 | | 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 57, Issue 4 / 2022 | Next article >> |
| V.V. Vasil'ev and L.V. Fedorov, "Stress Functions in Elasticity Theory," Mech. Solids. 57 (4), 770-778 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
4 |
Pages |
770-778 |
| DOI |
10.3103/S0025654422040197 |
| Title |
Stress Functions in Elasticity Theory |
| Author(s) |
V.V. Vasil'ev (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, vvvas@dol.ru)
L.V. Fedorov (JSC MIC "NPO Mashinostroyenia," Reutov, 143966 Russia) |
| Abstract |
The article is devoted to the study of stress functions that make it possible to identically satisfy the equilibrium equations of the classical elasticity theory and obtain a solution in stresses. To obtain the dependences between stresses and stress functions, the mathematical apparatus of the general theory of relativity is used, in particular, the property of the Einstein tensor to identically satisfy the equations of the conservation law, which, in relation to the theory of elasticity, are equilibrium equations. In this case, the metric coefficients of the Riemannian space, determined by the Einstein equations, are interpreted as functions of the stresses of the elasticity theory. As a result of the linearization of Einstein's equations, general relations between stresses and stress functions in an orthogonal coordinate system are obtained. Stress functions corresponding to the Cartesian coordinate system are considered. The possibilities of satisfying the equilibrium equations with the help of various combinations of stress functions are analyzed – the known systems of Maxwell, Morer and other possible combinations formed from one, two and three functions. As a solvability criterion of the problem of the theory of elasticity in stresses, the correspondence of the number of stress functions to the number of mutually independent equations of compatibility of deformations in stresses is used. |
| Keywords |
elasticity theory, stress functions, general relativity |
| Received |
18 November 2021 | Revised |
21 November 2021 | Accepted |
22 November 2021 |
| Link to Fulltext |
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