 | | 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 59, Issue 2 / 2024 | Next article >> |
| D.V. Georgievskii, "Compatibility of Deformations and the Thrice Differentiability of the Displacement Field," Mech. Solids. 59 (2), 731-733 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
2 |
Pages |
731-733 |
| DOI |
10.1134/S0025654423602173 |
| Title |
Compatibility of Deformations and the Thrice Differentiability of the Displacement Field |
| Author(s) |
D.V. Georgievskii (Lomonosov Moscow State University, Moscow, 119991 Russia; Ishlinsky Institute for Problems in Mechanics, RAS, Moscow, 119526 Russia; Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991 Russia, georgiev@mech.math.msu.su) |
| Abstract |
The question of the necessary class of smoothness of solutions to quasi-static problems in the mechanics of a deformable solid in terms of displacements is discussed. It is shown that in order for the equations of compatibility of deformations to become identities when substituting displacements into them, the existence of some third mixed derivatives of displacements is required. For a linearly elastic compressible isotropic elastic medium, a counterexample is given in which the displacement field, being a doubly differentiable solution to the boundary value problem for the system of Lamé equations in the entire domain, is not a solution to the problem in displacements at all points of this domain. |
| Keywords |
formulation in displacements, deformation, stress, compatibility equations, continuity, differentiability, volume forces, surface loads |
| Received |
17 August 2023 | Revised |
01 September 2023 | Accepted |
04 September 2023 |
| Link to Fulltext |
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