Dent patterns on the surface of a longitudinally compressed, non-linear elastic cylindrical shell

A novel version of reductive perturbation theory is proposed for analysing the dynamics of bends in a longitudinally compressed, non-linear elastic cylindrical shell near the stability threshold given by the linear theory. Soliton-like annular folds and patterns of diamond-shaped dents on the shell surface are predicted and analytically described. Similar formations, which are both stress concentrators and precursors of plastic flow of the material, contain information on the precritical stress state of the shell. It is shown that a shell with dents supports an external load, which is tens of percent less than the upper critical load in the linear theory of shells. The conditions for the formation of and explicit expressions for solitary waves that propagate along the generatrix of the shell on a background of arrays of folds and dents are found.