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.