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Axisymmetric prebuckled & early post-buckled states of an externally pressurized clamped spherical cap

From the same PhD thesis as the previous image.

The previous image is a modified form of Fig. 4.4 of Bushnell’s 1965 PhD thesis. (Dashed lines for imperfect shells have been added.)

The present image demonstrates early localization of the early post-buckled state in the neighborhood of the pole. The dimensionless geometric parameter, LAMBDA-squared = 200.

LAMBDA is a dimensionless geometric parameter that combines the thickness t of the spherical cap and the height H of its reference surface at the pole above the plane of its edge. The formula for the geometric parameter LAMBDA appears in three of the images relating to buckling of spherical caps. These three images are displayed later. See in particular the image from the paper:

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.

For LAMBDA-squared = 200 the clamped boundary of the spherical cap has negligible influence on the early post-buckling behavior in the neighborhood of the pole. Therefore, in the early postbuckling regime this clamped externally pressurized spherical cap with reasonably large LAMBDA behaves essentially as a complete spherical shell.

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