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Stability of a straight bar of variable rigidity

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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.

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References

  1. V. I. Feodos’ev, Strength of Materials (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  2. S. P. Timoshenko, Strength of Materials, Part II, Advanced Theory and Problems (D. Van Nostrand, Princeton, 1955; Fizmatgis, Moscow, 1965).

    Google Scholar 

  3. A. N. Dinnik, The Stability of Elastic Systems (ONTI, Moscow, 1935) [in Russian].

    Google Scholar 

  4. Sh. E. Mikeladze, New Methods for Integrating Differential Equations and Their Applications to Elasticity Problems (Gostekhizdat, Moscow-Leningrad, 1951) [in Russian].

    Google Scholar 

  5. L. Collatz, Eigenvalue Problems with Technical Applications (Chelsea, New York, 1948; Nauka, Moscow, 1968).

    Google Scholar 

  6. N. S. Bakhvalov and G. P. Panasenko, Averaging of Processes in Periodic Media (Nauka, Moscow, 1984) [in Russian].

    MATH  Google Scholar 

  7. B. E. Pobedrya, Mechanics of Composite Materials (Izd-vo MGU, Moscow, 1984) [in Russian].

    MATH  Google Scholar 

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Authors and Affiliations

  1. Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992, Russia

    V. I. Gorbachev & O. B. Moskalenko

Authors
  1. V. I. Gorbachev
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  2. O. B. Moskalenko
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Corresponding author

Correspondence to V. I. Gorbachev.

Additional information

Original Russian Text © V.I. Gorbachev, O.B. Moskalenko, 2011, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2011, No. 4, pp. 181–192.

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Gorbachev, V.I., Moskalenko, O.B. Stability of a straight bar of variable rigidity. Mech. Solids 46, 645–655 (2011). https://doi.org/10.3103/S0025654411040145

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  • DOI: https://doi.org/10.3103/S0025654411040145

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