Energy-based solution for the plastic buckling of stainless steel circular cylindrical shells

This paper presents an energy-based approximate solution for the plastic buckling of a stainless steel circular cylindrical shell due to a uniaxial compressive force. The solution is based on Ritz method. The implementation of the method is simplified by utilizing the Ramberg-Osgood model along with the total deformation theory to formulate the plasticity constitutive equations. The concept of minimum potential energy yields a single highly non-linear equation to be solved by Mathematica. The accuracy of the obtained solution is verified numerically by the finite element method, using ABAQUS, and experimentally by comparison with several experimental results obtained from the literature. The obtained results show excellent agreement among the analytical, numerical and experimental solutions, with a maximum deviation of 9% between the analytical and experimental values. A parametric study is performed using the validated analytical solution aiming to further investigate the effect of various stainless steel material parameters. Based on the parametric study results, closed-form expressions are derived for the buckling stress.