Rigid-Plastic Analysis of Symmetrically Loaded Cylindrical Shells

A general method is presented for finding the stress and incipient velocity distribution in a symmetrically loaded cylindrical shell at collapse. The results are based upon a linearized yield surface, and a method is given for obtaining this linearized surface directly. The techniques are illustrated with reference to open and closed cylindrical shells under uniform external pressure. In each case the shell is specified completely by a single parameter c defined as the ratio of the half-length of the shell to the geometric mean of the radius and half-thickness; $c=L/a!.$ It is found that for moderately large values of c, the limiting load is greater for the closed shell, while for small c the reverse is true.