The multi-modal formulation of Koiter's asymptotic method provides a systematic and efficient procedure to evaluate the initial post-buckling behaviour and to assess the nonlinear behavior of structures. This manuscript presents a displacement-based multi-modal formulation of Koiter's method for cylindrical shells, which are structures known for their high imperfection sensitivity and for having clustered bifurcation modes that highly interact. A third-order interpolation is used for the in-plane and out-of-plane displacements by means of the Bogner-Fox-Schmit-Castro (BFSC) element, with 4 nodes and 10 degrees-of-freedom per node, aiming at an accurate representation of the second-order fields required in the initial post-buckling analysis. The single-curvature of the shell is considered in the finite element kinematics and the study includes nonlinear kinematics from Von Kármán and Sanders. The mesh is obtained by closing the circumferentially oriented coordinate at the position where the mesh completes one revolution about the shell perimeter. The proposed formulation and implementation is verified in detail by comparing results for composite shells against established literature for multi-mode asymptotic expansions. A fast convergence of the proposed formulation is observed for linear buckling, pre-buckling state and the initial post-buckling coefficients. The developed formulation enables a close relationship between formulae and the implemented code, and is implemented using state-of-the-art collaborative software. The authors made the implemented routines in a publicly available data set with the aim to popularize Koiter's method.
Displacement-based multi-modal formulation of Koiter's method applied to cylindrical shells
