Imperfections in a two-dimensional hierarchical structure
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 st...
| Main Authors: | , , |
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| Format: | Article |
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American Physical Society
2014
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| Online Access: | https://eprints.nottingham.ac.uk/35075/ |
| _version_ | 1848794997866889216 |
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| author | Rayneau-Kirkhope, Daniel Mao, Yong Farr, Robert |
| author_facet | Rayneau-Kirkhope, Daniel Mao, Yong Farr, Robert |
| author_sort | Rayneau-Kirkhope, Daniel |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:25:05Z |
| format | Article |
| id | nottingham-35075 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:25:05Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-350752020-05-04T16:43:12Z https://eprints.nottingham.ac.uk/35075/ Imperfections in a two-dimensional hierarchical structure Rayneau-Kirkhope, Daniel Mao, Yong Farr, Robert 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. American Physical Society 2014-02-12 Article PeerReviewed Rayneau-Kirkhope, Daniel, 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 http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.023201 doi:10.1103/PhysRevE.89.023201 doi:10.1103/PhysRevE.89.023201 |
| spellingShingle | Rayneau-Kirkhope, Daniel Mao, Yong Farr, Robert Imperfections in a two-dimensional hierarchical structure |
| title | Imperfections in a two-dimensional hierarchical structure |
| title_full | Imperfections in a two-dimensional hierarchical structure |
| title_fullStr | Imperfections in a two-dimensional hierarchical structure |
| title_full_unstemmed | Imperfections in a two-dimensional hierarchical structure |
| title_short | Imperfections in a two-dimensional hierarchical structure |
| title_sort | imperfections in a two-dimensional hierarchical structure |
| url | https://eprints.nottingham.ac.uk/35075/ https://eprints.nottingham.ac.uk/35075/ https://eprints.nottingham.ac.uk/35075/ |