This paper presents the third of a series of solutions to the buckling of imperfect cylindrical shells subjected to an axial compressive load. In particular, the initial problem reviewed is the case of a homogeneous cylindrical shell of variable thickness that is of an axisymmetric nature. The equilibrium equations as first introduced by Donnell over seventy years ago are discussed and reviewed in establishing a basis for embarking upon a solution that utilizes finite difference methods to solve the resulting equilibrium and compatibility equations. The ultimate objective of these calculations is to achieve a quantitative assessment of the critical buckling load considering the small axisymmetric deviations from the nominal cylindrical shell wall thickness. Clearly in practice, large diameter, thin wall shells of revolution that form stacks are never fabricated with constant diameters and thicknesses over the entire length of the assembly. The method and results described herein are in stark contrast to the “knockdown factor” approach currently utilized in ASME Code Case 2286-1. The results obtained by finite difference method agree well with those published by Elishakoff and Williams for the prediction of buckling load.

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