Adaptive Tensegrity Module. Ⅰ: Closed-Form and Finite-Element Analyses

摘要

This paper describes the closed-form and discrete computational models for a geometrically nonlinear and linear static analysis of the adaptive tensegrity module presented in the companion paper. Due to the symmetry of the spatial tensegrity system, a simplified closed-form analysis is based on a two-dimensional (2D) solution of an equivalent prestressed triangular cable truss acting under a vertical point load. Novel concrete forms of the cable and deflection equations are derived. The analytical models serve to determine the response, i.e., horizontal components of cable forces and deflections as the basis for control commands. A three-dimensional (3D) discrete geometrically nonlinear analysis of the adaptive tensegrity module is based on the application of a nonlinear finite-element method. The results obtained by the nonlinear finite-element analysis are compared with those obtained by using both the simplified linear and nonlinear closed-form solutions. Physical relevance and mathematical correctness of the applied theoretical approaches were confirmed by the results. Finally, the numerical model is applied to assess the response of the prestressed tensegrity module considering the effects of large deformations and slackening of cables.