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Stable algorithm for the stress field around a multiply branched crack

(2005) In International Journal for Numerical Methods in Engineering 63(6). p.926-946
Abstract
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.
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
fast multipole method, stress intensity factor, integral equation, branched crack
in
International Journal for Numerical Methods in Engineering
volume
63
issue
6
pages
926 - 946
publisher
John Wiley & Sons
external identifiers
• wos:000229520400007
• scopus:20444490367
ISSN
1097-0207
DOI
10.1002/nme.1311
language
English
LU publication?
yes
id
9d18d983-82a1-4313-9541-a82d5747845c (old id 238738)
2007-08-24 13:16:07
date last changed
2019-03-12 01:55:47
```@article{9d18d983-82a1-4313-9541-a82d5747845c,
abstract     = {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.},
author       = {Englund, Jonas},
issn         = {1097-0207},
keyword      = {fast multipole method,stress intensity factor,integral equation,branched crack},
language     = {eng},
number       = {6},
pages        = {926--946},
publisher    = {John Wiley & Sons},
series       = {International Journal for Numerical Methods in Engineering},
title        = {Stable algorithm for the stress field around a multiply branched crack},
url          = {http://dx.doi.org/10.1002/nme.1311},
volume       = {63},
year         = {2005},
}

```