 | | 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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| << Previous article | Volume 57, Issue 5 / 2022 | Next article >> |
| K.N. Anakhaev, "The Problem of Nonlinear Cantilever Bending in Elementary Functions," Mech. Solids. 57 (5), 997-1005 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
5 |
Pages |
997-1005 |
| DOI |
10.3103/S0025654422050028 |
| Title |
The Problem of Nonlinear Cantilever Bending in Elementary Functions |
| Author(s) |
K.N. Anakhaev (Institute of Applied Mathematics and Automation of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, Nalchik, 360000 Russia, anaha13@mail.ru) |
| Abstract |
An analytical solution of the nonlinear problem of cantilever bending by a vertical force is presented, presented in elementary functions with calculation formulas for direct determination of the main parameters of a bent cantilever depending on the given value of the force load (module), such as coordinates of the cantilever outline, bending angles and curvature along the length of the cantilever, moments of forces and internal bending energy, as well as simplified formulas for finding the coordinates of the free end of the cantilever. Comparison of the obtained calculated values with graphical and tabular data of known numerical (exact) solutions gave a fairly high convergence of results (<1−2%), calculation examples are given. The obtained results can also be used to determine (inversely) the rigidity of the cantilever rods of arbitrary cross section, or the elastic modulus of the cantilever material at known sections, including when designing protective structures against dangerous slope geophysical processes. |
| Keywords |
cantilever, cantilever bending, nonlinear problem, Jacobi elliptic functions, elliptic integrals of the 1st and 2nd kind, bending moment of forces, internal bending energy |
| Received |
07 August 2021 | Revised |
08 October 2021 | Accepted |
11 October 2021 |
| Link to Fulltext |
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