by Parthasrathi Mandal
Thin-walled cylindrical shell structures are widely used in many industries. Due to the increasing use of high-strength materials in construction, and optimisation methods in analysis, the design of such structures is often buckling-critical. Unfortunately, the theoretical predictions (by classical theory) for buckling loads are often much higher than those found from experimental studies conducted since the 1930s. Moreover, there is large ‘scatter’ of the experimental buckling loads of identical specimens, tested in a similar fashion. The concepts of ‘non-linearity’ and ‘imperfection-sensitivity’ are widely accepted as explanations for these features of shell buckling.
Some simple experiments on self-weight buckling of thin, open-top, fixed-base, small-scale silicone rubber cylindrical shells are presented in this dissertation. The thicker shells buckled at almost the heights predicted by the ‘simple classical theory’. But in general the buckling heights were found to be proportional to thickness raised to the power of approximately 1.5 compared to 1.10 as in the ‘classical theory’. Moreover, the results showed very little ‘scatter’, although there was no conscious attempt to manufacture very accurate shells, and indeed, there were measurable imperfections in terms of thickness variations. These observations somehow defy the accepted hypothesis of ‘imperfection-sensitivity’. Much of this dissertation reports various attempts to resolve this paradox. The most successful of these involved a non-linear finite-element analysis, which showed that there is ‘post-buckling plateau’ load corresponding to the experimental buckling loads. Although no formal explanation of this plateau load is presented here, the recurrence of this feature for more than one shell suggests that the post-buckling, unusually is something like a classical phenomenon, in the sense that there exists a plateau load much like the eigenvalue predictions of classical theory, and with small scatter.
In an attempt to find out the relationship of our experimental results to the vast experimental data in the literature, it was found out that the slope of the best-fit line through the large quantity of test data in the literature has also a slope of approximately 1.5. However, the scatter in the literature data is much greater than in the present experiments. The most obvious explanation of the difference is that the open-topped shells in the present study are ‘statically determinate’, whereas the usual closed-ended shells used in the tests in the literature are ‘statically indeterminate’: the possibility of high ‘initial stresses’, may explain the ‘scatter’.
[Cambridge University | CUED | Structures Group | Geotechnical Group]
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