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Contact problems for several transversely isotropic elastic layers bonded to an elastic half‐space
Author(s) -
Fabrikant V.I.
Publication year - 2011
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.200900335
Subject(s) - transverse isotropy , integral transform , isotropy , half space , integral equation , mathematical analysis , mathematics , surface (topology) , space (punctuation) , domain (mathematical analysis) , geometry , physics , optics , computer science , operating system
The idea of generalized images, first used by the author for the case of crack problems, is applied here to solve a contact problem for n transversely isotropic elastic layers, bonded to each other and to an elastic half‐space, made of a different transversely isotropic material. A rigid punch of arbitrary shape is pressed against the top layer's free surface. The governing integral equation is derived for the case of two layers; it is mathematically equivalent to that of an electrostatic problem of an infinite row of coaxial charge disks in the shape of the domain of contact. This result is then generalized for an arbitrary number of layers. As a comparison, the method of integral transforms is also used to solve the problem. The main difference of our integral transform approach with the existing ones is in separating of our half‐space solution from the integral transform terms. It is shown that both methods lead to the same results, thus giving a new interpretation to the integral transform as a sum of an infinite series of generalized images.