Journal of Mathematical Sciences

, Volume 243, Issue 1, pp 101–110 | Cite as

Influence of Residual Welding Stresses on the Limit Equilibrium of a Transversely Isotropic Cylindrical Shell with Internal Crack of Any Configuration

  • B. І. Kindrats’kyi
  • Т. М. Nykolyshyn
  • Yu. V. Porokhovs’kyi

We reduce the elastoplastic problem of limit equilibrium of a transversely isotropic cylindrical shell weakened by an internal longitudinal plane crack of any configuration located in the field of residual stresses to the problem of elastic equilibrium of the same shell containing a through crack of unknown length. This problem, in turn, is reduced to a system of nonlinear singular integral equations. We propose an algorithm for the numerical solution of the obtained system together with the conditions of plasticity, boundedness of stresses, and uniqueness of displacements.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • B. І. Kindrats’kyi
    • 1
  • Т. М. Nykolyshyn
    • 2
  • Yu. V. Porokhovs’kyi
    • 2
  1. 1.“L’vivs’ka Politekhnika” National UniversityLvivUkraine
  2. 2.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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