A generalized Ritz-based method for nonlinear buckling of thin cylindrical shells

A generalized Ritz based approach that accounts for pre-buckling bending deformations as well as geometric non-linearity to find the buckling load for thin cylindrical shells under uniform axial compression is proposed. The approach accommodates within a unified framework, based on a shell and spring restraint system, the entire range of boundary conditions: ranging from free boundaries to compliant boundaries. The classical kinematic boundary conditions are recovered as limiting cases. The method involves choice of a single trial function that is invariant with respect to boundary conditions. The proposed approach is validated using existing analytical results, where available, and numerical solutions, otherwise.