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.

传统的张力结构包括位于张力构件的连续网络内部的隔离的压缩构件。在此贡献中，提出了一种简单的数值布局优化公式，并用于确定最小体积张力结构的拓扑，这些结构旨在承受外部施加的载荷。二进制变量和关联的约束用于限制（通常为一个）连接节点的压缩元素的数量。使用混合整数线性规划（MILP）的计算有效的两阶段程序用于识别能够承载外部施加的载荷和当这些载荷除去时存在的自应力的结构。尽管紧张结构通常被认为是固有的“最佳”结构，优化公式中附加约束的存在意味着它们永远不可能比传统的非张紧结构更好。建议的过程在MATLAB脚本（可下载）中编程，并使用一系列示例来演示所提出方法的有效性。