This study is mainly concerned with the analytical solutions of plastic bifurcation buckling of cylindrical shells under compressive load. The analysis is based on the J2 deformation theory with a linear hardening and proportional loading is adopted in the calculation. A symplectic solution system is established and Hamilton's governing equations are derived from the Hamilton variational principle. The basic problem in plastic buckling is converted into solving for the symplectic eigenvalues and eigensolutions, respectively. The obtained results reveal that boundary conditions have a very limited influence on bucking loads but its influence on buckling modes and plastic borders cannot be neglected. Meanwhile, it is demonstrated that the shell material properties significantly affect the plastic buckling behavior. This proposed symplectic method is shown to be a rigorous approach. It also provides a uniform and systematic way to any other similar problems.

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