A seventh-Order Accurate and Stable Algorithm for the Computation of Stress Inside Cracked Rectangular Domains
(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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/629400
- author
- Helsing, Johan ^{LU} and Jonsson, Anders
- organization
- publishing date
- 2004
- 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}, }