Abstract
The free-parameter perturbation method is applied to solve the problems of nonlinear stability of spehrical shallow shells under uniform load. As a modified perturbation method, the free-parameter perturbation method enables researchers to obtain all characteristic relations without choosing the certain perturbation parameter. Some examples were discussed to study the variety regulations of deflections and stress of shells in the process of buckling, and the results were compared with those of other researchers.
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YEH Kai-yuan, Gu Shu-xian. Nonlinear stability of a spherical shallow shell under uniformly distributed pressure[A]. In: the Chinese Association of Theoretical and Applied Mechanics.Proc Chinese National 1980Conf Computation Mechanics[C]. Guangzhou: 1981,280–287. (in Chinese)
YEH Kai-yuan, LIU Ren-huai, LI Si-lai. Nonlinear stabilities of thin circular shallow shells under actions of axisymmetrical uniformly distributed line loads[J].J Lanzou Univ, 1965,18(2):10–33. (in Chinese)
YEH Kai-yuan, LIU Ping. Nonlinear stability of spherical shallow shell under compound loads[J].Applied Mathematics and Mechanics (English Edition),1991,12(1):13–19.
WANG Hu, WANG Jun-kuel. Snap-buckling of thin shallow conical shells[J].Engineering Mechanics, 1990,7(1):27–33. (in Chinese)
CHEN Shan-lin. Free-parameter perturbation method[A]. In: ZHOU Zhe-wei Ed.Proceedings for Celebrating 90th Birthday of Professor CHIEN Wei-zang[C]. Shanghai: Shanghai Unviersity Press, 2003,35–43. (in Chinese)
YAN Sheng-ping. Nonlinear stability of spherical shallow shell under uniformly distributed pressure [J].Chinese J Appl Mech, 1988,5(3):20–29. (in Chinese)
CHIEN Wei-zang, YEH Kai-yuan. Problems of large deflection of thin circular plates[J].Chinese Journal of Physics, 1954,10(3):209–238. (in Chinese)
YEH Kai-yuan, SONG Wei-ping. Deformations and stability of spherical caps under centrally distributed pressure[J].Applied Mathematics and Mechanics (English Edition), 1988,9(10):915–922.
LI Yue-sheng, QI Dong-xu.Methods of Spline Functions[M]. Beijing: Science Press, 1979. (in Chinese)
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Contributed by CHEN Shang-lin
Biography: CHEN Shan-lin (1942≈)
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Shan-lin, C., Qi-zhong, L. Free-parameter perturbation-method solutions of the nonlinear stability of shallow spherical shells. Appl Math Mech 25, 963–970 (2004). https://doi.org/10.1007/BF02438344
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DOI: https://doi.org/10.1007/BF02438344