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This slide shows prediction from asymptotic theory of the sensitivity of the buckling loads of various structures, including thin externally pressurized spherical shells and thin axially compressed cylindrical shells, to small initial geometrical imperfections.
P is the load; Pc is the "classical" buckling load, that is, the buckling load of the perfect structure; b is the asymptotic Koiter "imperfection sensitivity" parameter; t is the effective shell wall thickness; delta is the amplitude of the post-buckling deflection; Ps is the collapse load of the imperfect structure; delta-bar is the amplitude of an imperfection.
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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