Postbuckling behavior of a circular cylindrical shell locally buckled under axial compression

Since Kármán and Tsien [1] treated the buckling of cylindrical shells under axial compression, introducing the nonlinear theory based on the finite deformation, this problem has been improved and enlarged by the cumulative efforts of subsequent investigators [2 to 6] and the large discrepancy between the experimental buckling values and the classical value has been gradually clarified. In almost all the previous analyses, cylindrical shells are assumed to buckle in a periodic pattern over the whole surface, but localized diamond-shaped buckling patterns have usually been found. Apart from some analyses on local buckling very close to the ends resulting from the end constraint, Yoshimura [4] and Hoff [7] treated the two-tier buckling, taking into account only the two tiers of periodic undamped waves. The difficulty encountered in such a local buckling is that the deflected shape is not exactly polyhedral. In this paper, the author will attempt to clarify the mechanism of the above-mentioned local buckling. The method of solution employed is based on the stationary principle of energy.