On the Buckling of an Elastic Holey Column

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    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 meters 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 localised (holescale) 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.
    Original languageEnglish
    JournalRoyal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
    Early online date15 Nov 2017
    DOIs
    Publication statusPublished - 15 Nov 2017

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