A systematic procedure for constructing connectivity matrices for 3D lattices comprising truncated regular octahedral tensegrity structures and its application to optimization

Abstract

This study concerns establishing a mathematical model to analyze and design tensegrity structures built from repetitions of elementary structures, called the truncated regular octahedral tensegrity (TROT). The TROT has three pairs of parallel square faces, each perpendicular to the others, and is preferable to build three-dimensional (3D) tensegrity lattices. The squares of each the pair are twisted for the structural stability purpose, and one simple way to form a lattice is to use the mirror image as its neighbor. Another connection type is also possible by employing the quadruplex prismatic tensegrity (QPT) as a bridge between the TROT. The connectivity matrix plays a central role in the analysis and design of tensegrity structures. This paper provides a systematic way to construct the connectivity matrices for these TROT tensegrity lattices. For a given space to fulfill and a force to bear, the number of the TROT, node locations (shape), length of the QPT bridge, etc. can be chosen arbitrarily. The provided connectivity matrix formulae allow us to automatically change these parameters during the evaluation process in the structural design. To show the effectiveness of the proposed formulae, for identical compressive forces from all sides, a minimal-mass design subjected to the force equilibrium (force balance) and yielding/buckling stress constraints is shown. A dynamical simulation of a TROT lattice under a uniaxial compressive force is also shown to evaluate the equilibrium state of the system.

Keywords

• truncated regular octahedral tensegrity
• tensegrity lattice
• connectivity matrix
• optimal design
• mechanical metamaterial