 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 49, Issue 5 / 2014 | Next article >> |
| D.B. Davtyan and D.A. Pozharskii, "Action of an Elliptic Punch on a Transversally Isotropic Half-Space," Mech. Solids. 49 (5), 578-586 (2014) |
| Year |
2014 |
Volume |
49 |
Number |
5 |
Pages |
578-586 |
| DOI |
10.3103/S0025654414050094 |
| Title |
Action of an Elliptic Punch on a Transversally Isotropic Half-Space |
| Author(s) |
D.B. Davtyan (Don State Technical University, pl. Gagarina 1, Rostov-on-Don, 344000 Russia)
D.A. Pozharskii (Don State Technical University, pl. Gagarina 1, Rostov-on-Don, 344000 Russia, pozharda@rambler.ru) |
| Abstract |
The 3D contact problem on the action of a punch elliptic in horizontal projection on a transversally isotropic elastic half-space is considered for the case in which the isotropy planes are perpendicular to the boundary of the half-space. The elliptic contact region is assumed to be given (the punch has sharp edges). The integral equation of the contact problem is obtained. The elastic rigidity of the half-space boundary characterized by the normal displacement under the action of a given lumped force significantly depends on the chosen direction on this boundary. In this connection, the following two cases of location of the ellipse of contact are considered: it can be elongated along the first or the second axis of Cartesian coordinate system on the body boundary. Exact solutions are obtained for a punch with base shaped as an elliptic paraboloid, and these solutions are used to carry out the computations for various versions of the five elastic constants. The structure of the exact solution is found for a punch with polynomial base, and a method for determining the solution is proposed. |
| Keywords |
theory of elasticity, contact problems, transversal isotropy |
| References |
| 1. | H. A. Elliot,
"Three-Dimensional Stress Distributions in Hexagonal Crystals,"
Proc. Cambridge Phil. Soc.
44 (4), 522-533 (1948). |
| 2. | H. A. Elliot,
"Axial Symmetric Stress Distribution in Aeolotropic Hexagonal Crystals.
The Problem of Plane and Related Problems,"
Proc. Cambridge Phil. Soc.
45, 621-630 (1949). |
| 3. | V. I. Fabrikant,
"Non-Traditional Contact Problem for Transversely Isotropic Half-Space,"
Quart. J. Mech. Appl. Math.
64 (2), 151-170 (2011). |
| 4. | D. V. Grilitskii and B. G. Shelestovskii,
"Axisymmetric Contact Problem of Thermoelasticity for
Transversally Isotropic Half-Space,"
Prikl. Mekh.
6 (8), 3-8 (1970). |
| 5. | V. I. Fabrikant,
"Spatial Contact Problem for a Rough Punch,"
Prikl. Mekh.
10 (7), 106-109 (1974). |
| 6. | V. I. Fabrikant,
"Non-Traditional Crack Problem for Transversely-Isotropic Body,"
Europ. J. Mech.
30, 902-912 (2011). |
| 7. | L. A. Galin,
Contact Problems of Elasticity
(Gostekhizdat, Moscow, 1953)
[in Russian]. |
| 8. | V. I. Dovnorovich,
Three-Dimensional Contact Problems of Elasticity Theory
(Izd-vo Belorus. Univ., Minsk, 1959)
[in Russian]. |
| 9. | V. M. Alexandrov,
On the Action of Elliptic Punch on an Elastic Half-Space,
in Author's Abstracts of Scientific Papers in 1959
(Izd-vo RGU, 1960),
pp. 45-47
[in Russian]. |
| 10. | I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko,
Nonclassical Mixed Problems of Elasticity
(Nauka, Moscow, 1974)
[in Russian]. |
| 11. | I. S. Gradshtein and I. M. Ryzhik,
Tables of Integrals, Sums, Series, and Products
(Nauka, Moscow, 1971)
[in Russian]. |
|
| Received |
20 September 2012 |
| Link to Fulltext |
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