

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