 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 54, Issue 5 / 2019 | Next article >> |
| D.A. Pozharskii, "Contact Problem for Inhomogeneous Cylinders with Variable Poisson's Ratio," Mech. Solids. 54 (5), 709-716 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
5 |
Pages |
709-716 |
| DOI |
10.3103/S0025654419050133 |
| Title |
Contact Problem for Inhomogeneous Cylinders with Variable Poisson's Ratio |
| Author(s) |
D.A. Pozharskii (Don State Technical University, Azov, 344002 Russia, pozharda@rambler.ru) |
| Abstract |
In cylindrical coordinates, the system of two elastic-equilibrium differential equations is
studied under the assumption of axial symmetry and the assumption that the Poisson’s ratio is an arbitrary, sufficiently smooth, function of the radial coordinate and the modulus of rigidity is constant. It
turns out that the elastic coefficient is variable with respect to the radial coordinate in this case. We
propose a general representation of the solution of this system, leading to the vector Laplace equation
and scalar Poisson equation such that its right-hand side depends on the Poisson’s ratio. Being projected, the vector Laplace equation is reduced to two differential equations such that one of them is the
scalar Laplace equation. Using the Fourier integral transformation, we construct exact general solutions of the Laplace and Poisson equations in quadratures. We obtain the integral equation of the axially symmetric contact problem on the interaction of a rigid band with an inhomogeneous cylinder and
find its regular and singular asymptotic solutions by means of the Aleksandrov method. |
| Keywords |
contact problem, elasticity, inhomogeneous cylinder |
| Received |
01 December 2017 | Revised |
27 March 2018 | Accepted |
20 April 2018 |
| Link to Fulltext |
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