Elastic Instability of a Cylindrical Shell Under Arbitrary Circumferential Variation of Axial Stress

The buckling stress of a cylindrical shell is determined for various circumferential distributions of axial stress. The development is based on small deflection theory, with finite difference techniques being applied to derive the general form of the governing algebraic linear homogeneous equations. The equations are cast in both the determinant and matrix forms, the latter being suitable for the commonly used matrix iteration solution. Numerical results are obtained by means of a highspeed digital computer for cases wherein the stress distribution is described by 32 circumferential elements. I t is found tha t the buckling stress for pure bending, and for more complicated circumferential stress distributions of the axial stress as well, is not much higher than for uniform axial compression. Cases are indicated where small deflection theory is directly applicable.