Torsional buckling analysis of thin and thick shells of revolution

Based on the classical thin shell theory and the ®rst-order shear deformation shell theory, two models are developed in this paper for predicting the torsional buckling loads of thin and thick shells of revolution. The material property of a shell of revolution is described as a general type of laminated composites and natural coordinates are used to de®ne its geometry in which any kind of kinematic boundary condition can be applied precisely. To e€ectively use the axi-symmetric property of a shell of revolution in the analysis, a multi-level substructuring technique is employed in which only one substructure is involved in each substructuring level so the size of the problem in real computation is always kept very small. The torsional buckling behaviours of a circular cylinder, a conic shell, an elliptic hyperboloid shell and an ellipsoid shell are investigated using these models