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A crack problem with four distinct harmonic functionsThe problem of an elastic solid containing a semi-infinite plane crack subjected to concentrated shears parallel to the edge of the crack is considered. A closed form solution using four distinct harmonic functions (none of which can be taken arbitrarily) is found to satisfy the finite displacement and inverse square root stress singularity at the edge of the crack. Explicit expressions in terms of elementary functions are given for the distribution of stress and displacement in the solid. These are obtained by employing Fourier and Kontorovich-Lebedev integral transforms and certain singular solutions of Laplace equations in three dimensions. The variations of the intensity of the local stress field along the crack border are shown graphically. An example is presented, which is in contrast with the conclusion established in the literature that one of the four Papkovich-Neuber functions in three-dimensional elasticity may be arbitrarily set to zero.
Document ID
19730014121
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Sih, G. C. (Lehigh Univ. Bethlehem, PA, United States)
Kassir, M. K. (City Univ. of New York N. Y., United States)
Date Acquired
September 2, 2013
Publication Date
May 1, 1972
Subject Category
Structural Mechanics
Report/Patent Number
IFSM-72-18
NASA-CR-112317
NASA-TR-72-2
Accession Number
73N22848
Funding Number(s)
CONTRACT_GRANT: NGR-39-007-066
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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