Buckling of a non-uniform, long cylindrical shell subjected to external hydrostatic pressure

Analytical solutions for elastic buckling of a non-uniform, long cylindrical shell that is subjected to external hydrostatic pressure are presented in this paper. The non-uniform shell has two regions: one with a nominal thickness and the other with reduced thickness. Symmetric and anti-symmetric buckling modes have been found to occur depending on the relative thickness of the two different regions and the angular extent of the section with the reduced thickness. A diagram showing the ranges of relative thickness and angular extent of the section with the reduced thickness is given for the occurrence of symmetric and anti-symmetric modes. In general, the buckling pressure decreases when either the relative thickness or the angular extent of the section with the reduced thickness increase. Finite element solutions for the elastic buckling pressure and modes are also found using ABAQUS and the results from analytical solutions are found to be in close agreement with finite element predictions.