 | | 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
|
| In English (Mech. Solids): | | 3212 |
|
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| V. V. Vasil'ev and L. V. Fedorov, "Geometric theory of elasticity and shape optimization for solids," Mech. Solids. 41 (1), 10-19 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
1 |
Pages |
10-19 |
| Title |
Geometric theory of elasticity and shape optimization for solids |
| Author(s) |
V. V. Vasil'ev (Moscow)
L. V. Fedorov (Moscow) |
| Abstract |
On the basis of the equations of the general relativity (GR) supplemented by
the relations for the stress-strain state of a continuum, the equations of the
geometric theory of elasticity are derived. These equations relate the
stress-strain state of the body to the Riemann space geometry. The geometric
properties of the space which models the deformed continuum are proposed to be
utilized for solving structural optimization problems. Applications of this
approach are demonstrated on the symmetric problems for a spherical body and a
disk. |
| References |
| 1. | D. Singh,
General Relativity [Russian translation],
Izd-vo Inostr. Lit-ry, Moscow, 1963. |
| 2. | E. Schmutzer,
Relativity. Modern Concept [Russian translation],
Mir, Moscow, 1981. |
| 3. | C. Mizner, K. Thorne, and D. Wheeler,
Gravitation. Volume 2 [Russian translation],
Einstein, Bishkek, 1996. |
| 4. | N. A. Kil'chevskii,
Fundamentals of Tensor Analysis with Applications in Mechanics [in Russian],
Naukova Dumka, Kiev, 1972. |
| 5. | V. V. Vasil'ev, "Stress state of solids and some geometric effects,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 30-34, 1989. |
| 6. | V. V. Vasil'ev and L. V. Fedorov, "On the problem of elasticity stated
in terms of stresses," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 82-92, 1996. |
| 7. | V. Z. Vlasov, "Equations of strain continuity
in curvilinear coordinates," in V. Z. Vlasov, Selected
Papers. Volume 1 [in Russian], Fizmatgiz, Moscow, 1962. |
| 8. | E. Kamke, Handbook on Ordinary Differential Equations [Russian translation],
Fizmatlit, Moscow, 1961. |
| 9. | P. K. Rashevskii, Riemannian Geometry and Tensor
Calculus [in Russian], Nauka, Moscow, 1976. |
|
| Received |
22 September 2004 |
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