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Imperfections in a two-dimensional hierarchical structure

Rayneau-Kirkhope, Daniel; Mao, Yong; Farr, Robert


Daniel Rayneau-Kirkhope

Associate Professor

Robert Farr


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.


Rayneau-Kirkhope, D., Mao, Y., & Farr, R. (2014). Imperfections in a two-dimensional hierarchical structure. Physical Review E, 89(2),

Journal Article Type Article
Acceptance Date Feb 5, 2014
Publication Date Feb 12, 2014
Deposit Date Jul 18, 2016
Publicly Available Date Jul 18, 2016
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 1550-2376
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 89
Issue 2
Article Number 023201
Public URL
Publisher URL
Copyright Statement Copyright information regarding this work can be found at the following address:


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Copyright Statement
Copyright information regarding this work can be found at the following address:

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