Mechanical response of 3-dimensional tensegrity lattices

Most available techniques for the design of tensegrity structures Can be grouped in two categories. On the one hand, methods that rely on the systematic application of topological and geometric rules to regular polyhedrons have been applied to the generation of tensegrity elementary cells. On the other hand, efforts have been made to either combine elementary cells or apply rules of self-similarity in order to generate complex structures of engineering interest, for example, columns, beams, and plates. However, perhaps due to the lack of adequate symmetries on traditional tensegrity elementary cells, the design of 3-dimensional tensegrity lattices has remained an elusive goal. In this work, we first develop a method to construct 3-dimensional tensegrity lattices from truncated octahedron elementary cells. The required space-tiling translational symmetry is achieved by performing recursive reflection operations on the elementary cells. We then analyze the mechanical response of the resulting lattices in the fully nonlinear regime via two distinctive approaches: we first adopt a discrete reduced-order model that explicitly accounts for the deformation of individual tensegrity members, and we then utilize this model as the basis for the development of a continuum approximation for the tensegrity lattices. Using this homogenization method, we study tensegrity lattices under a wide range of loading conditions and prestressed configurations. We present Ashby charts for yield strength to density ratio to illustrate how our tensegrity lattices can potentially achieve superior performance when compared to other lattices available in the literature. Finally, using the discrete model, we analyze the dynamic response of a finite tensegrity lattice impacting an elastic wall, where a strong asymmetry in the dispersion of tensile and compressive stress-waves propagating through the medium is observed. (C) 2016 Elsevier Ltd. All rights reserved.