A note on structural mode transitions in buckling of radially stretched annular plates

The different approximating assumptions used in deriving models for structural analysis by dimensional reduction of a 3d continuum to structural components like beams and plates or shells limit the applicability of these models by geometrical constraints. Hence, caution should be exercised when transitioning from the application range of one type of structure model to another one. This should be taken into account especially when stability analyses are performed. In order to demonstrate this, in this note, buckling of annular plates under tensile loading at the inner edge is treated as an example. The ratio between inner and outer radius is varied. For ratios approaching 1.0, plate buckling turns into buckling of circular beams. This is not only a question of accuracy of the solution but can lead to a substantial qualitative change of the character of buckling. Such considerations might be interesting from a theoretical point of view; in any case they are important from the engineering point of view.