Theoretical and Numerical Study on Buckling Analysis of Cylindrical Shell Structures by Galerkin and Finite Element Methods

The structural instability of cylindrical shells has long attracted scholarly attention due to its inherently nonlinear response and extensive engineering relevance. Although numerous investigations have examined buckling phenomena arising from individual loading modes such as axial compression or pure torsion, the complex behavior of shells subjected to simultaneous torsional and axial actions remains comparatively underexplored. In this study, an integrated approach combining theoretical formulations and finite element analyses is employed to comprehensively characterize the buckling responses of cylindrical shells under coupled torsional–axial loading conditions. The theoretical framework is developed using Donnell’s shell theory and solved through the Galerkin approximation. The predicted results exhibit strong agreement with finite element simulations. It is demonstrated that the buckling evolution of cylindrical shells under combined loading markedly differs from that produced by a single load component. Specifically, shells under torsion with minor compression display a stable deformation mode, whereas higher compression induces a transition toward a diamond-shaped buckling pattern. Such findings elucidate the coupled torsion–compression/tension effects governing buckling instabilities in cylindrical shells, offering valuable insight for the design of load-responsive foldable and origami-inspired structures driven by combined mechanical actions.