Octahedron family: The double-expanded octahedron tensegrity

Abstract

The octahedron family of tensegrity structures is presented in this research. The octahedron and the expanded octahedron (well-known tensegrities in the literature) are the first and second components of the family. A new tensegrity is presented: the double-expanded octahedron. This new tensegrity form was obtained following the connectivity pattern of the octahedron family presented in this work. The values of the force densities or force:length ratios that satisfy the minimum required rank deficiency of the force density matrix were computed analytically. Two types of solutions are obtained: full and folded forms. Results show that each lower member of the octahedron family is a folded form of a superior member of this family. Several examples are shown.

Nonlinear Analysis of Cable Net Structures

“…The importance of accurately determining the final deformed shape of cable net structures has to do not only with the structural, aesthetical and economical point of view, but in some cases with the operating requirements. An example is the case of deployable space antennas, where a key aspect for the operating requirements of a reflector in orbit is the finalshape [3,4,5]. Nevertheless, since 1971, the Force Density Method (FDM) provided an analytical way to find the values of deformation and forces in cable structures [6]; later on, the FDM was expanded by Sheck in 1974 [7].…”

The Z-octahedron family: A new tensegrity family

“…The existing form-finding methods can be generally classified into two categories: analytical and numerical. Analytical methods find the equilibrium shape of simple tensegrity forms with a high order of symmetry through a symbolic analysis (see [13,[18][19][20]). Regarding numerical methods, they can be applied to relatively complicated tensegrities with a high number of members or with lack of symmetry; examples of them can be seen in [12,14,[21][22][23].…”

“…A tensegrity family is defined as a group of tensegrity structures that share a common connectivity pattern [20]. The octahedron family is a good example of tensegrity family [20].…”

“…A tensegrity family is defined as a group of tensegrity structures that share a common connectivity pattern [20]. The octahedron family is a good example of tensegrity family [20]. The members of this family are: the octahedron, the expanded octahedron and the double-expanded octahedron.…”

“…In this work a new tensegrity family is defined: the Z-octahedron family. The members of the Z-octahedron family have been obtained replacing the elementary rhombic cells of the members of the octahedron family presented by [20] by elementary Z-shaped cells.…”