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A Seventh-Order Accurate and Stable Algorithm for the Computation of Stress Inside Cracked Rectangular Domains
KTH, Superseded Departments, Mechanics.
2004 (English)In: International Journal for Multiscale Computational Engineering, ISSN 1543-1649, Vol. 2, no 1, 47-68 p.Article in journal (Refereed) Published
Abstract [en]

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 Predholm 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.

Place, publisher, year, edition, pages
2004. Vol. 2, no 1, 47-68 p.
Keyword [en]
stress analysis, polygonal domain, stress intensity factor, T-stress, cracks, integral equation of Predholm type
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-138125DOI: 10.1615/IntJMultCompEng.v2.i1.40ISI: 000208553000004OAI: diva2:680411
Knut and Alice Wallenberg Foundation, 98-568 99-380

QC 20131218

Available from: 2013-12-18 Created: 2013-12-18 Last updated: 2013-12-18Bibliographically approved

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