Initial prestress design and optimization of tensegrity systems based on symmetry and stiffness

Abstract

This study mainly focuses on initial prestress design of tensegrity structures with given shapes. For symmetric structures with multiple self-stress modes, two efficient methods, respectively applying singular value decomposition on the constrained equilibrium matrix and performing eigenvalue analysis without manual classifications of member types, are proposed to compute the independent states of self-stress retaining full symmetry. For structures with multiple symmetric states of self-stress, a novel optimization model for the purpose of maximizing the global rigidity of the structure is presented to determine the combination coefficients of the independent symmetric self-stress states. A penalty function is employed to consider both hard and soft constraints including stability conditions, unilateral property of members and prestress distribution evenness. The fitness-ranking-based genetic algorithms with and without incorporating isolation niche technique are developed to solve such optimization problem. Several numerical examples are tested to demonstrate the efficiency of the proposed methods.