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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.
ISSN: 1364-5021
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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