 | | 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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| N. G. Khomasuridze, "Some passages to the limit in elasticity theory and "Sapondzhyan’s paradox"," Mech. Solids. 42 (3), 367-374 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
3 |
Pages |
367-374 |
| Title |
Some passages to the limit in elasticity theory and "Sapondzhyan’s paradox" |
| Author(s) |
N. G. Khomasuridze (Vekua Institute of Applied Mathematics, Tbilisi State University, Universitetskaya 2, Tbilisi, 380052, Georgia, nurikhomasuridze@hotmail.com) |
| Abstract |
We consider bending of thin plates with polygonal and curvilinear edges and indicate analogies and differences between the boundary conditions and boundary value problems arising in these two cases if the polygon is inscribed in the curvilinear contour and the number k of vertices of the polygon tends to infinity.
We believe that the so-called Sapondzhyan paradox that arises when solving the boundary value problems for supported plates with a curvilinear contour and a k-gonal contour inscribed in it as k→∞ can be called a paradox only by misunderstanding. Sapondzhyan’s paradox was studied in several papers briefly surveyed in the monograph [1]. Apparently, the interpretation of "paradoxes" and the results proposed in the present paper are published for the first time.
Sapondzhyan’s paradox can be generalized to the case of bending of the so-called sliding-fixed plates (i.e., the generalized shear force and the rotation angle are zero on the plate contour) with a curvilinear contour and a k-gonal contour inscribed in it as k→∞.
In the case of three-dimensional elasticity problems, we present boundary conditions and boundary value problems similar to those listed above and consider the situations resulting in "paradoxes" similar to those arising in plate bending. We give the corresponding explanations and interpretations. |
| References |
| 1. | Ya. G. Panovko,
Mechanics of Deformable Solids
(Nauka, Moscow, 1985)
[in Russian]. |
| 2. | V. L. Biderman, Mechanics of Thin-Walled Structures
(Mashinostroenie, Moscow, 1977) [in Russian]. |
| 3. | O. N. Sapondzhyan,
"Bending of a Freely Supported Polygonal Plate,"
Izv. AN. Arm.SSR. Ser. Fiz.-Mat. i Estestv. Nauk
5 (2), 29-46 (1952). |
| 4. | V. V. Novozhilov,
Theory of Elasticity
(Sudpromgiz, Leningrad, 1958)
[in Russian]. |
| 5. | N. G. Khomasuridze, "Thermoelastic Equilibrium of a Rectangular
Parallelepiped with Nonhomogeneous Symmetry and Antisymmetry
Conditions on Its Faces," Georgian Math. J. 7 (4), 701-722
(2000). |
|
| Received |
14 July 2004 |
| Link to Fulltext |
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