Koiter’s Reduction Finite Element Method for Nonlinear Stability Analysis of Thin-Walled Shells

Thin-walled structures are widely used in aeronautical and aerospace engineering. Conical and cylindrical shells structures, under axial compression, are prone to failure by buckling and typically show a snap-back phenomenon in the end-shortening curve. Path-following technologies based on Newton-type methods have difficulties to trace reliably the snap-back response due to the extremely sharp turning angle near the limit point. In this paper, a Koiter’s reduction finite element method, termed the Koiter–Newton (KN) method, is presented to trace reliably the post-buckling path of cylinders and cones considering either linear buckling modes or dimples from lateral perturbation loads as geometric imperfection. A robust algorithm based on the bifurcation-detection technique is applied during the solution of the reduced order model to achieve a successful path-tracing. The numerical results presented reveal that the nonlinear prediction obtained from Koiter’s perturbation theory at the unloaded state of the structure is numerically accurate up to the buckling load and the initial post-buckling path.