Advertisement

Journal of Mathematical Sciences

, Volume 212, Issue 1, pp 98–105 | Cite as

Stressed State of a Shell of Double Curvature with Two Collinear Cracks Under Bending

  • K. M. Dovbnya
  • Yu. V. Hryhorchuk
Article

We study an isotropic shell of double curvature weakened by two through collinear cracks whose faces are in contact in the case of bending of the shell. The solution of the problem is obtained by the method of singular integral equations and the numerical method of mechanical quadratures. We perform the numerical investigations of the dependences of force and moment intensity factors on the sizes of the cracks, the distance between them, and the curvature of the middle surface of the shell.

Keywords

Intensity Factor Stress Intensity Factor Singular Integral Equation Shell Theory Middle Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. N. Dovbnya and A. A. Silkina, “On the evaluation of the error of application of the theory of special orthotropy in the numerical analyses of shells of any curvature with two parallel cracks,” Visn. Donets’k. Univ. Ser. А, No. 1, 139–143 (2004).Google Scholar
  2. 2.
    I. P. Shatskii, “Problem of a notch with contacting edges in a flexible shallow shell,” Izv. Ros. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 164–173 (1998).Google Scholar
  3. 3.
    I. P. Shatskii and N. V. Makoviichuk, “Balance of a shallow spherical shell with regard for the contact of crack faces in bending,” Teor. Prikl. Mekh., Issue 41, 146–150 (2005).Google Scholar
  4. 4.
    I. P. Shats’kyi, “Integral equations of the problem of bending of a shallow shell weakened by a notch with contacting edges,” Dop. Akad. Nauk Ukr. RSR. Ser. A, No. 2, 26–29 (1991).Google Scholar
  5. 5.
    I. Shats’kyi and M. Makoviichuk, “Balance of a spherical shallow shell with regard for the closure of collinear cracks in bending,” Fiz.-Mat. Model. Inform. Tekhnol., Issue 12, 189–195 (2010).Google Scholar
  6. 6.
    V. P. Shevchenko, E. N. Dovbnya, and V. A. Tsvang, “Orthotropic shells with cracks (cuts), in: A. N. Guz’ (editor), Mechanics of Composites, Vol. 7: A. N. Guz’, A. S. Kosmodamianskii, V. P. Shevchenko, et al., Stress Concentration [in Russian], A.S.K., Kiev (1998), pp. 212–249.Google Scholar
  7. 7.
    R. Liu, J. Zhao, and X. J. Wu, “An improved shell theory applied for failure analysis of pressure vessels,” in: Proc. of the ASME- 2011. Pressure Vessels and Piping Conf., Vol. 3, Baltimore (2011), pp. 715–726.Google Scholar
  8. 8.
    R. Liu, T. Zhang, X. J. Wu, and C. H. Wang, “Determination of stress intensity factors for a cracked shell under bending with improved shell theories,” J. Aerosp. Eng., 19, No. 1, 21–28 (2006).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • K. M. Dovbnya
    • 1
  • Yu. V. Hryhorchuk
    • 1
  1. 1.Donets’k National UniversityDonets’kUkraine

Personalised recommendations