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Buckling of externally pressurized cylindrical shells of intermediate or long length exhibits less imperfection sensitivity than does buckling of axially compressed cylindrical shells or externally pressurized spherical shells.
The dimensions of typical individual buckles of externally pressurized cylindrical shells are much larger than those of an axially compressed cylindrical shell, and buckling eigenvalues corresponding to different modes of buckling are not densely clustered as they are for axially compressed cylindrical shells.
Here, in the top frame we see a comparison of test v. theory as a function of the “Batdorf” parameter Z. Note that in the region where test points fall below theory the Koiter asymptotic imperfection sensitivity parameter b is negative, indicating a degree of imperfection sensitivity (bottom frame).
The curve with the most negative values of b for small Z arises because, for small Z (short shells), the axial component of compression generated by the external hydrostatic pressure produces behavior similar to that of a uniformly axially compressed cylindrical shell.
Pc is the buckling pressure of the perfect shell; D is the bending stiffness of the shell wall; b is the Koiter "imperfection sensitivity" parameter.
These kinds of asymptotic analyses were carried out by Koiter in 1945 and by Budiansky, Hutchinson, and colleagues in the 1960s and 1970s.
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