Harnessing Symmetry in Stiffness Matrix Formulation for Tensegrity Structures with Equal Cable Length via Linear Stiffness Theory

Tensegrity structures, due to their lightweight and self-equilibrating characteristics, have found extensive applications across various engineering fields. The introduction of equal cable length as an additional geometric constraint enables a high degree of geometric symmetry, resulting in uniform internal force distribution and predictable mechanical responses. However, existing stiffness matrix assembly methods predominantly rely on conventional node-element topological connectivity matrices confined to classical one-to-one force-displacement systems, struggling to exploit the geometric regularities inherent in equal-length constraints and highly symmetric configurations. To address this, the paper proposes a stiffness matrix modeling method tailored for equal-cable-length tensegrity structures within the linear stiffness framework. A generalized connectivity matrix is introduced to unify the topological description of struts and cables while integrating displacement compatibility, internal equilibrium, and geometric constraints into a cohesive algebraic system. Leveraging symmetry properties and member categorization by loading type, the method embeds equal-length and symmetry grouping information directly into assembly, significantly reducing independent variables and construction complexity. A finite element model is established for numerical implementation, and experiments on a three-bar tensegrity structure validate the theoretical model, with minor deviations confirming its reliability.