Abstract

In this paper, we continue the development of mathematically rigorous theory of "near-flip" buckling of slender bodies of arbitrary geometry, based on hyperelasticity. In order to showcase the capabilities of this theory, we apply it to buckling of axially compressed circular cylindrical shells. The theory confirms the classical formula for the buckling load, whereby the perfect structure buckles at the stress that scales as the first power of shell's thickness. However, in the case of imperfections of load, the theory predicts scaling instability of the buckling stress. Depending on the type of load imperfections, buckling may occur at stresses that scale as thickness to the power 1.5 or 1.25, corresponding to the lower and upper ends, respectively, of the historically accumulated experimental data.