Tensegrity structure statics with slack cables

Purpose This study proposes a non-smooth static analysis method for tensegrity structures to address the issue of slack cables in nonlinear deformation. Slack cables introduce discontinuities in structural behavior, causing instability in numerical computations. Design/methodology/approach The static equilibrium system is reformulated as a linear complementarity problem (LCP), ensuring stability even in structures with numerous slack cables. An index matrix is used to reduce the system dimension by eliminating fixed degrees of freedom, while a dynamic step size strategy based on the structure’s total potential energy improves convergence. Findings Several numerical examples demonstrate that the stability of the solution is improved, especially in systems with a large number of slack cables. Moreover, the equilibrium equations are simplified to involve only the degrees of freedom of free nodes, which enhances computational efficiency. Originality/value The proposed method allows for static analysis of any prestressed tensegrity structure within an acceptable error range and provides a theoretical formulation for slack cables in the structure.