Keywords: stability of cylindrical shells, plasticity, initial geometric imperfection, imperfection database, local buckling.

Thin-walled stiffened or unstiffened, metallic or composite shells are widely used structural elements in aeronautical and space applications. These structures are often highly sensitive to initial imperfections and therefore have buckling loads much lower than those computed for perfect structures. Analysis and testing of imperfect shells have been a major research area during the last century.

This paper will present the results of the buckling analysis and imperfection sensitivity of small cylindrical shells, and their comparison with experimental results. For the analytical work, a hierarchical multi-fidelity approach is used to solve the buckling problem.

An important aspect is inclusion of the effects of plasticity on buckling response of these thin-walled shells. The buckling response of such shells is often an elastic process, and therefore plasticity effects are ignored in the analysis. It will be shown that analyzing the buckling behavior of the shell based only on elastic buckling will not provide an acceptable comparison with experimental result, hence, requiring the inclusion of plasticity effects. It will be demonstrated that, due to both the geometric imperfections and the Poisson expansion of the shell, internal moments are introduced in the shell wall. The influence of these moments is very large; at of the theoretical buckling load the moments already generate stresses that exceed the yield stresses. Local buckling occurs at those locations where the geometric imperfections are the largest, even though the imperfections are less then the wall thickness.

It has been shown that a stability analysis of thin-walled cylindrical shells using a hierarchical approach with different levels of sophistication and fidelity gives the designer a very good picture of the behaviour of a shell. The solution calculated by a finite element program is not just automatically assumed to yield accurate numbers and accurate pictures of the responses anymore but are supported by a thorough semi-analytical study using the level-1 and level-2 modules. However, for the steel cans considered in this study, comparing the results of the elastic runs with the experiments showed still large discrepancy. It was necessary to include plasticity effects in the analysis. The plastic runs yielded a buckling load smaller then the experiment, with buckling patterns matching more closely with those of the experimentally observed ones. The computer results therefore were on the safe side. Further research need to be done on the imperfection sensitivity of shells in which plasticity plays a large role. The plastic material behaviour has to be measured, and finally the description of boundary conditions, the effect of boundary imperfections should be included.

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