Closed-form analytical solutions for thin shell buckling problem are useful in a wide range of analysis and design problems. In this paper, the profile of a cylindrical shell in the post-buckling regime of axisymmetric deformation is analysed, and the solution is shown to be a Jacobi elliptic sine function, for any load and axial deformation. The exact solution of the non-linear differential equation for the thin elastic shell profile holds for any deformation, up to the limit in which the shell is almost flattened by the applied load. Closed-form expressions are derived also for the load dependent axial deflection and stored energy. The analytical solution of the buckling loads and deformed profile are found to agree well with an equivalent numerical solution. Results show that an axially compressed cylindrical shell exhibits ideal behaviour for a safety shock energy absorber.
Buckling Cylindrical shell Elliptic functions Energy absorption
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