 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| V.V. Vasil'ev and S.A. Lurie, "Generalized Solution of the Problem on a Circular Membrane Loaded by a Lumped Force," Mech. Solids. 51 (3), 334-338 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
3 |
Pages |
334-338 |
| DOI |
10.3103/S0025654416030109 |
| Title |
Generalized Solution of the Problem on a Circular Membrane Loaded by a Lumped Force |
| Author(s) |
V.V. Vasil'ev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, vvvas@dol.ru)
S.A. Lurie (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Institute of Applied Mechanics, Russian Academy of Sciences, Leninskii pr. 32A, Moscow, 117334 Russia, lurie@ccas.ru) |
| Abstract |
The solution of the problem on a circular membrane loaded at the center by a lumped force is a classical example of a singular solution of equations of mathematical physics. In this paper, the problem is solved by using relations of the generalized theory of elasticity, which contain a structural parameter and permit obtaining a regular solution. An experiment for determining the structural parameter in the problem of bending of a membrane is described. |
| Keywords |
singular solution, nonclassical theories of elasticity, elastic membrane |
| References |
| 1. | S. G. Mikhlin,
Linear Partial Differential Equations
(Vysshaya Shkola, Moscow, 1977)
[in Russian]. |
| 2. | V. V. Vasil'ev and S. A. Lurie,
"Generalized Theory of Elasticity,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 16-27 (2015)
[Mech. Solids (Engl. Transl.)
50 (4), 379-388 (2015)]. |
| 3. | G. A. Korn and T. M. Korn,
Mathematical Handbook for Scientists and Engineers
(McGraw-Hill, New York, 1968; Nauka, Moscow, 1973). |
| 4. | M. Abramowitz and I. Stegun (Editors),
Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables
(Gov. Print off., Wasgington, 1964; Nauka, Moscow, 1979). |
|
| Received |
17 December 2015 |
| Link to Fulltext |
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