Skip to main content
Log in

The stressed state of elastoplastic shells with nonthrough cracks

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

We study the problem of the stressed state and limiting equilibrium of shells with nonthrough surface cracks. Several assumptions make it possible to reduce the three-dimensional problem to the two-dimensional problem and the latter to a system of singular integral equations whose solution is constructed using numerical methods. For cylindrical and spherical shells weakened by nonthrough cracks situated along the coordinate lines we carry out a numerical analysis of the dependence of the crack opening on the load and the geometric and physico-mechanical parameters of the shells.

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.

Similar content being viewed by others

Literature cited

  1. V. S. Girenko and V. I. Kir'yan, “Analysis of the influence of residual stresses on the strength of weld joints,”Avtom. Svarka, No. 12, 1–5 (1975).

    Google Scholar 

  2. A. A. Kaminskii and G. V. Galatenko, “A study of the growth of fatigue cracks in reinforced materials,”Prikl. Mekh.,20, No. 4, 54–60 (1984).

    Google Scholar 

  3. M. Ya. Leonov and V. V. Panasyuk, “Development of microscopic cracks in a solid body,”Prikl. Mekh.,5, No. 4, 391–501 (1959).

    Google Scholar 

  4. V. A. Osadchuk,The Stress-Strain State and Limiting Equilibrium of Shells with Cuts [in Russian], Naukova Dumka, Kiev (1985).

    Google Scholar 

  5. V. A. Osadchuk, V. I. Kir'yan, and M. M. Nikolishin, “The opening of the end of a through longitudinal crack in a cylindrical shell under the action of internal pressure,”Probl. Prochn., No. 10, 64–67 (1984).

    Google Scholar 

  6. V. A. Osadchuk, M. M. Nikolishin, and V. I. Kir'yan, “Application of an analog of the δk-model to determine the opening of a nonthrough crack in a closed cylindrical shell,”Fiz.-Khim. Mekh. Mater., No. 1, 88–92 (1986).

    Google Scholar 

  7. V. A. Osadchuk, M. M. Nikolishin, and T. E. Maselko, “Limiting equilibrium of a spherical shell on an elastic base and weakened by a crack,”Prikl. Mekh.,22, No. 10, 47–52 (1986).

    Google Scholar 

  8. V. V. Panasyuk, M. P. Savruk, and A. P. Datsyshin,Distribution of Stresses near Cracks in Plates and Shells [in Russian], Naukova Dumka, Kiev (1976).

    Google Scholar 

  9. Ya. S. Podstrigach and V. A. Osadchuk, “The stressed stated and limiting equilibrium of shells with cracks,”Itogi Nauki i Tekhniki. Mekh. Deform. Tver. Tela,18, 3–32 (1986).

    Google Scholar 

  10. Ya. S. Podstrigach, V. A. Osadchuk, E. M. Fedyuk, and M. M. Nikolishin, “The distortion method in the theory of thin shells with cracks,”Mat. Met. i Fiz.-Mekh. Polya, No. 1, 29–41 (1975).

    Google Scholar 

  11. V. I. Trufyakov, V. S. Girenko, and V. I. Kir'yan, “Mechanical regularities of the appearance of fragile yielding in the zone of weld seams,” in:Strength of Materials and Structures [in Russian], Naukova Dumka, Kiev (1985), pp. 363–371.

    Google Scholar 

  12. D. S. Dugdale, “Yielding of steel sheets containing stits,”J. Mech. Phys. Solids,8, No. 2, 100–104 (1960).

    Google Scholar 

  13. F. E. Erdogan and M. Ratwani, “Plasticity and the crack opening displacement in shells,”Int. J. Fract. Mech.,8, No. 4, 413–426 (1972).

    Google Scholar 

Download references

Authors

Additional information

Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 147–151.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nikolishin, M.M. The stressed state of elastoplastic shells with nonthrough cracks. J Math Sci 67, 2959–2963 (1993). https://doi.org/10.1007/BF01095877

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01095877

Keywords

Navigation