Static Buckling of Orthotropic Spherical Shells on Elastic Foundations
Publication: Journal of Engineering Mechanics
Volume 115, Issue 12
Abstract
This paper deals with the nonlinear axisymmetric static buckling analysis of cylindrically orthotropic full and annular shallow spherical shells continuously supported on elastic subgrades. Considering Winkler and Pasternak models for the elastic subgrade interaction, the buckling loads have been estimated using three criteria: (1) Sudden jump; (2) convergence failure; and (3) point of inflection. The effect of Winkler and Pastemak foundation‐stiffness parameters, shell material orthotropy, and annular ratio on the static buckling loads has been determined for several values of shell geometric parameter. The results reveal that these parameters have a significant influence on the buckling loads of the spherical shells. Both the clamped and simply supported boundary conditions are considered. In case of the hole, free edge conditions are assumed.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Budiansky, B. (1959). “Buckling of clamped shallow spherical shells.” Proc., IUTAM Symp. on Theory of Thin Elastic Shells, W. T. Koiter, ed., Delft, The Netherlands, 64–94.
2.
Dumir, P. C., Gandhi, M. L., and Nath, Y. (1984). “Axisymmetric static and dynamic buckling of orthotropic shallow spherical caps with flexible supports,” Acta Mechanica, 52, 93–106.
3.
Fox, L., and Parker, I. B. (1968). Chebyshev polynomials in numerical analysis. Oxford University Press, London.
4.
Fung, Y. C., and Sechler, E. E., eds. (1974). Thin‐shell structures: Theory, experiment and design. Prentice‐Hall Inc., Englewood Cliffs, N.J.
5.
Kaplan, A. (1974). “Buckling of shallow spherical shells.” Thin‐shell structures: Theory, experiment and design. Y. C. Fung, and E. E. Sechler, eds., Prentice‐Hall, Inc., Englewood Cliffs, N.J., 247–288.
6.
Keller, H. B., and Reiss, E. L. (1965). “Computers in solid mechanics—A case history.” American Mathematical Monthly, 72, 92–98.
7.
Kerr, A. D. (1964), “Elastic and viscoelastic foundation models.” J. Appl. Mech., 31, 491–498.
8.
Nath, Y., and Jain, R. K. (1986). “Nonlinear studies of orthotropic shallow spherical shells on elastic foundation.” Int. J. Nonlinear Mech., 21(6), 447–458.
9.
Stephens, W. B., and Fulton, R. E. (1969). “Axisymmetric static and dynamic buckling of spherical caps due to centrally distributed pressures.” AIAA J., 7, 2120–2126.
10.
Thompson, J. M. T. (1960). “Elastic buckling of thin spherical shells,” Proc., Nuclear Equipment Containment Buildings and Pressure Vessels, Butterworths, London, 257–285.
11.
Varadan, T. K. (1978). “Snap‐buckling of orthotropic shallow spherical shells.” J. Appl. Mech., American Society of Mechanical Engineers, 45, 445–447.
12.
Von Kármán, T., and Tsien, H. S. (1941). “The buckling of thin cylindrical shells under axial compression,” J. Aeronautical Sci., 8, 303.
13.
Weinitschke, H. J. (1958). “On the nonlinear theory of shallow spherical shells.” J. Math. and Phys., 38, 209–231.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 115 • Issue 12 • December 1989
Pages: 2621 - 2634
Copyright
Copyright © 1989 ASCE.
History
Published online: Dec 1, 1989
Published in print: Dec 1989
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.