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From:
Kaplan, A., "Buckling of Spherical Shells," Thin-Shell Structures: Theory, Experiment, and Design, edited by Y. C. Fung and E. E. Sechler, Prentice-Hall, Englewood Cliffs, N.J., 1974, pp. 248-288.
This plot pertains to spherical caps, not complete spherical shells. The quantity "lambda", plotted on the horizontal axis, is a sort of combination of R/t and the diameter of the base plane of the cap. In experiments, as "lambda" gets large the behavior of unavoidably imperfect test specimens approaches that of a complete imperfect spherical shell; that is, the effect of the local "imperfection" created by local axisymmetric prebuckling deformation in the neighborhood of the supported edge is much less significant than random unavoidable geometrical imperfections remote from the edge. Theoretically for small "lambda" you get buckling via axisymmetric snap-through, and for large "lambda" you get non-axisymmetric edge buckling at something like 70 to 90 per cent of the classical Zoelly formula for buckling of a complete spherical shell, depending on the edge boundary conditions.
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