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. 
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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/

[1] Galimov K. Z., Osnovy nelineinoi teorii tonkikh obolochek, Izd-vo Kazansk. un-ta, Kazan, 1975 | MR

[2] Bolotin V. V., Nekonservativnye zadachi teorii uprugoi ustoichivosti, Fizmatgiz, M., 1961 | MR

[3] Paimushin V. N., Shalashilin V. I., “O geometricheski nelineinykh uravneniyakh teorii bezmomentnykh obolochek s prilozheniyami k zadacham o neklassicheskikh formakh poteri ustoichivosti tsilindra”, PMM, 70:1 (2006), 100–110 | MR

[4] Paimushin V. N., “Problemy geometricheskoi nelineinosti i ustoichivosti v mekhanike tonkikh obolochek i pryamolineinykh sterzhnei”, PMM, 71:5 (2007), 855–893 | MR

[5] Grigolyuk E. I., Shklyarchuk F. N., “Uravneniya vozmuschennogo dvizheniya tela s tonkostennoi uprugoi obolochkoi, chastichno zapolnennoi zhidkostyu”, PMM, 34:3 (1970), 401–411 | Zbl

[6] Grigolyuk E. I., Kabanov V. V., Ustoichivost obolochek, Nauka, M., 1978 | MR

[7] Rikards R. B., Teters G. A., Ustoichivost obolochek iz kompozitnykh materialov, Zinatne, Riga, 1974

[8] Paimushin V. N., “Krutilnye, izgibnye i izgibno-krutilnye formy poteri ustoichivosti tsilindricheskoi obolochki pri kombinirovannykh vidakh nagruzheniya”, Izv. RAN. MTT, 2007, no. 3, 125–136

[9] Paimushin V. N., “Staticheskie i dinamicheskie balochnye formy poteri ustoichivosti dlinnoi ortotropnoi tsilindricheskoi obolochki pri vneshnem davlenii”, PMM, 72:6 (2008), 1014–1027

[10] Lukankin S. A., Paimushin V. N., “Staticheskie i dinamicheskie formy poteri ustoichivosti tsilindricheskoi obolochki pri deistvii vneshnego davleniya”, Izv. RAN. MTT, 2014, no. 1, 108–128