 | | 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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| << Previous article | Volume 42, Issue 3 / 2007 | Next article >> |
| A. I. Aleksandrovich and A. V. Gorlova, "Study of the plane problem for a physically nonlinear elastic solid by methods of the theory of functions of one complex Variable," Mech. Solids. 42 (3), 382-390 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
3 |
Pages |
382-390 |
| Title |
Study of the plane problem for a physically nonlinear elastic solid by methods of the theory of functions of one complex Variable |
| Author(s) |
A. I. Aleksandrovich (Computer Center, Russian Academy of Sciences, Vavilova 40, Moscow, 119333, Russia, aialex@ccas.ru)
A. V. Gorlova (Computer Center, Russian Academy of Sciences, Vavilova 40, Moscow, 119333, Russia) |
| Abstract |
Successful application of methods of complex analysis in linear elasticity problems, initiated by Kolosov, Muskhelishvili, Vekua, and their students, serves as a basis for similar studies in the field of analytical-numerical approximations to solutions of boundary value problems and various nonlinear equations of mathematical physics. In the present paper, we suggest a method for solving plane boundary-value problems for a special class of physically nonlinear elastic solids in the case of small strains. This general method, which can be used for a wide class of domains, is illustrated by the example of a square domain with boundary conditions given in stresses. These methods can also easily be used for boundary conditions of other types. |
| References |
| 1. | A. A. Il'yushin,
Continuum Mechanics
(Izd-vo MGU, Moscow, 1971)
[in Russian]. |
| 2. | A. I. Aleksandrovich, A. V. Gorlova, A. A. Demidova, and
D. F. Titorenko, "Solution of Physically and Geometrically
Nonlinear Elasticity Problems in Complex Variables" in Reports in Applied Mathematics CC RAS (VTs RAN, Moscow, 2004)
[in Russian]. |
| 3. | N. I. Muskhelishvili,
Some Fundamental Problems of Mathematical Elasticity Theory
(Nauka, Moscow, 1966)
[in Russian]. |
| 4. | B. V. Shabat,
Introduction to Complex Analysis
(Nauka, Moscow, 1985)
[in Russian]. |
|
| Received |
26 August 2005 |
| Link to Fulltext |
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