NURBS-based form-finding algorithm for double-curvature cable domes

Abstract

Cable domes are one of the most widely used types of cable structures due to their light weight, aesthetic view, and adaptable forms. However, feasibility and structural stability are key elements in designing new forms of cable domes. This paper uses, in a two-stage form-finding algorithm, two NURBS curves to develop a surface of translation (sweeping one curve over the other) or a surface of revolution (rotating one curve around z axis). The main aim of the algorithm is to control the curvature of the dome surface while searching for a feasible geometry, mainly in structures with unfeasible initial configurations, i.e., with zero self-stress states. Examples of these structures are the negative- and zero-Gaussian curvature cable domes of Geiger type. The algorithm starts with a global optimization technique that searches for an optimal feasible NURBS surface for the dome and followed by a local optimization technique that slightly calibrates the vertical locations of nodes to enhance the prestress equilibrium at free nodes. The NURBS surface, not only directs the form-finding process towards a smooth configuration by defining the appropriate degree of the surface, but also maintains the desired sag and rise of negative and positive curves, respectively, to the end of form-finding. The efficiency of the proposed algorithm is verified by applying it to a double-curvature cable dome from the literature. After that, a parametric study is carried out on the reference dome with multiple rise/sag ratios to investigate the effect of rise/sag on the feasibility and stability of such forms. To emphasize the significance of the algorithm in controlling the curvature of the surface, two new forms of cable domes are also developed; one is circular with zero-curvature and the other is elliptic with negative-curvature.