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

• Proposes a generalized Ritz method that accounts for pre-buckling deformations and geometric non-linearity to find buckling load for cylindrical shells.
• Accommodates in a single analytical framework entire range of boundary conditions: intermediate boundary conditions can be easily solved for.
• The Ritz trial functions remain invariant: they do not have to be tailored to the boundary conditions.
• The results using the proposed method show good match with nonlinear finite element solutions.

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.