By Jing Yao Zhang, Makoto Ohsaki
To facilitate a deeper figuring out of tensegrity buildings, this booklet specializes in their key layout difficulties: self-equilibrium research and balance research. specifically, excessive symmetry houses of the buildings are also used. stipulations for self-equilibrium in addition to super-stability of tensegrity buildings are provided intimately. An analytical approach and an effective numerical technique are given for self-equilibrium research of tensegrity buildings: the analytical process offers with symmetric constructions and the numerical process promises super-stability. using crew illustration concept, the textual content extra presents analytical super-stability stipulations for the constructions which are of dihedral in addition to tetrahedral symmetry. This e-book not just serves as a reference for engineers and scientists yet is usually an invaluable resource for upper-level undergraduate and graduate scholars. conserving this target in brain, the presentation of the publication is self-contained and unique, with an abundance of figures and examples.
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Additional info for Tensegrity Structures: Form, Stability, and Symmetry
110) always have unique solutions as given in Eq. 111) . This idea of force density method for cable-nets has been successfully extended to the form-finding problems of tensile membrane structures , by modelling them as cable-nets. This can be done because these two types of (tensile) structures share the following two common mechanical properties: 1. Both of cable-nets and membrane structures are attached to fixed nodes; 2. There exist only (positive) tensile forces in cable-nets or tensile stresses in membranes.
53) have been used. The force density matrix E ∈ R5×5 is calculated as follows, by substituting the force densities in Eq. 114) into Eq. 109): ⎛ 8 ⎜ −2 t ⎜ −2 E= √ ⎜ 24 ⎜ ⎝ −2 −2 −2 0 0 1 1 −2 0 0 1 1 −2 1 1 0 0 ⎞ −2 1⎟ ⎟ 1⎟ ⎟. 116) −2 1 1 0 0 which show that the self-equilibrium equations are satisfied with the given geometry realization (nodal coordinates) as well as prestresses. , there are in total r¯ E zero eigenvalues in E. The eigenvectors corresponding to these zero eigenvalues are denoted by φ i (i = 1, 2, .
The two-dimensional structure in Fig. , m = 2, n = 1, and nf = 2. The connectivity matrices Cs ∈ R2×3 , C ∈ R2×1 , and Cf ∈ R2×2 of the structure respectively are 1 2 3 −1 0  , C = 1 C = 1 0 −1  s 1 , Cf = 1 −1 0 . 89) Geometry realization of the structure is adopted as follows: x = (0) , xf = −1 , y = (0) , yf = 1 0 . 91) and the member length vector l ∈ R2 is l= 1 . 92) 42 2 Equilibrium From Eq. 34), the equilibrium matrix D ∈ R2×2 corresponding to the only one free node is D= = Dx Dy = C UL−1 C VL−1 1 −1 .
Tensegrity Structures: Form, Stability, and Symmetry by Jing Yao Zhang, Makoto Ohsaki