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Mathematical model of an internal crack in an elastoplastic cylindrical shell

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Abstract

We propose a mathematical model that makes it possible to reduce the problem of the stressed state and limit equilibrium of a cylindrical anisotropic elastoplastic shell with internal crack to a system of nonlinear singular integral equations with discontinuous functions on the right-hand sides. We construct an algorithm for numerical solution of such systems together with the conditions of plasticity and boundedness of stresses near the crack. For a transversally isotropic shell, we carry out a numerical analysis of the dependence of the opening of the internal crack front on the load and geometric and mechanical parameters.

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References

  1. Power-Generating Equipment. Strength Analyses and Tests. Methodical Recommendations MR 108.7-87 [in Russian], NPO TsNIITMASh, Moscow (1986).

  2. M. M. Nykolyshyn, “The stressed state of elastoplastic shells with nonthrough cracks”,Mat. Metody Fiz.-Mekh. Polya, No. 35, 147–151 (1992).

    Google Scholar 

  3. V. A. Osadchuk,Stress-Strain State and Limit Equilibrium of Cracked Shells [in Russian], Naukova Dumka, Kiev (1985).

    Google Scholar 

  4. V. A. Osadchuk and M. M. Nykolyshyn, “Application of an analog of the δc-model for investigation of the strength of elastoplastic cracked shells”,Fiz-Khim. Mekh. Mater., No. 3, 5–15 (1996).

    Google Scholar 

  5. V. A. Osadchuk, I. B. Prokopovych, and L. M. Sen'kiv, “The fundamental solution of the equations of torsional equilibrium of an anisotropic cylindrical shell”,Dopov. Akad. Nauk Ukr. RSR, Ser. A, No. 6, 43–46 (1991).

    Google Scholar 

  6. Ya. S. Pidstryhach and V. A. Osadchuk, “On determination of the stressed state of a closed cylindrical cracked shell”Dopov. Akad. Nauk Ukr. RSR, Ser. A, No. 1, 79–83 (1972).

    Google Scholar 

  7. Ya. S. Pidstryhach, V. A. Osadchuk, E. M. Fedyuk, and M. M. Nykolyshyn, “The distortion method in the theory of thin cracked sells”,Mat. Metody Fiz-Mekh. Polya, No. 1, 29–41 (1975)

    Google Scholar 

  8. L. M. Sen'kiv, “The symmetric problem of elastic equilibrium for a Timoshenko-type orthotropic, sharply sloping, cylindrical shell with transverse cut”, in:IV International Conference on Mechanics of Inhomogenous Structures: Abstracts of Papers (Ternopil', Sept. 1995) [in Ukrainian], Ternopil' (1995), p. 125.

  9. F. Erdogan, “Plastic strip model for a thin shell”, in:Prospects Fract. Mech., Leyden (1974), pp. 609–612.

  10. J. L. Sanders, “Dugdale model for circumferential through-cracks in pipes loaded by bending”,Int. J. Fract. 34, No. 1, 71–81 (1987).

    Google Scholar 

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Authors
  1. V. A. Osadchuk
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  2. T. M. Nykolyshyn
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Additional information

Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences L'viv. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 111–116, April–June, 1998

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Osadchuk, V.A., Nykolyshyn, T.M. Mathematical model of an internal crack in an elastoplastic cylindrical shell. J Math Sci 99, 1648–1654 (2000). https://doi.org/10.1007/BF02674188

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  • DOI: https://doi.org/10.1007/BF02674188

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