Lower bound to limit pressure for cylindrical shell with part-through slot

A lower bound to the limit pressure of a cylindrical shell with a rectangular slot part through the thickness at mid-length is computed using a linear optimization technique. The sides of the slot are axial and circumferential. The analysis has been carried out for internal pressure applied to the cylinder such that the longitudinal pressure end force is (a) not taken by the cylindrical shell, (b) wholly taken by the cylindrical shell. Different proportions of rectangular slot and different radius to thickness ratios of the cylinder have been considered. Results are presented for a range of parameters.