Skip to main content
SpringerLink
Log in

Three-dimensional stability theory of deformable bodies. Stability of construction elements

  • Published:
Soviet Applied Mechanics Aims and scope

Conclusion

In [8, 9] and in the present paper we analyzed the possibilities of using the approximate approach [15, 18] in the three-dimensional stability theory of deformable bodies as applied to effects of internal and surface instability and to stability of thinwalled structural elements. The analysis mentioned has been performed by comparing for standard problems the results obtained by the approximate approach [15, 18] with the results for the similar problems, obtained within the three-dimensional linearized stability theory of deformable bodies (for example [2–5, 7, 10, 19]), constructed with the accuracy usually adopted in mechanics. The following conclusions are drawn as a result of the analysis.

Applied to effects of internal and surface instability, the approximate approach leads to result in disagreement with the corresponding results of the three-dimensional linearized stability theory of deformable bodies.

As applied to the study of stability of thin-walled structural elements, the use of the approximate approach is justified if we restrict ourselves to a calculational accuracy of critical loads corresponding to that of the Kirchhoff-Love hypothesis.

In connection with the discussion above, numerous publications carried out on the basis of the approximate approach require further study to clarify the validity limits of the results obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature Cited

  1. A. N. Guz', “Accuracy of the Kirchhoff-Love hypothesis for determination of critical forces in the theory of elastic stability,” Dokl. Akad. Nauk SSSR,179, No. 3, 552–554 (1968).

    Google Scholar 

  2. A. N. Guz', Stability of Three-Dimensional Deformable Bodies [in Russian], Naukova Dumka, Kiev (1971).

    Google Scholar 

  3. A. N. Guz', Stability of Elastic Bodies for Finite Deformations [in Russian], Naukova Dumka, Kiev (1973).

    Google Scholar 

  4. A. N. Guz', Foundations of Stability Theory of Mines [in Russian], Naukova Dumka, Kiev (1977).

    Google Scholar 

  5. A. N. Guz', Stability of Elastic Bodies under Hydrostatic Stress [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  6. A. N. Guz', “Analysis of computational schemes in stability theory of structural elements of composite materials,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 4, 31–36 (1980).

    Google Scholar 

  7. A. N. Guz', Mechanics of Brittle Destruction of Materials with Initial Stress [in Russian], Naukova Dumka, Kiev (1983).

    Google Scholar 

  8. A. N. Guz', “Three-dimensional stability theory of deformable bodies. Internal instability,” Prikl. Mekh.,21, No. 11, 3–17 (1985).

    Google Scholar 

  9. A. N. Guz', “Three-dimensional stability theory of deformable bodies. Internal instability,” Prikl. Mekh.,22, No. 1, 3–18 (1986).

    Google Scholar 

  10. A. N. Guz' and I. Yu. Babich, Three-Dimensional Theory of Bars, Plates, and Shells [in Russian], Vishcha Shkola, Kiev (1981).

    Google Scholar 

  11. A. N. Guz' and A. N. Sporykhin, “Three-dimensional theory of inelastic stability,” Prikl. Mekh.,19, No. 7, 3–22; No. 8, 3–27 (1982).

    Google Scholar 

  12. A. N. Guz' and V. N. Chekhov, “Linearized theory of fold formation in the thick core of the earth,” Prikl. Mekh.,11, No. 1, 3–14 (1975).

    Google Scholar 

  13. Zh. S. Erzhanov and A. K. Egorov, Theory of the Fold Formation Process in Rocks (Mathematical Description) [in Russian], Nauka, Alma-Ata (1968).

    Google Scholar 

  14. L. V. Ershov and D. D. Ivlev, “Bulge of a thick-walled tube under the action of internal pressure,” Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 8, 149–152 (1957).

    Google Scholar 

  15. A. Yu. Ishlinskii, “Treatment of stability problems of equilibrium elastic bodies from the point of view of mathematical elasticity theory,” Ukr. Mat. Zh.,6, No. 2, 140–146 (1954).

    Google Scholar 

  16. I. D. Legenya, “Stability of a thick rectangular simply supported slab under the action of compressing loads,” Dokl. Akad. Nauk SSSR,140, No. 4, 776–779 (1961).

    Google Scholar 

  17. I. D. Legenya, “Stability of a compressed plate with account of rotational angles,” Dokl. Akad. Nauk SSSR,149, No. 4, 802–805 (1963).

    Google Scholar 

  18. L. S. Leibenzon, Application of Harmonic Functions to the Stability Problem of Spherical and Cylindrical Shells (Collected Works, Vol. 1) [in Russian], Izd. Akad. Nauk SSSR, Moscow (1951).

    Google Scholar 

  19. V. V. Novozhilov, Foundations of Nonlinear Elasticity Theory [in Russian], Gostekhizdat, Moscow (1948).

    Google Scholar 

  20. Zh. S. Erzhanov, A. K. Egoroy, I. A. Garagash, et al., Theory of Fold Formation in the Earth's Core [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  21. J. L. Nowinski, “On the elastic stabiity of thick columns,” Acta Mech., No. 7/4 (1969).

Download references

Authors
  1. A. N. Guz'
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 22, No. 2, pp. 3–17, February, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guz', A.N. Three-dimensional stability theory of deformable bodies. Stability of construction elements. Soviet Applied Mechanics 22, 97–108 (1986). https://doi.org/10.1007/BF00886996

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00886996

Keywords

Search

Navigation