Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2011-4pp.645-655

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Total articles in the database: 10864
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V.I. Gorbachev and O.B. Moskalenko, "Stability of a Straight Bar of Variable Rigidity," Mech. Solids. 46 (4), 645-655 (2011)
Year 2011 Volume 46 Number 4 Pages 645-655
DOI 10.3103/S0025654411040145
Title Stability of a Straight Bar of Variable Rigidity
Author(s) V.I. Gorbachev (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia, vigorby@mail.ru)
O.B. Moskalenko (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia, kazantseva.olga@gmail.com)
Abstract We consider the longitudinal compression of a straight bar whose rigidity is a periodic integrable function of the longitudinal coordinate. For a hinged bar with one clamped end, we obtain approximate analytic formulas that permit obtaining the critical compressing loads under which an adjacent, curved form of equilibrium is possible. In the case of a bar of stepwise varying rigidity that consists of a single period (the limit case), we compare the results obtained by our formulas with the already known exact solutions of the stability equation. A good agreement between the approximate and exact results is shown.
Keywords mechanics of deformable solids, elasticity, stability, bar of variable cross-section, averaging method
References
1.  V. I. Feodos'ev, Strength of Materials (Nauka, Moscow, 1979) [in Russian].
2.  S. P. Timoshenko, Strength of Materials, Part II, Advanced Theory and Problems (D. Van Nostrand, Princeton, 1955; Fizmatgis, Moscow, 1965).
3.  A. N. Dinnik, The Stability of Elastic Systems (ONTI, Moscow, 1935) [in Russian].
4.  Sh. E. Mikeladze, New Methods for Integrating Differential Equations and Their Applications to Elasticity Problems (Gostekhizdat, Moscow-Leningrad, 1951) [in Russian].
5.  L. Collatz, Eigenvalue Problems with Technical Applications (Chelsea, New York, 1948; Nauka, Moscow, 1968).
6.  N. S. Bakhvalov and G. P. Panasenko, Averaging of Processes in Periodic Media (Nauka, Moscow, 1984) [in Russian].
7.  B. E. Pobedrya, Mechanics of Composite Materials (Izd-vo MGU, Moscow, 1984) [in Russian].
Received 08 June 2009
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