Keywords: plates, compression, post-buckling, elastic, strength, initial imperfection.

The paper discusses the use of the theory of elasticity to determine the post-buckling strength of uniformly loaded square simply supported thin plates with sinusoidal shaped initial imperfections and longitudinal edges free to wave in plane. Based on the findings from a finite element parameter study two main types of failure are distinguished: edge failure and centre failure. The parameters determining which failure mode occurs are explained. To determine the elastic post-buckling behaviour of plates a modified large-deflection solution is proposed, which is simpler to use than existing large-deflection solutions reported in literature. It is shown that determining the post-buckling strength as the elastic load corresponding to first membrane yield gives very conservative results for plates failing by edge failure. More accurate strength prediction is obtained by deriving empirical expressions for a fictitious elastic strain at failure.

The finite element simulations were carried out, on square, simply supported plates with initial imperfections in the shape of the first buckling mode, and a reference slenderness varying between 1 and sqrt(8). The analytically predicted failure loads calculated using analytical solutions for the small-deflection elastic behaviour of plates, determining the failure load as the elastic load corresponding to first membrane yield [1], were compared to those determined with the finite element simulations. Because for loads larger than about twice the buckling load the changes in the buckling form must be accounted for, the large-deflection solution [2] and the modified large-deflection solution [3] was also applied. It was found that for plates with a reference slenderness lambda close to 1, and small initial imperfections, the predicted failure loads are slightly un-conservative, while for plates with increasing slenderness, and increasing initial imperfections, they become more and more conservative (up to 30%) [4]. Closer attention was paid to the failure modes of the plates in the finite element simulations; two different failure modes (centre and edge failure) were distinguished.

For the prediction of the fictitious elastic strain at failure a distinction has been made between plates failing by edge failure and plates failing by centre failure. It has been shown how empirically derived expressions for the fictitious elastic strain at failure can be used to obtain accurate strength predictions. The proposed method can be regarded as a modification of the effective width method for strength described by Rhodes [1]. The proposed method enables the determination of the effective width for strength with an explicit influence of initial imperfections.

1

J. Rhodes, "Effective widths in plate buckling", in "Developments in thin walled structures 1", J. Rhodes, A.C. Walker, (Editors), Applied Science publishers, London, United Kingdom, 119-158, 1982.

2

D.G. Williams, A.C. Walker, "Explicit solutions for the design of initially deformed plates subjected to compression", Proc. Instn. Civ. Engrs. Part 2, 763-787, 1975. doi:10.1680/iicep.1975.3638

3

M.C.M. Bakker, M. Rosmanit, H. Hofmeyer, "Elastic post-buckling analysis of compressed plates using a two-strip model", Thin Walled Structures, 45, 502-516, 2007. doi:10.1016/j.tws.2007.04.006

4

M.C.M. Bakker, M. Rosmanit, H. Hofmeyer, "Post-Buckling Strength of Uniformly Compressed Plates", International Colloquium on stability and ductility of steel structures, Portugal, 189-96, 2006.

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