A seventh-Order Accurate and Stable Algorithm for the Computation of Stress Inside Cracked Rectangular Domains
Author
Summary, in English
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.
Department/s
- Mathematics (Faculty of Engineering)
- Harmonic Analysis and Applications
Publishing year
2004
Language
English
Pages
47-68
Publication/Series
International Journal for Multiscale Computational Engineering
Volume
2
Issue
1
Full text
- Available as PDF - 498 kB
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Document type
Journal article
Publisher
Begell House
Topic
- Mathematics
Status
Published
Research group
- Harmonic Analysis and Applications
- Harmonic Analysis and Applications
ISBN/ISSN/Other
- ISSN: 1543-1649