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This slide shows a comparison between test and theory for buckling of spherical caps of increasing depth (or increasing radius/thickness). Obviously, the buckling loads of deep spherical caps or complete spherical shells under external pressure are extremely sensitive to initial imperfections, just as are thin cylindrical shells under axial compression.
p is the external pressure; pcl is the "classical" buckling pressure, that is, the buckling pressure of the perfect shell; H is the "rise" of the apex of the spherical cap above the plane of its boundary; h is the shell wall thickness; nu is Poisson's ratio.
The "Symmetric Theory" portion of the theoretical curve is for shallow caps of the type shown in frame (c) on the next slide.
The "Asymmetric Theory" portion of the theoretical curve is for deeper caps of the type shown in frames d-f on the next slide. The curve is "scalloped" because the bifurcation buckling modes must have an integral number of circumferential waves. The number corresponding to the critical buckling mode increases as the "shallowness" parameter, Lambda, increases.
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