Numerical models for nonlinear analysis of elastic shells with eigenmode-affine imperfections

Nonlinear finite-element analysis provides a powerful tool for assessing the buckling strength of shells. Since shells are generally sensitive to initial geometric imperfections, a reliable prediction of their buckling strength is possible only if the effect of geometric imperfections is accurately accounted for. A commonly adopted approach is to assume that the imperfection is in the form of the bifurcation buckling mode (eigenmode-affine imperfection) of a suitable magnitude. For shells of revolution under axisymmetric loads, this approach leads to the analysis of a shell with periodically symmetric imperfections. Consequently, sector models spanning over one or half the circumferential wave of the imperfection may be considered adequate. This paper presents a study which shows that a simple nonlinear analysis of the imperfect shell may not deliver the correct buckling load, due to the tendency of the shell to develop mode changes in the deformation process before reaching the limit point. This inadequacy exists not only with short sector models (half-wave or whole-wave models) but also with more complete models (half-structure or whole-structure models) for different reasons. The paper concludes with recommendations on the proper use of the four different kinds of models mentioned above in determining shell buckling strengths.