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PHYSICAL-MATHEMATICAL SCIENCES
To solve the problem of nonlinear bending of the console
K. N. Anakhaev Institute of Applied Mathematics and Automation –
branch of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences,
360000, Russia, Nalchik, 89 A Shortanov street
Abstract:
An improved technique for solving the classical nonlinear problem of bending the console from the action of a vertical force is presented. New design dependencies are proposed, which allow
directly (without selection) to establish the analytical relationship of the module of elliptic functions and
integrals with a force similarity coefficient determined for the initially defined characteristics of the console and the active load, comparing the results of the calculation of which with the exact values of the
module gave a fairly close coincidence (< 1%). The above makes a direct solution of the problem under
consideration possible with the definition of the main parameters of the bent console, such as the coordinates of the shape of the console, bending angles, etc. The obtained results can be used, in particular, in
designing protective structures against dangerous prone geophysical processes, etc.
Keywords:
console, cantilever bend, nonlinear problem, elliptical Jacobi functions, elliptical integrals
of 1 and 2 kind, force similarity coefficient.
Received: 19.01.2022 Accepted: 02.03.2022
Citation:
K. N. Anakhaev, “To solve the problem of nonlinear bending of the console”, News of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, 2022, no. 2, 11–16
Linking options:
https://www.mathnet.ru/eng/izkab424 https://www.mathnet.ru/eng/izkab/y2022/i2/p11
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Abstract page: | 40 | Full-text PDF : | 16 | References: | 11 |
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