Contact problems for several transversely isotropic elastic layers on a smooth elastic half-space |
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Authors: | V I Fabrikant |
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Institution: | 1.Prisoner #167 932D,Drummond jail,Drummondville,Canada |
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Abstract: | 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, with smooth interfaces, resting on a smooth 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 charged 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. |
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Keywords: | |
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