 | | 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 49, Issue 3 / 2014 | Next article >> |
| B.A. Zhukov, "Inverse Problems of Determining the Shape of Incompressible Bodies under Finite Strains," Mech. Solids. 49 (3), 280-289 (2014) |
| Year |
2014 |
Volume |
49 |
Number |
3 |
Pages |
280-289 |
| DOI |
10.3103/S0025654414030042 |
| Title |
Inverse Problems of Determining the Shape of Incompressible Bodies under Finite Strains |
| Author(s) |
B.A. Zhukov (Volgograd State Technical University, pr. Lenina 28, Volgograd, 400131 Russia, zhukov.b.a@gmail.com) |
| Abstract |
Transformations preserving the volume under finite strains are given for some classes of two-dimensional problems. Several settings of nonlinear elasticity problems meant for determining the shape of mechanical rubber objects from a given configuration in a strained state are proposed on the basis of these transformations. Two axisymmetric problems are solved as an example. In the first problem, we determine the shape of a rubber bushing in a combined rubber-metal joint which has a prescribed configuration in the assembled state. In the second problem, we determine the shape of the rubber element of a cylindrical compression damper in working state. |
| Keywords |
finite strain, hyperelasticity, incompressibility, shape determination |
| References |
| 1. | R. Courant,
Partial Differential Equations
(Mir, Moscow, 1964)
[in Russian]. |
| 2. | A. M. Bogoroditskii,
"Axially Symmetric Problem of the Nonlinear Theory of Elasticity for an Incompressible Medium,"
Prikl. Mat. Mekh.
28 (3), 597-600 (1964)
[J. Appl. Math. Mech. (Engl. Transl.)
28 (3), 736-740 (1964)]. |
| 3. | V. I. Arnold,
Mathematical Methods of Classical Mechanics
(Nauka, Moscow, 1974)
[in Russian]. |
| 4. | A. I. Lurie,
Nonlinear Theory of Elasticity
(Nauka, Moscow, 1980)
[in Russian]. |
|
| Received |
01 December 2011 |
| Link to Fulltext |
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