 | | 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
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| In English (Mech. Solids): | | 4760 |
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| S.A. Lurie and P.A. Belov, "Compatibility Equations and Stress Functions in Elasticity Theory," Mech. Solids. 57 (4), 779-791 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
4 |
Pages |
779-791 |
| DOI |
10.3103/S0025654422040136 |
| Title |
Compatibility Equations and Stress Functions in Elasticity Theory |
| Author(s) |
S.A. Lurie (Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, 125040 Russia; Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, salurie@mail.ru)
P.A. Belov (Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, 125040 Russia) |
| Abstract |
Two formulations of problems in the theory of elasticity in stresses are considered. The first one is based on Papkovich's compatibility equations. The second one is based on the Saint-Venant compatibility equations. It is shown that the Cesaro formulas in both formulations make it possible to introduce as a vector of indefinite Lagrange multipliers the vector of partial solutions of inhomogeneous equilibrium equations satisfying the Neumann vector problem. On the other hand, it is shown that the compatibility equations introduced as links between distortions (Papkovich compatibility) or deformations (Saint-Venant compatibility) allow one to introduce the corresponding tensors of indefinite Lagrange multipliers. It is shown that these tensors can be considered as functions of stresses. In the first setting, the stress function tensor of the second rank has nine components, since it is generally asymmetric. In the second formulation, the stress function tensor is symmetrical and has six components. In particular, the possibility of introducing three stress functions is also discussed. |
| Keywords |
elasticity theory, stress functions, Papkovich's compatibility equations, Saint-Venant's compatibility equations, principle of possible displacements, Lagrange’s method of indefinite multipliers |
| Received |
17 January 2022 | Revised |
19 January 2022 | Accepted |
20 January 2022 |
| Link to Fulltext |
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