Self-equilibrium and super-stability of truncated regular polyhedral tensegrity structures: a unified analytical

solution

by Li-Yuan Zhang, Yue Li, Yan-Ping Cao, Xi-Qiao Feng, and Huajian Gao

Proceedings AVolume 468(2147):3323-3347

November 8, 2012

©2012 by The Royal Society

Relationships of different states of tensegrity structures.

Li-Yuan Zhang et al. Proc. R. Soc. A 2012;468:3323-3347

©2012 by The Royal Society

Regular and truncated platonic solids: (a) regular polyhedra, (b) truncated regular polyhedra, (c) critical truncated polyhedra and (d) hyper-truncated polyhedra.

Li-Yuan Zhang et al. Proc. R. Soc. A 2012;468:3323-3347

©2012 by The Royal Society

Truncated regular tetrahedral tensegrity: (a) the edges and vertices of a truncated regular tetrahedron, and (b) the strings, bars and nodes of the corresponding truncated regular

tetrahedral tensegrity.

Li-Yuan Zhang et al. Proc. R. Soc. A 2012;468:3323-3347

©2012 by The Royal Society

Self-equilibrium solutions with the minimum eigenvalue of force density matrix being negative, hence violating the positive semi-definite condition of super-stability for truncated regular (a)

cubic, (b) octahedral, (c) dodecahedral and (d) icosahedral tens...

Li-Yuan Zhang et al. Proc. R. Soc. A 2012;468:3323-3347

©2012 by The Royal Society

Un-truncated tetrahedron: (a) its geometry and (b) the corresponding tensegrity.

Li-Yuan Zhang et al. Proc. R. Soc. A 2012;468:3323-3347

©2012 by The Royal Society

Self-equilibrium and possibly super-stable solutions for truncated regular (a) tetrahedral, (b) cubic, (c) octahedral, (d) dodecahedral and (e) icosahedral tensegrities.

Li-Yuan Zhang et al. Proc. R. Soc. A 2012;468:3323-3347

©2012 by The Royal Society

Critical truncated tensegrity structures associated with (a) tetrahedron, (b) cube and octahedron, and (c) dodecahedron and icosahedron.

Li-Yuan Zhang et al. Proc. R. Soc. A 2012;468:3323-3347

©2012 by The Royal Society

A special self-equilibrated state of truncated tetrahedral tensegrity with zero force densities in the remaining-strings.

Li-Yuan Zhang et al. Proc. R. Soc. A 2012;468:3323-3347

©2012 by The Royal Society

Hyper-truncated tetrahedron: (a) its geometry and (b) the corresponding tensegrity.

Li-Yuan Zhang et al. Proc. R. Soc. A 2012;468:3323-3347

©2012 by The Royal Society

Example self-equilibrated configurations of truncated regular polyhedral tensegrities which are (a) super-stable and (b) not super-stable.

Li-Yuan Zhang et al. Proc. R. Soc. A 2012;468:3323-3347

©2012 by The Royal Society