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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 4, Pages 46–56 (Mi ivm9103)  

This article is cited in 1 scientific paper (total in 1 paper)

Static and dynamic buckling modes of spherical shells subjected to external pressure

V. N. Paimushinab

a Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
b Kazan National Research Technical University named after A. N. Tupolev, 10 K. Marks str., Kazan, 420111 Russia

Abstract: We investigate the possibilities for simplification of previously proposed refined linearized equations of forced motion to identify by dynamic method the buckling modes of isotropic spherical shells undergoing external hydrodynamic pressure. In the analysis of classical flexural buckling shapes of spherical shells it is shown that preserving of nonconservative parametric terms in governing equations of formulated problem, which are related with loading of the shell with follower pressure practically does not affect the value of critical load and the resulting buckling mode shapes in shell.

Keywords: shell, hydrostatic pressure, following and not following forces, spherical shell, refined equation of forced motion, analytical solution, stability, dynamic method, frequency of vibrations, critical load.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation


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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:4, 37–46

Bibliographic databases:

UDC: 517.958+539.3
Received: 23.09.2014

Citation: V. N. Paimushin, “Static and dynamic buckling modes of spherical shells subjected to external pressure”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 4, 46–56; Russian Math. (Iz. VUZ), 60:4 (2016), 37–46

Citation in format AMSBIB
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\by V.~N.~Paimushin
\paper Static and dynamic buckling modes of spherical shells subjected to external pressure
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 4
\pages 46--56
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\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 4
\pages 37--46
\crossref{https://doi.org/10.3103/S1066369X1604006X}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962636783}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. J. Awrejcewicz, A. V. Krysko, M. V. Zhigalov, V. A. Krysko, “Chaotic dynamic buckling of rectangular spherical shells under harmonic lateral load”, Comput. Struct., 191 (2017), 80–99  crossref  isi  scopus
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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