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Title: | Optimum structure to carry a uniform load between pinned supports: Exact analytical solution |
Authors: | Tyas, A Pichugin, AV Gilbert, M |
Keywords: | Topology optimization;Michell structure;Prager structure;Hencky net;Parabolic arch |
Issue Date: | 2011 |
Publisher: | The Royal Society |
Citation: | Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, 467(2128), 1101 - 1120, 2011 |
Abstract: | Recent numerical evidence indicates that a parabolic funicular is not necessarily the optimal structural form to carry a uniform load between pinned supports. When the constituent material is capable of resisting equal limiting tensile and compressive stresses, a more efficient structure can be identified, comprising a central parabolic section and networks of truss bars emerging from the supports. In the current article, a precise geometry for this latter structure is identified, avoiding the inconsistencies that render the parabolic form non-optimal. Explicit analytical expressions for the geometry, stress and virtual-displacement fields within and above the structure are presented. Furthermore, a suitable displacement field below the structure is computed numerically and shown to satisfy the Michell–Hemp optimality criteria, hence formally establishing the global optimality of this new structural form. |
Description: | This article is available open access through the publisher’s website at the link below. Copyright @ 2010 The Royal Society. |
URI: | http://rspa.royalsocietypublishing.org/content/467/2128/1101 http://bura.brunel.ac.uk/handle/2438/9042 |
DOI: | http://dx.doi.org/10.1098/rspa.2010.0376 |
ISSN: | 1364-5021 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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