Variability in large-sample postbuckling behavior of two small thin walled structures

In thin shell buckling, geometric imperfections are important contributors to observed scatter in experimentally determined postbuckling behavior. Buckling experiments with large shells are difficult and expensive to conduct, and hence the sample sizes of buckling tests reported in the literature are generally small. To study statistical variability of buckling loads for a large number of notionally identical thin shells, we have carried out 100 buckling experiments each for two thin shell geometries. One shell geometry is a dome-like shell with a flat base (a bowl), and the other is a truncated cone with a flat base (a tumbler). The test shells are industrially produced, inexpensive, made of stainless steel, and easily available in India as utensils for domestic use. We provide detailed geometric and material characterization of these thin shell specimens. These shells were compressed axially between rigid plates. Buckling for both shell geometries was elastoplastic in nature. The experimental buckling load–displacement curves of 100 specimens for the bowl show variability in buckling loads by a factor of two, and stable postbuckling response. The corresponding curves for 100 specimens of the tumbler show variations of as much as a factor 5, with many snap-throughs, and unstable postbuckling response for larger compressions. We present two sets of axisymmetric elastoplastic finite element simulations of the tumbler, with both (a) tractions directly applied on a predetermined region and (b) through contact with a rigid plate. The latter set of simulations show approximately twice as much sensitivity to geometrical imperfections. Our results may guide new assessments of factors of safety in buckling, as laid down in design codes, when there is a chance of such interactions between contact loading and geometry.