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Stability of Systems Composed of the Shells of Revolution with Variable Gaussian Curvature

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We analyze the stability of elastic systems composed of the shells of revolution with variable curvature and complex structures in the field of conservative axisymmetric loads of different nature. Within the framework of classical and refined theories of shells, we determine the limit and bifurcation critical values of the acting loads based on the geometrically nonlinear statement of the problem and a criterion of dynamic stability. To solve the corresponding nonlinear and eigenvalue problems, we propose to use a numerical-analytic approach based on their rational reduction to one-dimensional linear boundaryvalue problems in the meridional coordinate and their numerical solution by the discrete-orthogonalization method. We present test examples that confirm the applicability of the proposed procedure to the analyzed class of problems. The limit and bifurcation values of the critical loads in the shell system are analyzed depending on its geometric parameters.

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Authors and Affiliations

  1. S. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Ya. М. Grigorenko, О. І. Bespalova & N. P. Boreiko

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  1. Ya. М. Grigorenko
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  2. О. І. Bespalova
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  3. N. P. Boreiko
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Correspondence to N. P. Boreiko.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 62, No. 1, pp. 127–142, January–March, 2019.

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Grigorenko, Y.М., Bespalova, О.І. & Boreiko, N.P. Stability of Systems Composed of the Shells of Revolution with Variable Gaussian Curvature. J Math Sci 258, 527–544 (2021). https://doi.org/10.1007/s10958-021-05564-3

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  • DOI: https://doi.org/10.1007/s10958-021-05564-3

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