Shape optimization of a new tensegrity torus

Abstract

This paper studies the shape optimization of a new tensegrity torus. The topology and configuration of the novel tensegrity torus are first introduced. Considering multiple symmetric properties of the tensegrity torus, the topology and configuration of the torus can be parameterized into four variables. A structural analysis method based on pseudo-inverse is used to solve the underdetermined equilibrium equations of self-stressed tensegrity structures. Minimal mass design of tensegrity torus in loading and unloading states is then proposed to minimize the total mass in given configuration subjected to yielding, buckling and global stability constraints. Based on the minimal mass design procedures, the shape optimization of the torus is conducted and the optimal configuration is obtained by doing a constrained nonlinear optimization of the shape parameters. Numerical results show the efficiency of the proposed shape optimization method of tensegrity tori in two states. A physical model is constructed to verify the feasibility of this structural system.