Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Method of discrete approximation of the functional in stability problems of shells of revolution

  • 15 Accesses

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

Literature Cited

  1. 1.

    D. V. Babich and A. S. Strel'chenko, “Stability of variable-thickness shells of revolution,” Stability of Spatial Structures [in Russian], Kiev Structural Engineering Institute, Kiev, 48–51 (1978).

  2. 2.

    V. V. Bolotin, “On reduction of three-dimensional problems of elastic stability theory to one- and two-dimensional problems,” Trans. All-Union Conf. on Stability Problems in Struct. Mech, Moscow, 1–5 October, 1963, 166–179, Moscow (1965).

  3. 3.

    V. V. Gaidaichuk, E. A. Gotsulyak, and V. I. Gulyaev, “Bifurcation of solutions of nonlinear toroidal shell equations under the effect of external pressure,” Prikl. Mekh.,14, No. 9, 38–45 (1978).

  4. 4.

    E. I. Grigolyuk and V. V. Kabanov, Shell Stability [in Russian], Nauka, Moscow (1978).

  5. 5.

    L. Collacz, Eigenvalue Problems [Russian translation], Nauka, Moscow (1968).

  6. 6.

    Yu. V. Lipovtsev, “Difference method of solving stability problems of shells of revolution,” Theory of Plates and Shells [in Russian], 166–172, Nauka, Moscow (1971).

  7. 7.

    A. Z. Lokshin, V. A. Postnov, and B. N. Slavorotsov, “On the question of the influence of boundary conditions on the stability of an orthotropic cylindrical shell subjected to the action of transverse and longitudinal pressure,” Report to the Fourteenth Sci.-Tech. Conf. on Struct. Mech. of Ships, Leningrad, June, 1966 [in Russian], Leningrad, 119–124 (1966).

  8. 8.

    V. I. Myachenkov, “Stability of orthotropic shells of revolution subjected to axisymmetric loads,” Izv. Akad. Nauk SSSR, Mekhan. Tverd. Tela, No. 1, 106–113 (1968).

  9. 9.

    A. A. Samarskii and V. B. Andreev, Difference Methods for Elliptic Equations [in Russian], Nauka, Moscow (1976).

  10. 10.

    A. V. Karmishin, V. A. Lyaskovets, V. I. Myachenkov, and A. N. Frolov, Statics and Dynamics of Thin-Walled Shell Structures [in Russian], Mashinostroenie, Moscow (1975).

Download references

Additional information

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 19, No. 2, pp. 38–44, February, 1983.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Babich, D.V. Method of discrete approximation of the functional in stability problems of shells of revolution. Soviet Applied Mechanics 19, 126–131 (1983). https://doi.org/10.1007/BF00882329

Download citation


  • Stability Problem
  • Discrete Approximation