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IssuesArchive of Issues2017-5pp.575-580

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R.A. Kayumov, "Postbuckling Behavior of Compressed Rods in an Elastic Medium," Mech. Solids. 52 (5), 575-580 (2017)
Year 2017 Volume 52 Number 5 Pages 575-580
DOI 10.3103/S0025654417050120
Title Postbuckling Behavior of Compressed Rods in an Elastic Medium
Author(s) R.A. Kayumov (Kazan State University of Architecture and Civil Engineering, ul. Zelenaya 1, Kazan, 420043 Russia, kayumov@rambler.ru)
Abstract The postbuckling of rods loaded by a compressive force P in an elastic medium is considered. The resolving nonlinear equation is obtained, and a method for solving this equation is given. It is shown that, for large lengths, in contrast to the case without elastic medium, the deflection increases as the force P decreases after the loss of stability. Several simple finite-element models, namely, the problems of compression of multilink rods with links connected by springs, are considered to confirm this effect.
Keywords loss of stability, rod, elastic medium, postbuckling bending, nonlinear equation
References
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2.  A. S. Volmir, Stability of Elastic Systems (Fizmatgiz, Moscow, 1963) [in Russian].
3.  N. A. Alfutov, Calculations of Stability of Elastic Systems (Mashinostroenie, Moscow, 1960) [in Russian].
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5.  A. N. Guz' and I. Yu. Babuch, Three-Dimensional Stability Theory of Rods, Plates, and Shells, (Vishcha Shkola, Kiev, 1980) [in Russian].
6.  A. N. Guz', Stability of Elastic Bodies in Finite Deformations (Naukova Dumka, Kiev, 1973) [in Russian].
7.  N. S. Astapov and V. M. Kornev, "Postbuckling Behavior of an Ideal Bar on an Elastic Foundation," Zh. Prikl. Mekh. Tekhn. Fiz. 35 (2), 130-142 (1994) [J. Appl. Mech. Phys. (Engl. Transl.) 35 (2), 286-296 (1994)].
8.  N. S. Astapov, "Models for the Buckling of Bars on an Elastic Base," Zh. Prikl. Mekh. Tekhn. Fiz. 37 (3), 174-177 (1996) [J. Appl. Mech. Phys. (Engl. Transl.) 37 (3), 444-446 (1996)].
9.  V. N. Paimushin, "Problems of Geometric Non-Linearity and Stability in the Mechanics of Thin Shells and Rectilinear Columns," Prikl. Mat. Mekh. 71 (5), 855-893 (2007) [J. Appl. Math. Mech. (Engl. Transl.) 71 (5), 772-805 (2007)].
10.  V. N. Paimushin, "Theory of Stability for Three-Layer Plates and Shells: Stages of Development, State-of-the-Art, and Prospects," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 148-162 (2001) [Mech. Solids (Engl. Transl.) 36 (2), 127-137 (2001)].
11.  R. A. Kayumov and B. F. Tazyukov, "Stability of Bent Thin Elastic Plate Loaded by Transverse Force," Izv. Vyssh. Uchebn. Zaved. Aviats. Tekhnika, No. 4, 12-15 (2001).
12.  S. P. Ivanov and O. G. Ivanov, Laminate Systems in Contact with Elastic Meidum (MarGTU, Ioshkar-Ola, 2008) [in Russian].
13.  V. D. Kurguzov, "Modeling of Thin Film Separation in Compression," Vychisl. Mekh. Sploshnykh Sred 7 (1), 91-99 (2014).
14.  A. R. Shugurov and A. V. Panin, "Mechanisms of Periodic Deformation of the "Film-Substrate" System under the Action of Compressing Stresses," Fizich. Mezomekh. 12 (3), 23-32 (2009).
Received 21 April 2015
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