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Two arbitrarily located normal forces and a penny‐shaped crack: a complete solution
Author(s) -
Fabrikant V. I.
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19990925)22:14<1201::aid-mma77>3.0.co;2-v
Subject(s) - mathematics , isotropy , transverse isotropy , space (punctuation) , plane (geometry) , mathematical analysis , elementary function , complex plane , body force , geometry , classical mechanics , physics , philosophy , linguistics , quantum mechanics
The following problem is considered: a penny‐shaped crack is located in the plane z =0 of a transversely isotropic elastic space and interacts with two equal and opposite normal forces, which are located arbitrarily, but symmetrically with respect to the plane of the crack. An exact closed‐form solution is obtained and expressed in terms of elementary functions for the fields of stresses and displacements in the whole space. This kind of problem deemed to be intractable by the methods of contemporary mathematical analysis, and has never been attempted before, even in the case of an isotropic body. Copyright © 1999 John Wiley & Sons, Ltd.