Stability Analysis of A Circular Cylindrical Shell By the Equilibrium Method

Presented herein is a formulation for the buckling of a cylindrical shell subjected to external loads using an infinitesimal shell element defined in a convenient coordinate system. The governing equation in terms of the radial deflection is derived for the element by adopting an operator. The eighth order partial differential equation derived can be applied for cylindrical shells with various boundary conditions. For illustration, simply supported cylindrical shells subjected to axial compressive forces are studied using either a one-variable or a two-variable shape function. The critical stresses obtained for the buckling of cylindrical shells are compared with those by the finite element program SAP2000. The critical stress of the cylindrical shell is similar to that of the column, in that the critical stress decreases as the thickness ratio (the ratio of R/h) or the slenderness ratio increases. Good agreement has been obtained for most of the comparative cases, while the finite element results appear to be slightly higher for some cases.