Complex variable approach to the BEM for multiple crack problems

A boundary element method for straight multiple center and edge crack problems is developed in this paper. The method is constructed upon the systematic use of the elastic singularity solutions in complex variables. The crack opening is represented by the continuous distribution of dislocation dipol...

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Vydáno v:Computer methods in applied mechanics and engineering Ročník 141; číslo 3; s. 247 - 264
Hlavní autoři: Denda, Mitsunori, Dong, Y.F.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 1997
Elsevier
Témata:
Exact sciences and technology
Fracture mechanics (crack, fatigue, damage...)
Fracture mechanics, fatigue and cracks
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Structural and continuum mechanics
Crack array
Crack opening displacement
Stress intensity factors
Fracture mechanics
Dislocation dipole
Theoretical study
Boundary element method
Complex variable method
Crack propagation
ISSN:0045-7825, 1879-2138
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Shrnutí:A boundary element method for straight multiple center and edge crack problems is developed in this paper. The method is constructed upon the systematic use of the elastic singularity solutions in complex variables. The crack opening is represented by the continuous distribution of dislocation dipoles and the effect of the non-crack boundary by the continuous distributions of point forces and dislocation dipoles. The crack-tip singularity is embedded into the interpolation using orthogonal polynomials (i.e. Chebyshev and Jacobi) and their associated singular weight functions. The proposed analytical integration procedure of the Cauchy-type integrals defined over the crack eliminates the need for the quadrature formulae for numerical integration, streamlines, and enhances the accuracy of the traditional singular integral equation method for crack problems. The stress intensity factors for the fifteen problems analyzed in this paper have been accurate enough to substitute those given in stress intensity factor handbooks. Since non-crack boundary of arbitrary shape can be introduced at will the method is expected to give accurate stress intensity factors for complex real life problems.
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ISSN:0045-7825
1879-2138
DOI:10.1016/S0045-7825(96)01120-6