Abstract
In this paper, we considered the bending of a round shallow panel under the effect of excessive pressures on the lower and upper surfaces. A refined expression of the distributed transverse force that depends on both the pressure drop on the surface and the interaction of the average overpressure and curvature of the middle surface is used. This refinement is performed in a linear approximation. The panel edge is assumed to be isolated from excessive pressure. The classical theory of nonlinear bending of a round shallow panel under the effect of pressures on its surface is supplemented.
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References
Timoshenko, S., Theory of Plates and Shells, New York: McGraw-Hill, 1940.
Vol’mir, A.S., Gibkie plastinki i obolochki (Flexible Plates and Shells), Moscow: Gostekhizdat, 1956.
Feodos’ev, V.I., To the calculation of the clapping membrane, Prikl. Mat. Mekh., 1946, vol. 10, no. 2, pp. 295–300.
Nylander, H., Die durchschlaglast von platten, Oesterr. Ing.-Archiv., 1955, nos. 2–3, pp. 181–196.
Mushtari, Kh.M. and Galimov, K.Z., Nelineinaya teoriya uprugikh obolochek (Nonlinear Theory of Elastic Shells), Kazan: Tatknigoizdat, 1957.
Kornishin, M.S., Nelineinye zadachi teorii plastin i pologikh obolochek i metody ikh resheniya (Nonlinear Problems of the Theory of Plates and Shallow Shells and Methods for their Solution), Moscow: Nauka, 1964.
Kornishin, M.S. and Isanbaeva, F.S., Gibkie plastiny i paneli (Flexible Plates and Panels), Moscow: Nauka, 1968.
Svirskii, I.V., Metody tipa Bubnova-Galerkina i posledovatel’nykh priblizhenii (Methods of Bubnov-Galerkin Type and Successive Approximations), Moscow: Nauka, 1968.
Vorovich, I.I., Matematicheskie problemy nelineinoi teorii pologikh obolochek (Mathematical Problems of the Nonlinear Theory of Shallow Shells), Moscow: Nauka, 1989.
Shen, H.Sh., Postbuckling Behavior of Plates and Shells, Shanghai: Jiao Tong Univ., 2017.
Il’gamov, M.A., Influence of pressure of the surrounding medium on thin plate and film bending, Dokl. Akad. Nauk, 2017, vol. 476, no. 4, pp. 402–405.
Il’gamov, M.A., On the effect of ambient pressure on the bending of a plate, J. Mach. Manuf. Reliab., 2017, vol. 46, no. 5, pp. 442–447.
Il’gamov, M.A., Bending and stability of a thin plate when evacuating its surfaces, Dokl. Akad. Nauk, 2018, vol. 480, no. 5, pp. 542–544.
Acknowledgements
The authors are grateful to M.S. Ganeeva and Z.V. Skvortsova for discussing this article.
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Russian Text © The Author(s), 2019, published in Problemy Mashinostroeniya i Nadezhnosti Mashin, 2019, No. 3, pp. 27–35.
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Il’gamov, M.A., Moiseeva, V.E. Nonlinear Bending of a Shallow Panel under the Effect of Gas Pressure. J. Mach. Manuf. Reliab. 48, 211–218 (2019). https://doi.org/10.3103/S1052618819030075
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DOI: https://doi.org/10.3103/S1052618819030075