On optimisation of structures under stability constraints - a simple example

It is well known that optimisation of structures where instability phenomena are present can result in severe imperfection sensitivity [9, 10]. Classical examples are the simple Augusti model and stiffened plates [2, 4]. In both examples, the imperfection sensitivity is due to the interaction of two buckling modes. If the critical loads corresponding to the two buckling modes are well separated, the post-buckling paths are stable, however, when these loads approach to each other, secondary bifurcations occur on the primary post-buckling paths rendering the secondary post-buckling path highly unstable.