A Genetic Algorithm Based Form-finding of Tensegrity Structures with Multiple Self-stress States

Abstract

A form-finding method of tensegrity systems is a process of finding an equilibrium configuration and a key step in the design of tensegrity. Over the past few years, several studies have been made on the form-finding methods of tensegrity systems, however, these methods are limited in the tensegrity systems with multiple self-stress states. In this study, a numerical method is presented for form-finding of tensegrity structures with multiple states of self-stress by using a force density method combined with a genetic algorithm. The proposed method can design the desired tensegrity shape through a genetic algorithm with appropriate constraints. The design variable can be uniquely defined in the case of multiple states of self-stress using only the constraint of the member types. An eigenvalue decomposition of the force density matrix and a singular value decomposition of the equilibrium matrix are performed repeatedly in order to determine a feasible solution for nodal coordinates and force densities. A genetic algorithm is then adopted to uniquely define a single integral feasible set of force densities. Several numerical examples are presented to prove efficiency in searching for self-equilibrium configurations of tensegrity structures. In all cases, the single integral feasible self-stress states can be obtained.