Static and dynamic characterization of regular truncated icosahedral and dodecahedral tensegrity modules

Murakami, Hitoshi; Nishimura, Yoshitaka

doi:10.1016/s0020-7683(01)00030-0

Cited by 49 publications

(33 citation statements)

References 10 publications

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“…They considered structure symmetries to simplify the calculations of nodal force equilibrium and expressed their final results in three coupled equations. It can be shown that the solutions of Nishimura (2000) and Murakami & Nishimura (2001, 2003 are fully consistent with those in equations (4.9), (4.15), (4.23) and (4.31).…”

Section: (E) Truncated Regular Icosahedral Tensegritysupporting

confidence: 56%

“…Truncated regular polyhedral tensegrity structures can be constructed from truncated regular polyhedra (Murakami & Nishimura 2001;Li et al 2010b) following a few basic steps discussed below.…”

Section: Truncated Regular Polyhedral Tensegrity Structuresmentioning

confidence: 99%

“…The corresponding coefficients P 1 , P 2 and P 3 are The P 2,20 and P 3,20 are lengthy polynomials that are irrelevant for the present analysis. Substituting equations (4.24)-(4.26) into (3.11) leads to the following five equations: We note that the self-equilibrium conditions of truncated regular cubic, octahedral, dodecahedral and icosahedral tensegrities have been previously analysed by Nishimura (2000) and Murakami & Nishimura (2001, 2003, using icosahedral group graphs and a reduced equilibrium matrix. They considered structure symmetries to simplify the calculations of nodal force equilibrium and expressed their final results in three coupled equations.…”

Section: (E) Truncated Regular Icosahedral Tensegritymentioning

confidence: 99%

“…Based on the nodal force equilibrium conditions and symmetric congruent operations, Murakami & Nishimura (2001) analysed the self-equilibrated states of truncated regular dodecahedral and icosahedral tensegrities. Tibert & Pellegrino (2003) obtained an analytical self-equilibrium solution for truncated tetrahedral tensegrities expressed in terms of force densities.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Cao

et al. 2012

Proc. R. Soc. A.

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In spite of their great importance and numerous applications in many civil, aerospace and biological systems, our understanding of tensegrity structures is still quite preliminary, fragmented and incomplete. Here we establish a unified closed-form analytical solution for the necessary and sufficient condition that ensures the existence of self-equilibrated and super-stable states for truncated regular polyhedral tensegrity structures, including truncated tetrahedral, cubic, octahedral, dodecahedral and icosahedral tensegrities.

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Section: (E) Truncated Regular Icosahedral Tensegritysupporting

confidence: 56%

Section: Truncated Regular Polyhedral Tensegrity Structuresmentioning

confidence: 99%

Section: (E) Truncated Regular Icosahedral Tensegritymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Zhang

Cao

et al. 2012

Proc. R. Soc. A.

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“…An analytical solution for regular (Z-based) truncated tetrahedral tensegrity was proposed by several authors [4,13]. Also, the initial shapes and pre-stress modes for regular icosahedral and dodecahedral tensegrity modules were found analytically by [14]. Many researchers have presented form-finding results for the force density of the tensegrities as compared with the corresponding analytical solutions.…”

Section: Truncated Polyhedral Tensegritymentioning

confidence: 99%

Generalized Multiple Equilibrium Paths for a Truncated Polyhedral Tensegrity

2016

IJRCMCE

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Abstract-Generalized form-finding procedure for a truncated polyhedral tensegrity is presented by using force density method combined with a genetic algorithm. A constrained minimization problem consisting of eigenvalues of the force density matrix and the standard deviation of the force densities of the cables is performed. Multiple force density curves are obtained and compared with those of previous investigations for a truncated icosahedral tensegrity in terms geometry, energy and total length ratio of cableto-strut. Various new shapes of tensegrity are obtained from present analysis by searching feasible self-equilibrium stable configuration of the structure.

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