A simple layout optimization formulation for load-carrying tensegrity structures
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RESEARCH PAPER
A simple layout optimization formulation for load-carrying tensegrity structures K. I. U. Nanayakkara1 · Linwei He1
· Helen E. Fairclough1 · Matthew Gilbert1
Received: 21 January 2019 / Revised: 3 June 2020 / Accepted: 8 June 2020 © The Author(s) 2020
Abstract Traditional tensegrity structures comprise isolated compression members lying inside a continuous network of tension members. In this contribution, a simple numerical layout optimization formulation is presented and used to identify the topologies of minimum volume tensegrity structures designed to carry external applied loads. Binary variables and associated constraints are used to limit (usually to one) the number of compressive elements connecting a node. A computationally efficient two-stage procedure employing mixed integer linear programming (MILP) is used to identify structures capable of carrying both externally applied loads and the self-stresses present when these loads are removed. Although tensegrity structures are often regarded as inherently ‘optimal’, the presence of additional constraints in the optimization formulation means that they can never be more optimal than traditional, non-tensegrity, structures. The proposed procedure is programmed in a MATLAB script (available for download) and a range of examples are used to demonstrate the efficacy of the approach presented. Keywords Layout optimization · Tensegrity structures · Mixed integer linear programming
1 Introduction Tensegrity structures were pioneered by Fuller (1962) and Snelson (1965), and according to their original definitions tensegrity structures are arrangements of pin-jointed members with a maximum of one compression member (strut) at each joint, with no such limitation on tension members (cables). Fuller’s original aspiration was to use tensegrity
Responsible Editor: Anton Evgrafov Linwei He
[email protected] K. I. U. Nanayakkara [email protected] Helen E. Fairclough [email protected] Matthew Gilbert [email protected] 1
Department of Civil and Structural Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK
structures to form the ‘largest and strongest structure per pound of structural material employed’, considering applications such as very large stadium roofs. This indicates that tensegrity structures were considered to be highly structurally efficient, something that will be explored here. To date tensegrity structures have been used only occasionally for real-world terrestrial structures, and then largely for their architectural appeal, e.g. Kenneth Snelson’s Needle Tower (Snelson 2014), the Messeturm in Rostock (Schlaich 2004) and the Kurilpa Bridge in Brisbane (Arup 2009). Tensegrity structures have also been suggested for use in space due to the fact that their form can readily be controlled, aiding deployability (Tibert 2002; Furuya 1992). Subsequent workers—after Fuller and Snelson—have sought to provide more precise definitions of what constitutes a viable tensegrity structure,
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