The spatial problem of the stress state of non-thin elliptical cylindrical shells is solved using the analytical methods of separation of variables, approximation of functions by discrete Fourier series, and the numerical method of discrete orthogonalization. The shells are made of isotropic and orthotropic materials and acted upon by a local longitudinal load. The results obtained are presented in the form of plots and tables of fields of displacements and stresses.
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References
E. K. Ashkenazi, I. B. Gol’fman, L. P. Rozhkov, and N. P. Sidorov, Reinforced-glass Components in Ship Engineering [in Russian], Sudostroenie, Leningrad (1974).
G. G. Vlaikov, A. Ya. Grigorenko, and S. N. Shevchenko, Some Elasticity Problems for Anisotropic Cylinders with Noncircular Cross-Section [in Russian], NAN Ukrainy, Inst. Mekh. im. S. P. Timoshenko, Kyiv (2001).
S. K. Godunov, “Numerical solution of boundary-value problems for systems of linear ordinary differential equations,” Usp. Mat. Nauk, 16, No. 3, 171–174 (1961).
Ya. M. Grygorenko, O. I. Bespalova, and N. P. Boreiko, “Vibrations of conjugate shell systems in the field of combined loads,” Mat. Metody Fiz.- Mekh. Polya, 63, No. 3, 5–18 (2020).
Ya. M. Grigorenro, A. T. Vasilenko, I. G. Emel’yanov, et. al., Statics of Structural Elements, Vol. 8 of the twelve-volume series Composite Mechanics [in Russian], “A.S.K,” Kyiv (1999).
Ya. M. Grygorenko and L. S. Rozhok, “Application of discrete Fourier series to solving boundary-value static problems for elastic non-canonical bodies,” Mat. Metody Fiz.- Mekh. Polya, 48, No. 2, 79–100 (2005).
S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body [in Russian], Nauka, Moscow (1977).
V. P. Revenko, “Solutions of three-dimensional elasticity problems for orthotropic bodies,” Mat. Metody Fiz.- Mekh. Polya, 63, No. 3, 78–84 (2020).
L. S. Rozhok, “Studying the influence of local loading on the stress state of corrugated hollow cylinders,” Dop. NAN Ukrainy, No. 7, 56–59 (2006).
L. S. Rozhok, “Equilibrium of corrugated hollow elliptical cylinders under local loading,” Dop. NAN Ukrainy, No. 3, 90–94 (2009).
S. P. Timoshenko, Course of the Elasticity Theory [in Russian], Naukova Dumka, Kyiv (1972).
G. M. Fikhtengol’ts, Course of Differential and Integral Calculus [in Russian], Vol. 3, Nauka, Moscow (1949).
E. I. Bespalova and N. P. Boreiko, “Vibrations of compound shell systems under subcritical loads. Models,” Int. Appl. Mech., 56, No. 4, 415–423 (2020).
A. Ya. Grigorenko, V. A. Malanchuk, G. V. Sorochenko, et al., “Application of the inhomogeneous elasticity theory to the description of the mechanical state of a single-rooted tooth,” Int. Appl. Mech., 57, No. 3, 249–262 (2021).
Ya. M. Grigorenko and L. S. Rozhok, “Influence of orthotropy parameters on the stress state of hollow cylinders with elliptic cross-section,” Int. Appl. Mech., 43, No. 12, 1372–1379 (2007).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1961).
A. V. Marchuk, S. V. Reneiskaya, and O. N. Leshchuk, “Three-dimensional analysis of the free vibrations of layered composite plates based on the semianalytic finite-element method,” Int. Appl. Mech., 56, No. 4, 481–497 (2020).
V. F. Meish, Y. A. Meish, and V. F. Kornienko, “Dynamics of three-layer shells of different geometry with piecewise-homogeneous core under distributed loads,” Int. Appl. Mech., 57, No. 6, 659–668 (2021).
O. Ozguk, “Nonlinear buckling simulations of stiffened panel exposed to combinations of transverse compression, shear force and lateral pressure loadings,” J. Inst. Eng. India, Ser. C, 102, 397–408 (2021).
N. P. Semenyuk and N. B. Zhukova, “Stablity of a sandwich cylindrical shell with core subject to external pressure and pressure in the inner cylinder,” Int. Appl. Mech., 56, No. 1, 52–66 (2020).
E. A. Storozhuk, “Stress–strain state and stability of a flexible circular cylindrical shell with transverse shear strains,” Int. Appl. Mech., 57, No. 5, 554–567 (2021).
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Translated from Prykladna Mekhanika, Vol. 59, No. 2, pp. 28–40, March–April 2023.
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Grygorenko, O.Y., Rozhok, L.S. Stress State of Non-Thin Elliptical Cylindrical Shells Under a Local Longitudinal Load. Int Appl Mech 59, 153–165 (2023). https://doi.org/10.1007/s10778-023-01209-x
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DOI: https://doi.org/10.1007/s10778-023-01209-x