Keywords: elastic postbuckling, thin-walled beams, imperfection sensitivity.

Thin walled frames exibit a postbuckling behaviour that can be, depending on both geometric features and applied loads, asymmetric or symmetric. Now, although the former response leads to an imperfection sensitivity of the structure which is generally higher then the latter, this can not be assumed as a rule.

In this paper, using a suitable one-dimensional continuum [1] and the asymptotic bifurcation theory proposed by Koiter [2], the initial postbuckling of sample structures is studied in order to give a reasonable account of the typical behaviour of thin walled frames.

The analysis is performed in the framework of nonlinear elasticity and the one-dimensional model adopted refers to beams where cross sections can be considered rigid in their plane although being free to undergo warping deformation. This means that the results obtained hold in the cases in which global buckling modes are prevailing or modes involving in plane deformation of the cross sections are prevented.

In the case of asymmetric behaviour the analysis, as usual, ends with the assessment of the initial postbuckling slope of the bifurcated path. For the case of symmetric behaviour, instead, the initial curvature is also determined.

All the analyses have been performed by regarding the structures as perfect. The assessment of their imperfection sensitivity has been accomplished in a second step.

To this end, it must be stressed that the asymptotic approach proves to be a very effective tool. In fact, once the perfect structure has been examined, then the evaluation of the (nonlinear) equilibrium path resulting from an assigned imperfection, can be determined in a very straightforward way together with the load carrying capacity of the structure.

This enables the response of the studied frames when subjected of a number of possible initial imperfections, to be considered in a very easy way.

The results are compared with solutions present in the current literature. These comparisons show that the results obtained by means of the asymptotic theory are highly reliable.

1

N.L. Rizzi, V. Varano, "The effects of warping on the postbuckling behaviour of thin-walled structures", Thin-Walled Structures, 49, 1091-1097, 2011. doi:10.1016/j.tws.2011.04.001

2

B. Budiansky, "Theory of buckling and postbuckling behavior of elastic structures", in C.S. Yih, (Editor), "Advances in Applied Mechanics", 14, Academic Press, New York, 1974.

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