Mechanical response of three-dimensional tensegrity lattices

GT-MAP Seminars
Friday, October 21, 2016 - 15:00
2 hours
Skiles 006
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 three-dimensional  tensegrity lattices has remained an elusive goal. In this work, we first  develop a method to construct three-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 wave propagation on a finite tensegrity lattice impacting a rigid wall.