Abstract
A compact algorithm is proposed for exact calculation of the coordinates of the plane elastic line of an axially compressed flexible rod under any loads. Refined approximate formulas are obtained for calculation of the coordinates of the elastic line with an error not greater than 1% of the rod length even for loads which exceed the critical Euler load by 30%.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. N. Krylov, “Forms of equilibrium of compressed struts in buckling,” in:Selected Works [in Russian], Izd. Akad. Nauk SSSR, Moscow (1958).
E. P. Popov,Theory and Design of Flexible Elastic Rods [in Russian], Nauka, Moscow (1986).
Yu. S. Sikorskii,Theory of Elliptic Functions with Application to Mechanics [in Russian], OGIZ, Moscow (1936).
S. P. Timoshenko,Stability of Elastic Systems [in Russian], OGIZ, Moscow-Leningrad (1946).
N. S. Astapov, “Approximate formulas for deflections of compressed flexible rods,”Prikl. Mekh. Tekh. Fiz.,37, No. 4, 135–138 (1996).
A. N. Dinnik,Stability of Elastic Systems [in Russian], ONTI, Moscow-Leningrad (1935).
N. S. Astapov, “Postcritical behavior of a rod,” in:Dynamics of Continuous Media (collected scientific papers) [in Russian], Novosibirsk,92 (1989), pp. 14–21.
N. S. Astapov and V. M. Kornev, “Buckling of an eccentrically compressed elastic rod,”Prikl. Mekh. Tekh. Fiz.,37, No. 2, 162–169 (1996).
Additional information
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 200–203, May–June, 1999.
Rights and permissions
About this article
Cite this article
Astapov, N.S. An approximation of the form of a compressed flexible rod. J Appl Mech Tech Phys 40, 535–538 (1999). https://doi.org/10.1007/BF02468414
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02468414