A simple layout optimization formulation for load-carrying tensegrity structures

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.