Buckling of Imperfect, Axisymmetric, Homogeneous Shells of Variable Thickness: Perturbation Solution

Abstract

This paper presents the first of a series of solutions to the buckling of imperfect cylindrical shells subjected to an axial compressive load. The initial problem 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 70 years ago are thoroughly presented as basis for a solution employing perturbation methods. 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 shell wall thickness. Clearly in practice, large diameter thin wall shells of revolution that form stacks (as found in flue gas desulphurization absorber assemblies) are never fabricated with constant diameters and thicknesses over the entire length of the assembly. As such, ASME Boiler and Pressure Vessel Code Section VIII shell thickness tolerances as supplemented by ASME Code Case 2286-1 are reviewed and addressed in comparison to the resulting solutions with respect to the critical buckling loads. The method and results described herein are in stark contrast to the “knockdown factor” approach currently utilized in ASME Code Case 2286-1. Recommendations for further study of the imperfect cylindrical shell are also outlined in an effort to improve on the current rules regarding column buckling of large diameter shells designed in accordance with ASME Section VIII, Divisions 1 and 2 and ASME STS-1 in combination with the suggestions contained within Code Case 2286-1.