Minimal mass design of clustered tensegrity structures

Abstract

This paper presents a minimal mass design approach to the clustered tensegrity structures (CTS). By minimal mass, we mean, for a given clustered tensegrity structure subject to prescribed external loads, the minimal mass is achieved when all the structure members simultaneously fail (buckle or yield). This paper helps to find the lower bound of the required mass of the CTS. Firstly, we introduce the connectivity and clustering definitions through respective matrices and derive the nonlinear clustered tensegrity statics equation in terms of the nodal vector of the structure. Since the mass of each member is in a one-to-one correspondence to its force density (force by unit length), the static equilibrium equations of the CTS with respect to the force density and force vectors are also given. Then, we formulated the mass and gravity of hollow bars and strings subject to buckling and yielding conditions. Finally, a nonlinear optimization algorithm is presented to compute the minimal mass of any CTS with any given external force and topology. We also demonstrate that the traditional tensegrity structure (TTS) is a particular case of the CTS by defining the cluster matrix as an identity matrix. At last, numerical examples are given to validate the CTS minimal mass design approach. The method proposed by this research can be used for the lightweight design of tensegrity, truss, cable nets, membrane structures, etc.