A modified dynamic relaxation form-finding method for symmetrical tensegrity structures with group theory and fuzzy clustering

For tensegrity structures, there are many groups of cables and bars with symmetrical structures or similar internal forces. In this paper, an application of a fuzzy clustering algorithm in the context of form-finding processes for symmetric tensegrity structures is proposed. This algorithm aims to automate grouping, optimize form-finding strategies, and expedite convergence. Point sets are generated through the segmentation of structural components, and Hausdorff distance is used to extract spatial features. Following this, fuzzy clustering automatically groups components with geometric symmetry. The resultant clustering matrix facilitates the refinement of form-finding processes, thus reducing the computational load associated with solving the equilibrium matrix for internal forces within tensegrity structures. By clustering components with analogous internal forces, computational efficiency is enhanced. Additionally, this methodology refines numerical form-finding outcomes based on symmetrical attributes, improving form-finding precision.