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Design of Cylindrical Shells with Oblique Cuts in Refined Statement Using Spline-Approximation*

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The bending problem for a cylindrical shell with oblique cuts is solved using the equations of a model based on the straight-line hypothesis. The two-dimensional boundary-value problem obtained is reduced by the spline-approximation method to one-dimensional one solved by the method of discrete orthogonalization. The results calculated are compared with those obtained using the classical theory. Shells with different values of the cut angles are analyzed.

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References

  1. K. Z. Galimov and V. N. Paimushin, Theory of Shells of Complex Geometry (Geometrical Issues of the Shell Theory) [in Russian], Izd. KGU, Kazan (1985).

  2. Ya. M. Grigorenko and A. T. Vasilenko, Statics of Anisotropic Shells with Finite Shear Stiffness [in Russian], Naukova Dumka, Kyiv (1987).

  3. M. S. Kornishin, V. N. Paimushin, and S. V. Andreev, “Variational methods for stability analysis of thin shells of complex geometry,” in: Proc. of 12th All-Union Conf. on the Theory of Shells and Plates, Vol. 1 of the three-volume series [in Russian], Izd. Erevan, Univ., Erevan. (1980), pp. 67–72.

  4. M. S. Kornishin, V. N. Paimushin, and V. F. Snegirev, Computational Geometry in Problems of Shell Mechanics [in Russian], Nauka, Moscow (1989).

  5. V. M. Mal’kov, Design of a Cylindrical Shell with Oblique Cut, Vol. 3 of the series Studies on Elasticity and Plasticity [in Russian], Izd. LGU, Leningrad (1963).

  6. M. I. Estrin, “Design of a cylindrical shell fixed along an oblique contour,” Izv. AN SSSR, OTN, Mekh. Mashinostr., No. 2, 151–155 (1959).

  7. A. Ya. Grigorenko, W. H. Muller, Ya. M. Grigorenko, and G. G. Vlaikov, Recent Developments in the Anisotropic Heterogeneous Shell Theory, Vol. 1. General Theory and Applications of Classical Theory, Springer, Briefs in Appl. Sc. Tech., Cont. Mech. (2016).

  8. A. Ya. Grigorenko and S. A. Pankrat’ev, “Stress–strain state of complex-shaped orthotropic plates under variable load,” Int. Appl. Mech., 54, No. 4, 411–417 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Ya. Grigorenko, S. A. Pankrat’ev, and S. N. Yaremchenko, “Analysis of the stress–strain state of complex-shaped plates,” Int. Appl. Mech., 54, No. 6, 695–701 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  10. A. Ya. Grigorenko, S. A. Pankrat’ev, and S. N. Yaremchenko, “Influence of orthotropy on the stress–strain state of quadrangular plates of different shapes,” Int. Appl. Mech., 55, No. 2, 199–210 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  11. Ya. M. Grigorenko, A. Ya. Grigorenko, and G. G. Vlaikov, Problems of Mechanics for Anisotropic Inhomogeneous Shells on the Basis of Different Models, Akademperiodika, Kyiv (2009).

  12. Ya. M. Grigorenko, N. N. Kryukov, and N. S. Kholkina, “Spline-approximation solution of stress–strain problems for beveled cylindrical shells,” Int. Appl. Mech., 45, No. 12, 1357–1364 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  13. N. N. Kryukov, “Design of oblique and trapezoidal plates with the use of spline functions,” Int. Appl. Mech., 33, No. 5, 414–417 (1997).

    Article  ADS  Google Scholar 

  14. V. N. Paimushin, and S. V. Andreev, “Numerical study of the stress–strain state of one- and three-layer plates and shells of complex geometry,” Sov. Appl. Mech., 19, No. 7, 583–588 (1983).

    Article  ADS  Google Scholar 

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Correspondence to Ya. M. Grigorenko.

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This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).

Translated from Prikladnaya Mekhanika, Vol. 56, No. 3, pp. 76–83, May–June 2020.

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Grigorenko, Y.M., Grigorenko, A.Y., Kryukov, N.N. et al. Design of Cylindrical Shells with Oblique Cuts in Refined Statement Using Spline-Approximation*. Int Appl Mech 56, 326–333 (2020). https://doi.org/10.1007/s10778-020-01014-w

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  • DOI: https://doi.org/10.1007/s10778-020-01014-w

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