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from "Structural behavior and compressive strength of circular cylinders with longitudinal stiffening", NASA TN D-1251, May 1962 by James P. Peterson, Ralph O. Whitley and Jerry W. Deaton
This is an important slide to understand.
sigma(bar) is the applied stress; sigma(cr) is the stress at the load for which the flat sheet buckles; epsilon(bar) and epsilon(cr) are the corresponding axial strains.
The effective average axial stiffness of the initially buckled flat plate is approximately 0.4 times the axial stiffness of the unbuckled plate, and this effective average axial stiffness decreases gradually as the plate is loaded further and further into its post-buckled state.
Axially compressed curved panels (thin shells) exhibit much more complex imperfection-sensitive behavior.
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