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A seventh-Order Accurate and Stable Algorithm for the Computation of Stress Inside Cracked Rectangular Domains

Helsing, Johan LU and Jonsson, Anders (2004) In International Journal for Multiscale Computational Engineering 2(1). p.47-68
Abstract
A seventh-order accurate and extremely stable algorithm for the rapid computation of stress fields inside cracked rectangular domains is presented. The algorithm is seventh-order accurate since it incorporates basis functions, taking the asymptotic shape of the stress fields close to crack tips and corners into account at least up to order six. The algorithm is stable since it is based on a Fredholm integral equation of the second kind. The particular form of the integral equation represents the solution as the limit of a function which is analytic inside the domain. This allows for an efficient implementation. In an example, involving 112 discretization points on an elastic square with a center crack, values of normalized stress intensity... (More)
A seventh-order accurate and extremely stable algorithm for the rapid computation of stress fields inside cracked rectangular domains is presented. The algorithm is seventh-order accurate since it incorporates basis functions, taking the asymptotic shape of the stress fields close to crack tips and corners into account at least up to order six. The algorithm is stable since it is based on a Fredholm integral equation of the second kind. The particular form of the integral equation represents the solution as the limit of a function which is analytic inside the domain. This allows for an efficient implementation. In an example, involving 112 discretization points on an elastic square with a center crack, values of normalized stress intensity factors and T-stress with a relative error of 10−6 are computed in seconds on a workstation. More points reduce the relative error down to 10−15, where it saturates in double precision arithmetic. A large-scale setup with up to 1024 cracks in an elastic square is also studied, using up to 740,000 discretization points. The algorithm is intended as a basic building block in general-purpose solvers for fracture mechanics. It can also be used as a substitute for benchmark tables. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Journal for Multiscale Computational Engineering
volume
2
issue
1
pages
47 - 68
publisher
Begell House
ISSN
1543-1649
DOI
10.1615/IntJMultCompEng.v2.i1.40
language
English
LU publication?
yes
id
94f4824d-994b-46ae-8ff0-278a72903c89 (old id 629400)
date added to LUP
2007-12-11 14:42:19
date last changed
2017-03-15 09:39:36
@article{94f4824d-994b-46ae-8ff0-278a72903c89,
  abstract     = {A seventh-order accurate and extremely stable algorithm for the rapid computation of stress fields inside cracked rectangular domains is presented. The algorithm is seventh-order accurate since it incorporates basis functions, taking the asymptotic shape of the stress fields close to crack tips and corners into account at least up to order six. The algorithm is stable since it is based on a Fredholm integral equation of the second kind. The particular form of the integral equation represents the solution as the limit of a function which is analytic inside the domain. This allows for an efficient implementation. In an example, involving 112 discretization points on an elastic square with a center crack, values of normalized stress intensity factors and T-stress with a relative error of 10−6 are computed in seconds on a workstation. More points reduce the relative error down to 10−15, where it saturates in double precision arithmetic. A large-scale setup with up to 1024 cracks in an elastic square is also studied, using up to 740,000 discretization points. The algorithm is intended as a basic building block in general-purpose solvers for fracture mechanics. It can also be used as a substitute for benchmark tables.},
  author       = {Helsing, Johan and Jonsson, Anders},
  issn         = {1543-1649},
  language     = {eng},
  number       = {1},
  pages        = {47--68},
  publisher    = {Begell House},
  series       = {International Journal for Multiscale Computational Engineering},
  title        = {A seventh-Order Accurate and Stable Algorithm for the Computation of Stress Inside Cracked Rectangular Domains},
  url          = {http://dx.doi.org/10.1615/IntJMultCompEng.v2.i1.40},
  volume       = {2},
  year         = {2004},
}