Force Density Relation and Lightweight Modeling of Single Layer Tensegrity Structures

Abstract

A mathematical model is established using the space coordinates of nodes and vector matrix of components to study the construction method and lightweight nature of single-layer tensegrity structures on the basis of their geometric parameters. Connection matrix and configuration of the single-layer tensegrity structures are built using MATLAB software. The force balance equations of nodes of a three-bar tensegrity structure are established by introducing the force-density method, and the force-density relationship amongst the components is analysed. Thus, the configuration principle of single-layer tensegrity structure is verified. The force-density relationship between the components in the single-layer tensegrity structure is obtained. The change rule of the force-density relationship in different single-layer tensegrity structures is also analysed. Notably, p-1 stable configurations are present in the p-bar tensegrity structure. The force-density relationships of these p-1 configurations are in symmetrical distribution, that is, the j-th and (p-j)th configurations have the same force-density relationship. The lightweight nature of the structure is studied using the force-density relationship between the components, and the optimal structural parameter relationship is obtained when the structure has the lightest mass.