 | | 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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| V.V. Vasil'ev and S.A. Lurie, "Generalized Theory of Elasticity," Mech. Solids. 50 (4), 379-388 (2015) |
| Year |
2015 |
Volume |
50 |
Number |
4 |
Pages |
379-388 |
| DOI |
10.3103/S0025654415040032 |
| Title |
Generalized Theory of Elasticity |
| Author(s) |
V.V. Vasil'ev (Moscow State Aviation Technological University, ul. Orshanskaya 3, Moscow, 121552 Russia, vvvas@dol.ru)
S.A. Lurie (Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia; A. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, lurie@ccas.ru) |
| Abstract |
We obtain elasticity equations of higher (in the general case, infinite) order than the equations of the classical theory. In contrast to the numerous known versions of the nonclassical theory (Cosserat, nonsymmetric, microstructure, micropolar, multipolar, and gradient), which also result in higher-order equations and contain elasticity relations for traditional and couple stresses with a large number of elastic constants, our theory, regardless of the order of the equations, contains only one additional constant, which can be expressed in terms of the microstructure parameter of the medium. The basic equations of the generalized theory are presented for one-, two-, and three-dimensional problems; these equations take into account the stress gradients and can be written in terms of generalized stresses, strains, and displacements. A boundary value problem that does not require the introduction of couple stresses is stated for the generalized theory of elasticity. |
| Keywords |
theory of elasticity, nonclassical theory of elasticity, generalized stresses, microstructure parameter |
| References |
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| 10. | S. Lurie, D. Volkov-Bogorodsky, V. Zubov, and N. Tuchkova,
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Cohesion/Adhesion Interactions in Continuum Mechanics and Its
Applications for Filled Nanocomposites," Comput. Mater. Sci.
45 (3), 709-714 (2009). |
| 11. | S. Lurie, D. Volkov-Bogorodsky, A. Leontiev, and E. Aifantis,
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Applications to Composite Materials,"
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[in Russian]. |
| 14. | V. V. Vasil'ev and S. A. Lurie, "On the Solution Singularity in
the Plane Elasticity Problem for a Cantilever Strip," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 40-49 (2013) [Mech. Solids (Engl. Transl.) 48 (4), 388-396 (2013)]. |
|
| Received |
20 November 2014 |
| Link to Fulltext |
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