 | | 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
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| In English (Mech. Solids): | | 4810 |
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| M.D. Kovalenko, I.V. Menshova, A.P. Kerzhaev, and T.D. Shulyakovskaya, "Some Solutions of the Theory of Elasticity for a Rectangle," Mech. Solids. 56 (7), 1232-1242 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
7 |
Pages |
1232-1242 |
| DOI |
10.3103/S0025654421070153 |
| Title |
Some Solutions of the Theory of Elasticity for a Rectangle |
| Author(s) |
M.D. Kovalenko (Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, 125040 Russia, kov08@inbox.ru)
I.V. Menshova (Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow, 117997 Russia; Bauman Moscow State Technical University, Moscow, 105005 Russia, menshovairina@yandex.ru)
A.P. Kerzhaev (Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow, 117997 Russia, alex_kerg@mail.ru)
T.D. Shulyakovskaya (Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, 123995Russia, 5095739@mail.ru) |
| Abstract |
The ready-made formulas describing the solutions to boundary value problems of the theory
of elasticity in a rectangle in which two opposite sides are free and normal or tangential stresses are set
on the other two sides are presented. All cases of symmetry about the central axes are considered. The
solutions are represented as series in Papkovich–Fadle eigenfunctions. The series coefficients are
determined from simple closed formulas, such as Fourier integrals of the given boundary functions.
An example of comparing the exact solution to the solution obtained on the basis of the beam theory
is presented for a sufficiently narrow rectangle. |
| Keywords |
rectangle, Papkovich–Fadle eigenfunctions, exact solutions |
| Received |
19 November 2020 | Revised |
01 February 2021 | Accepted |
25 February 2021 |
| Link to Fulltext |
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