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Relationship between green's functions of tangential contact and crack problems for generally anisotropic bodies
Author(s) -
Fabrikant V. I.
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600020
Subject(s) - anisotropy , mathematical analysis , inverse , mathematics , property (philosophy) , green s , geometry , physics , optics , philosophy , epistemology
It was proved by the author [5][V. I. Fabrikant, 2016] that in the case of normal contact and crack problems for anisotropic bodies the kernels of the integral transforms of the responses to the singular loadings are inverse to one another. It does not look like this property was previously noticed by other authors. The case of the relationship between tangential contact and crack problems is obviously more complicated and deserves a separate investigation. Such relationship is established here. Several particular cases of anisotropy are considered as illustrative examples. It is also shown that the kernels of the governing integral equations can be computed exactly, using the theory of generalized functions.