Geodesic
Static and dynamic buckling modes of spherical shells subjected to external pressure
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 46-56

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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. 
@article{IVM_2016_4_a5,
     author = {V. N. Paimushin},
     title = {Static and dynamic buckling modes of spherical shells subjected to external pressure},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {46--56},
     publisher = {mathdoc},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_4_a5/}
}
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V. N. Paimushin. Static and dynamic buckling modes of spherical shells subjected to external pressure. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 46-56. http://geodesic.mathdoc.fr/item/IVM_2016_4_a5/