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Numerical determination of a class of generalized stress intensity factors
Author(s) -
Ioakimidis N. I.,
Theocaris P. S.
Publication year - 1979
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.1620140702
Subject(s) - stress intensity factor , mathematics , antiplane shear , mathematical analysis , elasticity (physics) , cauchy distribution , singular integral , cauchy's integral formula , collocation method , numerical analysis , boundary value problem , linear elasticity , integral equation , geometry , fracture mechanics , differential equation , ordinary differential equation , structural engineering , finite element method , initial value problem , cauchy problem , materials science , engineering , composite material
A modification of the collocation method for the numerical solution of Cauchy‐type singular integral equations appearing in plane elasticity and, especially, crack problems is proposed. This modification, based on a variable transformation, applies to the case when the unknown function of the singular integral equation behaves like A ( x − c ) α + B ( x − c ) β , where α < 0, 0 < β − α < 1, near an endpoint c of the integration interval. In plane elasticity such a point is either a crack tip or a corner point of the boundary of the elastic medium. Thus the method seems to be quite efficient for the numerical evaluation of generalized stress intensity factors near such points. A successful application of the method to the classical plane elasticity problem of an antiplane shear crack terminating at a bimaterial interface was also made.