Abstract
In this paper, nonlinear stability of thin elastic circular shallow spherical shell under the action of uniform edge moment is considered by the modified iteration method to obtain second and third approximations to decide the upper and lower critical loads. Results are plotted in curves for the engineering use and are compared with results of Hu Hai-chang's. We also investigate the neighbour situation of the critical point, i.e. the double points of the upper and lower critical loads and denote the range of validity of the second approximation. In the end, we obtain the special case, the design formulas of rigidity and stress as well as the corresponding curves as ν=0.3 of large deflection of circular plate under the same load. These results are also compared with Huang Tse-yen's.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hu hai-chang, On the snapping of thin spherical cap,Acta Physica Sinica, 10 (12) (1954), 105–136; Problem of large deflection of circular plate, Proceedings of Mechanical Problem, Volume 1, Second Kind, No. 1, Published by Academy of Science of China, (1954), 76–98,Scientia Sinica III, 4 (1954), 437–461.
Huang Tse-yen, Bending Problem of thin elastic circular plate under the action of uniform edge moment,Acta Physica Sinica, 12 (6) (1950), 597–606.
Von Karman, and Tsien Hsue-Shen, The Buckling of spherical shells by external pressure,J. Aero. Sci. 7, (1939), 43.
Way, S., Bending of circular plate with large deflection,A. S. M. E. Transactions, Applied Mech., 56, (1934), 627–636.
Simons, R. M., A power series solution of the nonlinear equations for axisymmetrical bending of shallow spherical shells.J. Math. Phs., 35, (2) (1956), 164.
Reiss, E. L., Greenberg, H. J., and Keller, H. B., Nonlinear deflections of Shallow spherical shells.J. Aero. Sci. 24, (7) (1957), 533–543.
Weinitschke, H., On the Stability Problem for Shallow Spherical Shells,J. Math. Phys., XXXVIII, 4 (1960), 209–231
Chien Wei-zang, Large deflection of a circular clamped plate under uniform pressure,Chinese Journal of Physics, 7, 2 (1947), 102–113.
Kaplan, A., and Fung, Y. C., A nonlinear theory of bending and buckling of thin elastic shallow spherical shells,NACA TN, 3213, (1954).
Кривошеев, Н. И., Муштари Х. М., Об пзгибе пологого сферического сегмента под деиствием внешнего нормалъного Давления. Известия Казанского Филиала Академии Наук СССР. серия физико-Математических и технических наук По.12 (1958), 69–83.
Yeh Kai-yuan, Liu Zen-huai, Li Szi-lai, Ping Ching-yuan, Non linear Stabilities of thin Elastic Circular Shallow Spherical Shells under actions of axisymmetrical uniform line distributed loads,Journal of Lanzhou University, No. 2 (Total No. 18), (1965), 10–23
Yeh Kai-yuan, Liu Zen-huai etc., Nonlinear Stability of this elastic circular spherical shell under the action of uniformly distributed external pressure, unpublished.
Liu Zen-huai, Nonlinear Stability of circular shallow spherical shell with a hole in the center under the action of uniform moment at inner edge,Mechanics, No. 3 (1977), 206.
Chien Wei-zang, The intunsic theory of thin shells and plates,Quart. Appl. Math., 1 (1944), 297–327; 2 (1944), 43–59, 120–135.
Φеодосъев, В. И., Theory and Calculation on Elastic Elements of Fine Instruments (in Russian) 1950)
Yeh Kai-yuan, Liu Zen-huai, Chang Chuan-dzi, Shue Ih-fan, Nonlinear Stability Problem of thin elastic shallow spherical shells II Nonlinear Stability of thin elastic circular shallow spherical shell under the action of uniform edge moment.Ke Xue Tong Bao, No. 2 (1965), 145–147.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kai-yuan, Y., Zen-huai, L., Chuan-dzi, C. et al. Nonlinear stability of thin elastic circular shallow spherical shell under the action of uniform edge moment. Appl Math Mech 1, 71–90 (1980). https://doi.org/10.1007/BF01872629
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01872629