Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2022-5pp.997-1005

Archive of Issues

Total articles in the database: 10864
In Russian (. . ): 8009
In English (Mech. Solids): 2855

<< 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 2021Revised 08 October 2021Accepted 11 October 2021
Link to Fulltext
<< Previous article | Volume 57, Issue 5 / 2022 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100