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.
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.
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.
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.
