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Fig. 1 (a) Sketch of the undeformed configuration of a holey column, indicating the geometry of the ‘unit cells’ and a typical finite-element mesh. (b) Illustration of the Euler mode (centre) and alternating mode (right) of a deformed two-hole column. Each buckled state occurs through a pitchfork bifurcation, which breaks a reflection symmetry of the uncompressed column. (c) The alternating mode with an odd number of holes, which does not break a reflection symmetry. In (b),(c), the shading indicates the distribution of strain energy in the deformed state (as defined in [12]), from black (low strain) to yellow (maximum strain for that column).
From:
C.G. Johnson, U. Jain, A.L. Hazel, D. Pihler-Puzovic and T. Mullin,
“On the buckling of an elastic holey column”, Proceedings of the Royal Society A, Vol. 473, No. 2207, 15 November 2017, DOI: 10.1098/rspa.2017.0477
ABSTRACT: We report the results of a numerical and theoretical study of buckling in elastic columns containing a line of holes. Buckling is a common failure mode of elastic columns under compression, found over scales ranging from metres in buildings and aircraft to tens of nanometers in DNA. This failure usually occurs through lateral buckling, described for slender columns by Euler’s theory. When the column is perforated with a regular line of holes, a new buckling mode arises, in which adjacent holes collapse in orthogonal directions. In this paper, we firstly elucidate how this alternate hole buckling mode coexists and interacts with classical Euler buckling modes, using finite-element numerical calculations with bifurcation tracking. We show how the preferred buckling mode is selected by the geometry, and discuss the roles of localized (hole-scale) and global (column-scale) buckling. Secondly, we develop a novel predictive model for the buckling of columns perforated with large holes. This model is derived without arbitrary fitting parameters, and quantitatively predicts the critical strain for buckling. We extend the model to sheets perforated with a regular array of circular holes and use it to provide quantitative predictions of their buckling
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