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Use of ‘simple solutions’ for boundary integral methods in elasticity and fracture analysis
Author(s) -
Lutz Earlin,
Ingraffea Anthony R.,
Gray Leonard J.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620350902
Subject(s) - singularity , mathematics , traction (geology) , mathematical analysis , surface (topology) , simple (philosophy) , degenerate energy levels , cauchy distribution , elasticity (physics) , fracture (geology) , boundary (topology) , geometry , materials science , physics , philosophy , epistemology , quantum mechanics , geomorphology , composite material , geology
The 'simple solutions' or 'indirect' method of analysing Cauchy and hypersingular integrands in the gradient (flux or traction) boundary integral equation (BIE) is applied to linear elastic fracture analysis. Because of the geometric singularity of the crack surface, application of the simple solutions formulas on the crack face requires integration over a temporary 'closure surface' rather than the remainder of the body. Closure surface constructions are exhibited for crack surfaces, allowing the gradient BIE to be applied as a constraint equation on a crack surface where the primary BIE is degenerate. Computational results are given for two benchmark fracture problems.