 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 48, Issue 4 / 2013 | Next article >> |
| D.V. Georgievskii, "Symmetrization of the Tensor Operator of the Compatibility Equations in Stresses in the Anisotropic Theory of Elasticity," Mech. Solids. 48 (4), 405-409 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
4 |
Pages |
405-409 |
| DOI |
10.3103/S0025654413040079 |
| Title |
Symmetrization of the Tensor Operator of the Compatibility Equations in Stresses in the Anisotropic Theory of Elasticity |
| Author(s) |
D.V. Georgievskii (Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991 Russia, georgiev@mech.math.msu.su) |
| Abstract |
The general form of the term whose addition to the left-hand side of the compatibility equation in stresses in anisotropic elasticity symmetrizes the rank four differential tensor operator of these equations is obtained. In the case of an arbitrary type of anisotropy, this term contains two arbitrary parameters of dimension of elastic compliances. The symmetrized compatibility equations themselves contain only one of these parameters, and the combination of the terms with this parameter can be separated from the terms containing the tensor of elastic compliances. |
| Keywords |
compatibility equations, equilibrium equations, anisotropy, elastic compliance, symmetrization |
| References |
| 1. | B. E. Pobedrya,
Numerical Methods in the Theory of Elasticity and Plasticity
(Izd-vo MGU, Moscow, 1995)
[in Russian]. |
| 2. | B. E. Pobedrya,
"A New Formulation of the Problem of the Mechanics of a Deformable Solid in Stresses,"
Dokl. Akad. Nauk SSSR
253 (2), 295-297 (1980)
[Soviet Math. Dokl. (Engl. Transl.)
22 (1), 88-91 (1981)]. |
| 3. | D. V. Georgievskii,
"Linear Algebraic Symmetrization of the Beltrami-Michel Equations Operator,"
Dokl. Ross. Akad. Nauk
448 (4), 410-412 (2013)
[Dokl. Phys. (Engl. Transl.)
588 (2), 56-58 (2013)]. |
| 4. | V. A. Kucher, X. Markenscoff, and M. V. Paukshto,
"Some Properties of the Boundary-Value Problem of Linear Elasticity in Terms of Stresses,"
J. Elasticity
74 (2), 135-145 (2004). |
| 5. | N. M. Borodachev,
"Solutions of the Spatial Elasticity Problem in Stresses,"
Prikl. Mekhanika 42 (8), 3-35 (2006). |
| 6. | M. U. Nikabadze,
"On the Compatibility Conditions and Equations of Motion in Micropolar Linear Elasticity,"
Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 1, 63-66 (2012)
[Moscow Univ. Math. Bull.]. |
|
| Received |
10 January 2013 |
| Link to Fulltext |
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