Loading [MathJax]/jax/output/SVG/config.js
Prikladnaya Mekhanika i Tekhnicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Prikl. Mekh. Tekh. Fiz.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2002, Volume 43, Issue 5, Pages 124–131 (Mi pmtf2677)  
This article is cited in 18 scientific papers (total in 18 papers)

Nonlinear bending of thin elastic rods

Yu. V. Zakharova, K. G. Okhotkinb

a Kirenskii Institute of Physics, Siberian Division, Russian Academy of Sciences, Krasnoyarsk, 660036
b Siberian State Technology University, Krasnoyarsk, 660049
Full-text PDF (558 kB) Citations (18)
Abstract: Exact solutions of the problem of nonlinear bending of thin rods under various fixing conditions and point dead loads are obtained. The solutions written in a unified parametric form and expressed in terms of the elliptic Jacobi functions are classified. These solutions depend on a single parameter – modulus of elliptic functions.
Received: 29.04.2002
English version:
Journal of Applied Mechanics and Technical Physics, 2002, Volume 43, Issue 5, Pages 739–744
DOI: https://doi.org/10.1023/A:1019800205519
Bibliographic databases:
Document Type: Article
UDC: 539.3
Language: Russian
Citation: Yu. V. Zakharov, K. G. Okhotkin, “Nonlinear bending of thin elastic rods”, Prikl. Mekh. Tekh. Fiz., 43:5 (2002), 124–131; J. Appl. Mech. Tech. Phys., 43:5 (2002), 739–744
Citation in format AMSBIB
\Bibitem{ZakOkh02}
\by Yu.~V.~Zakharov, K.~G.~Okhotkin
\paper Nonlinear bending of thin elastic rods
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2002
\vol 43
\issue 5
\pages 124--131
\mathnet{http://mi.mathnet.ru/pmtf2677}
\elib{https://elibrary.ru/item.asp?id=17274717}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2002
\vol 43
\issue 5
\pages 739--744
\crossref{https://doi.org/10.1023/A:1019800205519}
Linking options:
  • https://www.mathnet.ru/eng/pmtf2677
  • https://www.mathnet.ru/eng/pmtf/v43/i5/p124
    • This publication is cited in the following 18 articles:
    1. Dmitriy M. Zuev, Dmitrii M. Makarov, Kirill G. Okhotkin, Springer Proceedings in Physics, 1067, Proceedings of the XII All Russian Scientific Conference on Current Issues of Continuum Mechanics and Celestial Mechanics, 2024, 356  crossref
    2. Wing-Sum Law, Sofia Di Toro Wyetzner, Raymond Zhen, Sean Follmer, 2024 IEEE International Conference on Robotics and Automation (ICRA), 2024, 9696  crossref
    3. Wang Xianheng, Wang Mu, Qiu Xinming, “Sign problems in elliptic integral solution of planar elastica theory”, European Journal of Mechanics - A/Solids, 100 (2023), 105032  crossref
    4. D. M. Zuev, D. D. Makarov, K. G. Okhotkin, “Experimental and analytical study of geometric nonlinear bending of a cantilever beam under a transverse load”, J. Appl. Mech. Tech. Phys., 63:2 (2022), 365–371  mathnet  crossref  crossref  mathscinet  elib
    5. K. N. Anakhaev, “The Problem of Nonlinear Cantilever Bending in Elementary Functions”, Mech. Solids, 57:5 (2022), 997  crossref
    6. D. Weaire, A. Mughal, J. Ryan-Purcell, S. Hutzler, “Description of the buckling of a chain of hard spheres in terms of Jacobi functions”, Physica D: Nonlinear Phenomena, 433 (2022), 133177  crossref
    7. Yin-lei Huo, Xue-sheng Pei, Meng-yao Li, “Large deformation analysis of a plane curved beam using Jacobi elliptic functions”, Acta Mech, 233:9 (2022), 3497  crossref
    8. Fei Gao, Wei-Hsin Liao, Xinyu Wu, “Being gradually softened approach for solving large deflection of cantilever beam subjected to distributed and tip loads”, Mechanism and Machine Theory, 174 (2022), 104879  crossref
    9. K. N. Anakhaev, “On the Calculation of Nonlinear Buckling of a Bar”, Mech. Solids, 56:5 (2021), 684  crossref
    10. D M Zuev, Yu V Zakharov, “Large deflection of a cantilever beam under transverse loading. A modification of linear theory.”, IOP Conf. Ser.: Mater. Sci. Eng., 822:1 (2020), 012039  crossref
    11. D. M. Zuev, K. G. Okhotkin, “Modified formulas for maximum deflection of a cantilever under transverse loading”, S&T, 4:1 (2020), 28  crossref
    12. D. Singhal, V. Narayanamurthy, “Large and Small Deflection Analysis of a Cantilever Beam”, J. Inst. Eng. India Ser. A, 100:1 (2019), 83  crossref
    13. Milan Batista, “Analytical treatment of equilibrium configurations of cantilever under terminal loads using Jacobi elliptical functions”, International Journal of Solids and Structures, 51:13 (2014), 2308  crossref
    14. Giovanni Mingari Scarpello, Daniele Ritelli, “Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions”, International Journal of Mathematics and Mathematical Sciences, 2011 (2011), 1  crossref
    15. M. L. Blow, J. M. Yeomans, “Superhydrophobicity on Hairy Surfaces”, Langmuir, 26:20 (2010), 16071  crossref
    16. I. A. Lobacha, S. A. Babin, S. I. Kablukov, E. V. Podivilov, A. S. Kurkov, “Field distribution and mode interaction in twin-core fiber”, Laser Phys., 20:2 (2010), 311  crossref
    17. Yu. V. Zakharov, K. G. Okhotkin, N. V. Filenkova, A. Yu. Vlasov, “Exact and approximate formulas for deflections of an elastically fixed rod under transverse loading”, J. Appl. Mech. Tech. Phys., 48:1 (2007), 126–134  mathnet  mathnet  crossref
    18. S. Baragetti, “A Theoretical Study on Nonlinear Bending of Wires”, Meccanica, 41:4 (2006), 443  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
    Statistics & downloads:
    Abstract page:77
    Full-text PDF :26
     
      Contact us:
    math-net2025_04@mi-ras.ru     		 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025