 | | 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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| V.V. Vasil'ev, "Kirchhoff and Thomson-Tait Transformations in the Classical Theory of Plates," Mech. Solids. 47 (5), 571-579 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
5 |
Pages |
571-579 |
| DOI |
10.3103/S0025654412050111 |
| Title |
Kirchhoff and Thomson-Tait Transformations in the Classical Theory of Plates |
| Author(s) |
V.V. Vasil'ev (Moscow State Aviation Technological University, Orshanskaya 3, Moscow, 121552 Russia, vvvas@dol.ru) |
| Abstract |
The transformation of the torque into the transverse force is considered; this transformation is traditional in the educational literature [1] and was proposed by Kirchhoff [2] and Thomson and Tait [3] to match the order of the differential equation of the classical theory of plates with the number of boundary conditions. It is shown that this transformation is not universal and its mathematical and physical justification depends on the conditions of the plate fixation and loading. It is shown that this justification is absent for the most widely used problems of bending of a rectangular plate freely supported and fixed on the contour. |
| Keywords |
theory of plates, boundary conditions |
| References |
| 1. | S. P. Timoshenko and S. Woinowsky-Krieger,
Theory of Plates and Shells
(McGraw-Hill, New York, 1959; Fizmatgiz, Moscow, 1963. |
| 2. | G. Kirchhoff,
"Uber das Gleichgewicht und die Bewegung einer Elastischen Scheibe,"
J. Reine Angew. Math.
40, 51-58 (1850). |
| 3. | W. Thomson and P. Tait,
Treatise on Natural Philosophy, Part 2
(Cambridge Univ. Press, Cambridge, 1883). |
| 4. | S. D. Poisson,
"Memoire sur l'equilibre et le mouvement des corps e'lastiques,"
Memoires Acad. Sci. Paris
18, 357-570 (1829). |
| 5. | P. A. Zhilin,
"On the Poisson and Kirchhoff Theories of Plates from the Standpoint
of the Contemporary Theory of Plates ,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 48-64 (1992)
[Mech. Solids (Engl. Transl.)]. |
| 6. | P. A. Zhilin,
"On the Classical Plate Theory and the Kelvin-Tait Transformation,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 134-140 (1995)
[Mech. Solids (Engl. Transl.)
30 (4), 124-129 (1995)]. |
| 7. | N. A. Alfutov,
"On Some Paradoxes of the Theory of Elastic Plates,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 65-72 (1992)
[Mech. Solids (Engl. Transl.)]. |
| 8. | V. G. Rekach,
Solution of Elasticity Problems. Handbook
(Vysshaya Shkola, Moscow, 1966)
[in Russian]. |
| 9. | E. Reissner,
"On the Theory of Bending of Elastic Plates,"
J. Math. Phys.
23 (4), 184-191 (1944). |
| 10. | V. V. Vasil'ev,
"Classical Theory of Plates: Historical Perspective and State-of-the-Art,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 46-58 (1998)
[Mech. Solids (Engl. Transl.)
33 (3), 35-45 (1998)]. |
| 11. | M. Schafer,
"Uber eine Verfeinerung der Klassischen Theorie dünner schwach gebegener Platten,"
ZAMM
32 (6), 161-171 (1952). |
| 12. | A. Kromm,
"Uber die Randquerkafter bei gestutzten Platten,"
ZAMM
35 (6/7), 231-242 (1955). |
| 13. | M. P. Sheremet'ev, B. L. Pelekh, and O. P. Dyachina,
"A Study of the Effect of Shear Strains on the Bending of a
Square Slab by a Concentrated Force,"
Prikl. Mekh.
4 (4), 1-7 (1968)
[Int. Appl. Mech. (Engl. Transl.)
4 (4), 1-4 (1968)]. |
|
| Received |
25 May 2012 |
| Link to Fulltext |
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