Buckling and post-buckling of cylindrical shells under combined torsional and axial loads

The buckling behavior of cylindrical shells has gained significant interest over the past century due to its rich nonlinear behavior and broad engineering applications. While the buckling of cylindrical shells under a single load (e.g., compression or torsion) has been extensively studied, the buckling behavior under combined torsional and axial loads remains largely unexplored. In this paper, based on a combination of experiments, theoretical modeling, and finite element simulations, we systematically investigate the buckling and post-buckling behavior of cylindrical shells under combined torsional and axial loads. Three different types of combined loads are considered: compression with pre-torsion, torsion with pre-tension, and torsion with pre-compression. The theoretical model is established within the framework of the Donnell shell theory and solved using the Galerkin method, through which the critical buckling load, critical circumferential wavenumber, buckling pattern, and post-buckling equilibrium path of clamped-clamped thin cylindrical shells under various types of loads can be determined. The theoretical predictions agree well with finite element simulations and qualitatively capture the various buckling phenomena observed in the experiments. It is found that cylindrical shells exhibit quite different post-buckling behavior under combined loads compared to under a single compressive or torsional load. For instance, when a clamped-clamped thin cylindrical shell is subjected to pure torsion or torsion with a relatively small pre-compression, it consistently shows a diagonal-shaped pattern during deformation. However, with a relatively large pre-compression, the shell transitions from a diagonal-shaped pattern to a twisted diamond-shaped pattern. Our work reveals the role of torsion-compression/tension coupling in the buckling instabilities of cylindrical shells, which can guide the design of cylindrical shell buckling-inspired foldable structures such as origami systems driven by combined loads.