Buckling of uniformly axially compressed axially stiffened cylindrical shells. This slide shows the effect of outside and inside stiffening on buckling load (top frame) and the asymptotic imperfection sensitivity factor b vs the “Batdorf” parameter Z (bottom frame).

Z is the “Batdorf parameter”; L is the length of the shell; R is the radius; t is the wall thickness of the skin of the shell; Nc(stiff) is the buckling load of the perfect stiffened shell; Nc (unstiff) is the buckling load of the unstiffened shell , and b is the Koiter asymptotic imperfection sensitivity factor.

Note that the imperfection sensitivity factor b is much “milder” (less negative) than for axially compressed thin monocoque cylindrical shells, for which b = -1. Also, note that the buckling load of the perfect shell with inside stiffeners is much lower than that for the same shell with outside stiffeners, but that the Koiter factor, b, indicates less imperfection sensitivity for the internally stiffened shells than for the externally stiffened shells.Therefore, in an actual fabricated shell that has unavoidable imperfections the advantage of external versus internal stiffeners is somewhat diminished.

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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