Doubly Periodic Contact Problems for a Layer with an Unknown Contact Zone

Doubly periodic contact problems are considered for an elastic layer with an unknown contact area. One face of the layer is in conditions of sliding or rigid embedding. The problems are reduced to integral equations whose kernels do not contain quadratures. For the case of full contact of the other...

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Bibliographic Details
Published in:Mechanics of solids 2023-09, Vol.58 (7), p.2602-2609
Main Authors: Zolotov, N. B., Pozharskii, D. A.
Format: Article
Language:English
Subjects:
Classical Mechanics
Contact pressure
Elastic layers
Exact solutions
Integral equations
Mathematical analysis
Mechanical properties
Numerical methods
Physics
Physics and Astronomy
Quadratures
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Summary:Doubly periodic contact problems are considered for an elastic layer with an unknown contact area. One face of the layer is in conditions of sliding or rigid embedding. The problems are reduced to integral equations whose kernels do not contain quadratures. For the case of full contact of the other face of the layer with a two-dimensional sinusoidal rigid surface, the problems have an exact solution, which is used to debug programs that implement the numerical method of non-linear Galanov integral equations, which makes it possible to simultaneously determine the contact area and contact pressures. The mechanical characteristics are calculated for the introduction of a system of elliptical paraboloids and the transition from a discrete to a continuous contact area is studied.
ISSN:0025-6544
1934-7936
DOI:10.3103/S0025654423070257