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.