On the Plane Geometry Design Method of the Loop-free Hyperbolic Single-layer Cable Structures

Abstract

The plane geometry design of the cable-net structure is the basis for the form-finding and structural design. The loop-free single-layer cable-net structure is a new cable-net scheme, but due to its special and complex shape, it is difficult to determine its plane geometry according to architectural requirements. In this paper, the moving support node method is proposed, which can quickly get the plane geometry of a loop-free single-layer cable-net structure. The form-finding is proceeded based on the existing small elastic modulus method. There are two constraints when using the moving support node method. One is that the projection of all cables is straight line, and the other is that the distance between the two cables of each support node and the inner boundary of the target is equal. The aim is to minimize the sum of the distances from all cables to the inner boundary of the target. Using the plane geometry control parameters and the plane coordinates of the support nodes as decision variables, the plane geometry closest to the target inner and outer boundaries is get through optimization analysis. According to the derivation of the formula, the plane projection shape of a loop-free single-layer cable-net structure is mainly related to three parameters, including the number of supports, the difference between the node numbers of the supports at both ends of each cable, and the target curve equations of the inner and outer boundaries. Finally, taking the roof structure of Linyi Olympic Stadium as an instance, the feasibility of the plane geometry design method of the loop-free single-layer cable-net structures based on the moving support node method is verified.