Tensegrity structures have remarkable configurations and are drawing the attention of architects and engineers. They possess inextensional mechanisms and self-stress states at a static equilibrium configuration under no external loads. For geometry with its nodes fixed, different connectivity patterns of the compression bars and tension cables might bring some novel tensegrity structures. Thus, form-finding is the key to designing novel tensegrity structures. Here, we develop a discrete optimization model for the form-finding and convert it into a modified traveling salesman problem (TSP). The ant colony system (ACS) is used to search for feasible solutions, where all the predetermined nodes are taken as different cities in the network. An objective function that considers the stability and the relative stiffness is developed to obtain the optimized configurations of tensegrity structures. Examples based on some regular geometries (including a hexagon and two polyhedra) and two nonregular geometries are carried out using the proposed technique. Many different configurations of the pin-jointed assemblies are transformed into interesting tensegrity structures. To verify the proposed method, some physical models are constructed and compared to the tensegrity structures obtained from the form-finding process. We conclude that this novel algorithm can be applicable to the form-finding of both regular and nonregular tensegrity structures.

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