Imperfections in a two-dimensional hierarchical structure

Rayneau-Kirkhope, Daniel and Mao, Yong and Farr, Robert (2014) Imperfections in a two-dimensional hierarchical structure. Physical Review E, 89 (2). 023201/1-023201/11. ISSN 1550-2376

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Abstract

Hierarchical and fractal designs have been shown to yield high mechanical efficiency under a variety of loading conditions. Here a fractal frame is optimized for compressive loading in a two-dimensional space. We obtain the dependence of volume required for stability against loading for which the structure is optimized and a set of scaling relationships is found. We evaluate the dependence of the Hausdorff dimension of the optimal structure on the applied loading and establish the limit to which it tends under gentle loading. We then investigate the effect of a single imperfection in the structure through both analytical and simulational techniques. We find that a single asymmetric perturbation of beam thickness, increasing or decreasing the failure load of the individual beam, causes the same decrease in overall stability of the structure. A scaling relationship between imperfection magnitude and decrease in failure loading is obtained. We calculate theoretically the limit to which the single perturbation can effect the overall stability of higher generation frames.

Item Type: Article
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Physics and Astronomy
Identification Number: https://doi.org/10.1103/PhysRevE.89.023201
Depositing User: Mao, Yong
Date Deposited: 18 Jul 2016 09:53
Last Modified: 15 Sep 2016 20:17
URI: http://eprints.nottingham.ac.uk/id/eprint/35075

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