TECHNICAL PAPERS
Feb 1, 1983

Bifurcation in Tension of Nonlinear Spherical Caps

Publication: Journal of Engineering Mechanics
Volume 109, Issue 1

Abstract

The loss of stability by so‐called bifurcation in tension of geometrically nonlinear plates and spherical caps loaded by axisymmetrical cross forces is examined. These phenomena are manifested by a transition from axisymmetrical forms to the nonsymmetrical ones with formation of wrinkles. They may occur on plates, and also on caps when the loading acts on their inner (concave) side. In these cases, the meridians are stretched at every point. It is necessary to distinguish between these phenomena and bifurcation in compression. The latter is impossible for plates and shallow caps and may occur only on relatively deep caps when the loading acts outside (convex side). Experimental observations of the stability loss by bifurcation in tension are described. Qualitative investigations of the writer indicate, in particular, that the considered phenomena cannot occur when the edge supports are fixed.

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References

1.
Bushnell, D., “Bifurcation Phenomena in Spherical Shells under Concentrated and Ring Loads,” AIAA Journal, Vol. 5, 1967, pp. 2034–2040.
2.
Bushnell, D., “Nonsymmetric Buckling of Internally Pressurized Ellipsoidal and Torispherical Elastic‐Plastic Pressure Vessel Heads,” Journal of Pressure Vessel Technology, Vol. 99, 1977, pp. 54–63.
3.
Bushnell, D., and Galletly, G. D., “Stress and Buckling of Internally Pressurized Elastic‐Plastic Torispherical Vessel Heads—Comparisons of Tests and Theory,” Journal of Pressure Technology, Vol. 99, 1977, pp. 39–53.
4.
Cheo, L. S., and Reiss, E. L., “Unsymmetric Wrinkling of Circular Plates,” Journal of Applied Mechanics, Vol. 31, 1973, pp. 75–91.
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Fitch, J. R., and Budiansky, B., “Buckling and Postbuckling Behavior of Spherical Caps under Axisymmetric Load,” AIAA Journal, Vol. 8, 1970, pp. 686–693.
6.
Gerlaku, I. D., and Shilkrut, D. I., “Determination of Bifurcation Load Values for Axisymmetrically Loaded Shells of Revolution with Allowance for Asymmetric Deformations,” Izv. Akad. Nauk. SSR Mech. Tverd. Tela, Vol. 5, 1970 (in Russian), pp. 184–190.
7.
Huang, N. C., “Unsymmetrical Buckling of Shallow Spherical Shells,” Transactions, American Society of Mechanical Engineers, E 31, No. 3, 1964, pp. 447–457.
8.
Shilkrut, D. I., “Problems in the Qualitative Theory of Nonlinear Shells,” Izd.‐vo “Shtijntza,” 1974, Kishinev (in Russian).
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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 109Issue 1February 1983
Pages: 289 - 295

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Published online: Feb 1, 1983
Published in print: Feb 1983

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Dov I. Shilkrut
Prof., Dept. of Mechanical Engrg., Ben‐Gurion Univ. of the Negev, Beer Sheva, Israel

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