Buckling of Thin Truncated Conical Shells with Circular Cross-Section Using a Geometric Nonlinear GBT Formulation

This work outlines the theoretical foundations of a newly proposed Generalized Beam Theory (GBT) framework for geometrically nonlinear analysis of thin truncated conical shells with circular cross-sections. In addition to providing nonlinear load–displacement paths, the proposed formulation can be used to predict bifurcation loads and their corresponding buckling modes. The present study focuses on the latter capability, enabling a detailed understanding of instability mechanisms while offering significant computational savings compared to refined shell finite element analyses. A parametric study is conducted for three loading cases - axial compression, pure torsion, and pure bending. Special emphasis is placed on the transitions between deformation modes, which are efficiently captured through the GBT modal decomposition. The formulation is validated through comparisons with refined shell finite element solutions, and the discrepancies across all loading cases and geometries considered remain very small, highlighting the robustness and predictive accuracy of the proposed approach.