 | | 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: | | 13288 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8164
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| In English (Mech. Solids): | | 5124 |
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| << Previous article | Volume 60, Issue 4 / 2025 | Next article >> |
| A.D. Chernyshov and V.V. Goryainov, "Rectangular Plate on an Elastic Base with Arbitrary Boundary Conditions and Arbitrary Load," Mech. Solids. 60 (4), 2474-2490 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
4 |
Pages |
2474-2490 |
| DOI |
10.1134/S0025654425600734 |
| Title |
Rectangular Plate on an Elastic Base with Arbitrary Boundary Conditions and Arbitrary Load |
| Author(s) |
A.D. Chernyshov (Voronezh State University of Engineering Technologies, Voronezh, 394000 Russia, chernyshovad@mail.ru)
V.V. Goryainov (Voronezh State Technical University, Voronezh, 394006 Russia, gorvit77@mail.ru) |
| Abstract |
In this paper, the principle of obtaining conditions for matching input data is formulated.
A set of matching conditions is obtained, failure to fulfill which leads to large unavoidable errors in the
corners of the rectangle. The problem is solved in analytical form using the method of universal fast
expansions. The obtained approximate analytical solution is compared with the test one, the error in
determining the plate deflection, torque and bending moments, shear forces and stress tensor components is investigated. It is found that when using a sixth-order boundary function and only one term in
the cosines and one term in the sines in the Fourier series in universal fast expansions, the accuracy of
the obtained solution significantly exceeds the accuracy of specifying the input parameters of the problem determined by the concept of a continuous medium. In this case, the approximate analytical solution can formally be considered exact. |
| Keywords |
plate, biharmonic equation, deflection, torsional and bending moments, shear forces, stress tensor components, universal fast expansions, fast trigonometric interpolation, high accuracy |
| Received |
15 February 2025 | Revised |
10 March 2025 | Accepted |
12 March 2025 |
| Link to Fulltext |
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