Skip to main content
Log in

On the Choice of the Mathematical Model of Spherical Shell for Strength Calculation

Mechanics of Solids Aims and scope Submit manuscript

Cite this article


Aerospace and other systems usually have spherical tanks, as the most optimal in terms of weight ratio. The functional units of such systems are connected by frames. Consequently, tanks (spherical shells) are loaded locally in them. In this case, the strength of the shell is determined by the stresses in the places of their concentration.

The importance of solving the problems of the strength of a spherical shell attracts the attention of researchers in terms of simplifying mathematical models for engineering calculations with controlled error.

In the article, quantitative criteria for the well-known simplified mathematical models (the theory of shallow shells and asymptotic) are determined for use in solving strength problems with controlled error.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions


  1. V. Z. Vlasov, SelectedWorks, Vol. 1. Sketch of scientific activity “TheGeneral Theory of Shells.” Articles (Izdat. AN SSSR,Moscow, 1962) [in Russian].

    Google Scholar 

  2. A. L. Goldenveizer, Theory of Elastic Thin Shells (Nauka, Moscow, 1976) [in Russian].

    Google Scholar 

  3. A. P. Filin, Elements of the Theory of Shells (Stroiizdat, Leningrad Division, Leningrad, 1975) [in Russian].

    Google Scholar 

  4. V. V. Novozhilov, K. F. Chernykh, and E. I. Mikhailovskii, The Linear Theory of Thin Shells (Politekhnika, Leningrad, 1991) [in Russian].

    Google Scholar 

  5. Yu. I. Vinogradov, V. P. Georgievskii, and M. V. Konstantinov, “Goldenweizer Asymptotics in Strength Calculations of Spherical Reservoirs,” Vestnik MGTU im. N.E. Baumana. Mashinostr., No. 3, 119–133 (2015).

    Google Scholar 

  6. G. B. Men’kov, Solution of Problems of Deformable Shell Mechanics by Functional Normalization Method, Candidate’s Dissertation in Physics and Mathematics (Kazan, 1999) [in Russian].

    Google Scholar 

  7. Y. I. Vinogradov and G. B. Men’kov, A Method for Functional Normalization for Boundary Value Problems in the Theory of Shells (Editorial URSS,Moscow, 2001) [in Russian].

    Google Scholar 

  8. Y. M. Grigorenko, L. A. Il’in, and A. D. Kovalenko, Theory of Thin Conical Shells and Their Applications in Machine Engineering (Izdat. AN UkrSSR, Kiev, 1963) [in Russian].

    Google Scholar 

  9. Yu. I. Vinogradov and M. V. Konstantinov, “Analysis of a Spherical Tank under a Local Action,” Izv. Akad. Nauk.Mekh. Tverd. Tela, No. 2, 109–120 (2016) [Mech. Solids. (Engl. Transl.) 51 (2), 223–233 (2016)].

    Google Scholar 

  10. Yu. I. Vinogradov, “Influence of Frame Rigidity on DeformationMechanics of Cylindrical Shells,” Izv. Vyssh. Uchebn. Zaved.Mashinostr., No. 9, 20–25 (2013).

    Google Scholar 

  11. A. A. Amosov, Yu. A. Dubinsky, and N. V. Kopchenova, Computational Methods for Engineers (Vysshaya Shkola,Moscow, 1994) [in Russian].

    Google Scholar 

  12. M. V. Konstantinov, “Vlasov Mathematical Model Inaccuracy Quantitative Assessment for a Shallow Spherical Shell,” Nauka Obraz. Nauch. Izd.MGTU im. N. E. Baumana, No. 12, 858–877 (2014).

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Yu. I. Vinogradov.

Additional information

Original Russian Text © A.V. Belyaev, Yu.I. Vinogradov, M.V. Konstantinov, 2018, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2018, No. 3, pp. 105–118.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Belyaev, A.V., Vinogradov, Y.I. & Konstantinov, M.V. On the Choice of the Mathematical Model of Spherical Shell for Strength Calculation. Mech. Solids 53, 329–339 (2018).

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: