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Stressed State of a Cylindrical Orthotropic Shell Containing a Crack at an Angle

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On the basis of the method of distortions in the Kirchhoff–Love theory of thin shells, we reduce the problem of elastic equilibrium of a cylindrical orthotropic shell containing a notch made along a helical curve to a system of integral equations. We investigate the influence of orthotropy, orientation, and length of the notch on the intensity factors of forces and moments.

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References

  1. E. K. Ashkenazi and E. V. Ganov, Anisotropy of Structural Materials. A Handbook [in Russian], Mashinostroenie, Leningrad (1980).

  2. P. A. Dzyuba, E. F. Prokopalo, and O. O. Solonin, “Strength of a cylindrical shell weakened by randomly located rectilinear notches in tension by an axial force,” Met. Rozv’yaz. Prykl. Zadach Mekh. Tverd. Deformivn. Tila, Issue 10, 97–108 (2009).

  3. A. I. Kalandiya, Mathematical Methods of Two-Dimensional Elasticity [in Russian], Nauka, Moscow (1973).

    Google Scholar 

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

    MATH  Google Scholar 

  5. V. A. Osadchuk, I. B. Prokopovych, and L. M. Sen’kiv, “Fundamental solution of the equations of elastic equilibrium of an anisotropic cylindrical shell,” Dop. Akad. Nauk Ukr. RSR, No. 6, 43–46 (1991).

    Google Scholar 

  6. V. V. Panasyuk, M. P. Savruk, and A. P. Datsyshyn, Distribution of Stresses in the Vicinity of Cracks in Plates and Shells [in Russian], Naukova Dumka, Kiev (1976).

    Google Scholar 

  7. Ya. S. Podstrigach and R. N. Shvets, Thermoelasticity of Thin Shells [in Russian] Naukova Dumka, Kiev (1978).

  8. I. B. Prokopovich, L. M. Sen’kiv, and I. P. Laushnik, “Elastic equilibrium of nonshallow cylindrical shells with notches,” Prikl. Probl. Prochn. Plastichn., Issue 54, 175–184 (1996).

  9. V. P. Shevchenko and K. M. Dovbnya, “Method of boundary integral equations in problems of statics of shallow orthotropic shells with notches and holes,” Mat. Met. Fiz.-Mekh. Polya, 46, No. 1, 47–59 (2003).

    MATH  Google Scholar 

  10. V. P. Shevchenko and K. M. Dovbnya, “System of boundary integral equations for an orthotropic shell containing a notch of arbitrary configuration,” Mat. Met. Fiz.-Mekh. Polya, 44, No. 1, 103–108 (2001).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    L. М. Sen’kiv

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  1. L. М. Sen’kiv
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 3, pp. 122–127, July–September, 2015.

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Sen’kiv, L.М. Stressed State of a Cylindrical Orthotropic Shell Containing a Crack at an Angle. J Math Sci 226, 152–159 (2017). https://doi.org/10.1007/s10958-017-3526-x

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  • DOI: https://doi.org/10.1007/s10958-017-3526-x

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