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- W2145962437 abstract "Hypersingular integrals of the typeIα(Tn,m,r)=−11Tn(s)(1−s2)m−1/2(s−r)αds,|r|<1andIα(Un,m,r)=−11Un(s)(1−s2)m−1/2(s−r)αds,|r|<1are investigated for general integers α (positive) and m (nonnegative), where Tn(s) and Un(s) are the Chebyshev polynomials of the first and second kinds, respectively. Exact formulas are derived for the cases α=1,2,3,4 and m=0,1,2,3; most of them corresponding to new solutions derived in this paper. Moreover, a systematic approach for evaluating these integrals when α>4 and m>3 is provided. The integrals are also evaluated as |r|>1 in order to calculate the stress intensity factors. Examples involving crack problems are given and discussed with emphasis on the linkage between mathematics and mechanics of fracture. The examples include classical linear elastic fracture mechanics, functionally graded materials, and gradient elasticity theory. An appendix, with an alternative derivation of the formulae, supplements the paper." @default.
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- W2145962437 date "2003-04-01" @default.
- W2145962437 modified "2023-09-23" @default.
- W2145962437 title "Integral equations with hypersingular kernels––theory and applications to fracture mechanics" @default.
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- W2145962437 doi "https://doi.org/10.1016/s0020-7225(02)00134-9" @default.
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