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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2007, Volume 48, Issue 1, Pages 151–160 (Mi pmtf2004)  
Exact and approximate formulas for deflections of an elastically fixed rod under transverse loading

Yu. V. Zakharova, K. G. Okhotkinb, N. V. Filenkovac, A. Yu. Vlasovc

a Kirenskii Institute of Physics, Siberian Division, Russian Academy of Sciences, Krasnoyarsk, 660036
b Siberian State Aerospace University, Krasnoyarsk, 660014
c Siberian State Technology University, Krasnoyarsk, 660049
Full-text PDF (295 kB)
Abstract: An exact solution is obtained for the nonlinear bending problem of a thin rod elastically fixed at one end and loaded by a transverse concentrated load of constant direction at the other end. The solution is written in parametric form and expressed in terms of the Jacobi elliptic functions. Based on the exact solutions, approximate formulas are proposed for the de.ection of the rod tip.
Keywords: rod bending, elastic fixing conditions, Jacobi elliptic functions.
Received: 19.12.2005
Accepted: 14.02.2006
English version:
Journal of Applied Mechanics and Technical Physics, 2007, Volume 48, Issue 1, Pages 126–134
DOI: https://doi.org/10.1007/s10808-007-0017-8
Bibliographic databases:
Document Type: Article
UDC: 539.3
Language: Russian
Citation: 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”, Prikl. Mekh. Tekh. Fiz., 48:1 (2007), 151–160; J. Appl. Mech. Tech. Phys., 48:1 (2007), 126–134
Citation in format AMSBIB
\Bibitem{ZakOkhFil07}
\by Yu.~V.~Zakharov, K.~G.~Okhotkin, N.~V.~Filenkova, A.~Yu.~Vlasov
\paper Exact and approximate formulas for deflections of an elastically fixed rod under transverse loading
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2007
\vol 48
\issue 1
\pages 151--160
\mathnet{http://mi.mathnet.ru/pmtf2004}
\elib{https://elibrary.ru/item.asp?id=17249408}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2007
\vol 48
\issue 1
\pages 126--134
\crossref{https://doi.org/10.1007/s10808-007-0017-8}
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