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Zhao, M. H.; Shen, Y. P.; Liu, Y. J.; Liu, G. N.

The method of analysis of cracks in three-dimensional transversely isotropic media: Boundary intergral equation approach. (English) Zbl 0973.74648

Eng. Anal. Bound. Elem. 21, No. 2, 169-178 (1998).
Summary: The fundamental solutions are obtained for a unit-concentrated displacement discontinuity in a three-dimensional transversely isotropic medium. The method of solution involves reducing the problem to a system of hyper-singular integral equations by application of these fundamental solutions. We obtain near crack border elastic displacement and stress. Stress intensity factors can be expressed in terms of the displacement discontinuity on the crack surface. Further, we establish an analogy between the boundary integral equations for arbitrarily shaped cracks in a transversely isotropic and elastic medium such that once the stress intensity factors in the transversely isotropic medium can be determined directly from that of the isotropic elastic medium. Results for the penny-shaped crack are obtained as an example.

Cited in 5 Documents

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
74R10 Brittle fracture
74E10 Anisotropy in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics

Keywords:

stress intensity factors; transversely isotropic medium; displacement discontinuity; fundamental solutions; system of hyper-singular integral equations; penny-shaped crack
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References:

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