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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
Article
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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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References

  1. 1.
    R. M. Kushnir, M. M. Nykolyshyn, and V. A. Osadchuk, Elastic and Elastoplastic Limit States of Shells with Defects [in Ukrainian], Spolom, Lviv (2003).Google Scholar
  2. 2.
    V. A. Osadchuk, Stress-Strain State and Limit Equilibrium for Shells with Cuts [in Russian], Naukova Dumka, Kiev (1985).Google Scholar
  3. 3.
    V. V. Panasyuk, Mechanics of Quasibrittle Fracture of Materials [in Russian], Naukova Dumka, Kiev (1991).Google Scholar
  4. 4.
    B. L. Pelekh, Theory of Shells with Finite Shear Stiffness [in Russian], Naukova Dumka, Kiev (1973).Google Scholar
  5. 5.
    Ya. S. Podstrigach, V. A. Osadchuk, and A. M. Margolin, Residual Stresses, Long-Term Strength, and Reliability of Glass Structures [in Russian], Naukova Dumka, Kiev (1991).Google Scholar
  6. 6.
    Yu. Porokhovs’kyi, “Determination of residual stresses in welded joints of piecewise homogeneous shells based on the refined theory of shells,” Mashynoznavstvo, Nos. 5–6 (167–168), 30–34 (2011).Google Scholar
  7. 7.
    W. Prager, Probleme der Plastizitätstheorie, Birkhauser, Basel–Stuttgart (1955).Google Scholar
  8. 8.
    G. B. Talypov, Welding Strains and Stresses [in Russian], Mashinostroenie, Leningrad (1973).Google Scholar
  9. 9.
    F. Erdogan, “Plastic strip model for thin shell,” in: G. C. Sih, H. C. van Elst, and D. Broek (editors.): Prospects of Fracture Mechanics, Noordhoff, Leyden (1974), pp. 609–612.Google Scholar
  10. 10.
    J. L. Sanders, Jr., “Dugdale model for circumferential through cracks in pipes loaded by bending,” Int. J. Fract., 34, No. 1, 71–81 (1987).Google Scholar
  11. 11.
    S. P. Timoshenko, “On the correction for shear of the differential equation for transverse vibrations of prismatic bars,” Phil. Mag., Ser. 6, 41, No. 245, 744–746 (1921),  https://doi.org/10.1080/14786442108636264.CrossRefGoogle Scholar

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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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