Imperfections in a two-dimensional hierarchical structure

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

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.

Citation

Rayneau-Kirkhope, D., Mao, Y., & Farr, R. (2014). Imperfections in a two-dimensional hierarchical structure. Physical Review E, 89(2), Article 023201. https://doi.org/10.1103/PhysRevE.89.023201

• 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
• DOI: https://doi.org/10.1103/PhysRevE.89.023201
• Public URL: https://nottingham-repository.worktribe.com/output/723243
• Publisher URL: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.023201