Buckling and deformation of Hollomon's power-law tubes

A long, thin, inextensible cylindrical tube made of Hollomon's power-law material acted upon by a uniform normal pressure is considered. The nonlinear boundary value problem that governs the equilibrium states of such a tube is formulated as a differential system of equations. Perturbation solutions are obtained for the cases of small pressure values in the neighborhood of the critical buckling pressures. Numerical solutions based on a special initial value problem Matlab solver, Newton's and shooting methods are obtained. The results show that a high strength material tube deforms similarly to an elastic material tube for values of strain hardening exponent.