Near-flip buckling and scaling instability of critical loads.
Yury Grabovsky, Temple University
Buckling of many slender structures have common features that permit
a general description of this type of stability loss, which we call
``near-flip'' buckling. The theory gives a recipe for evaluating
asymptotics of the critical load as a function of the slenderness
parameter. Especially interesting is the case of buckling of axially
compressed cylindrical shells, where relative wall thickness serves
as the slenderness parameter. The classical buckling load formula
predicts 4-5 times higher value than observed in experiments. This
discrepancy is explained by high sensitivity to imperfections of
load and shape. However, the exact mechanism of this sensitivity
remains elusive. The application of the theory of ``near-flip''
buckling reveals a scaling instability of the critical stress caused
by imperfections of load. The same mechanism could also be at play
in the case of imperfections of shape.