Elastic-plastic bifurcation analysis of cylindrical shells with axisymmetric variable thickness

This study focuses on the elastic-plastic bifurcation analysis of axial compressed thin-walled cylindrical shells with variable thickness. The general asymptotic formula of the elastic-plastic critical buckling load, which is a function of the Coefficient of the Thickness Variation (CTV) and the buckling load of shells with constant thickness, is derived based on the hybrid perturbation-weighted residual method. The general formula can be reduced to the classical elastic buckling solution in Koiter (1994) when considering the elastic case with the first-order term. Furthermore, a finite element bifurcation analysis procedure is also presented by adopting the incremental J2 deformation theory of plasticity through a custom user-defined subroutine appended to the nonlinear finite element software ABAQUS. The robustness of this numerical scheme and the theoretical formula is confirmed by the decent agreement with the available experimental results in the literature. In the end, the influence of the thickness variation parameter and D/t on the elastic-plastic buckling load of shells with varying thickness is also discussed.