图书馆订阅: Guest
Begell Digital Portal Begell 数字图书馆 电子图书 期刊 参考文献及会议录 研究收集
国际多尺度计算工程期刊
影响因子: 1.016 5年影响因子: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN 打印: 1543-1649
ISSN 在线: 1940-4352

国际多尺度计算工程期刊

DOI: 10.1615/IntJMultCompEng.v2.i1.40
22 pages

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

Johan Helsing
Numerical Analysis, Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 LUND, Sweden
Anders Jonsson
Department of Solid Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

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.


Articles with similar content:

Calculation of the Characteristics of the Multichannel Queueing System with Pure Losses and Feedback
Journal of Automation and Information Sciences, Vol.47, 2015, issue 5
Khaver Nurmagomed kyzy Kuliyeva , Agasi Zarbali ogly Melikov, Leonid A. Ponomarenko
Optimal Control Processes Modeling under Uncertainty in Economic Systems with Hierarchy
Journal of Automation and Information Sciences, Vol.39, 2007, issue 2
Inna I. Sugonyak, Alexander G. Nakonechnyi
AN ADAPTIVE DOMAIN DECOMPOSITION PRECONDITIONER FOR CRACK PROPAGATION PROBLEMS MODELED BY XFEM
International Journal for Multiscale Computational Engineering, Vol.11, 2013, issue 6
Haim Waisman, Luc Berger-Vergiat
A HERMITE SPECTRAL METHOD FOR A FOKKER-PLANCK OPTIMAL CONTROL PROBLEM IN AN UNBOUNDED DOMAIN
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 3
Masoumeh Mohammadi, Alfio Borzi
Fast Calculation of Elastic Fields in a Homogeneous Medium with Isolated Heterogeneous Inclusions
International Journal for Multiscale Computational Engineering, Vol.7, 2009, issue 4
Sergey Kanaun