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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. P. Popov, Theory and Calculation of Flexible Elastic Rods [in Russian], Nauka, Moscow (1986).
E. P. Popov, Nonlinear Static Problems of Thin Rods [in Russian], OGIZ, Leningrad-Moscow (1948).
W. Weaver, S. P. Timoshenko, D. H. Young, Vibration Problems in Engineering, John Wiley and Sons (1990).
A. S. Vol’mir, Stability of Deformable Systems [in Russian], Nauka, Moscow (1967).
Yu. V. Zakharov and A. A. Zakharenko, “Dynamic instability in the nonlinear problem of a cantilever, ” Vychisl. Tekhnol., 4, No. 1, 48–54 (1999).
Yu. V. Zakharov and K. G. Okhotkin, “Nonlinear bending of thin elastic rods,” J. Appl. Mech. Tech. Phys., 43, No. 5, 739–744 (2002).
Yu. V. Zakharov, K. G. Okhotkin, and A. D. Skorobogatov, “Bending of bars under a follower load, ” J. Appl. Mech. Tech. Phys., 45, No. 5, 756–763 (2004).
A. P. Seiranyan, “Lagrange problem of the most rational shape of a column,” Usp. Mekh., No. 2, 45–96 (2003).
Yu. V. Zakharov, K. G. Okhotkin, and A. Yu. Vlasov, “Approximate formulas for sagging deflections of an elastic rod under transverse loading,” J. Appl. Mech. Tech. Phys., 43, No. 5, 745–747 (2002).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 151–160, January–February, 2007.
Rights and permissions
About this article
Cite this article
Zakharov, Y.V., Okhotkin, K.G., Filenkova, N.V. et al. Exact and approximate formulas for deflections of an elastically fixed rod under transverse loading. J Appl Mech Tech Phys 48, 126–134 (2007). https://doi.org/10.1007/s10808-007-0017-8
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10808-007-0017-8