By Jing Yao Zhang, Makoto Ohsaki
To facilitate a deeper knowing of tensegrity constructions, this publication 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 constructions are offered intimately. An analytical procedure and an effective numerical process are given for self-equilibrium research of tensegrity constructions: the analytical technique offers with symmetric buildings and the numerical approach promises super-stability. using crew illustration conception, the textual content extra offers analytical super-stability stipulations for the constructions which are of dihedral in addition to tetrahedral symmetry. This booklet not just serves as a reference for engineers and scientists yet can be an invaluable resource for upper-level undergraduate and graduate scholars. protecting this goal in brain, the presentation of the booklet is self-contained and specific, with an abundance of figures and examples.
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Additional resources for Tensegrity Structures: Form, Stability, and Symmetry
3 Static and Kinematic Determinacy 33 (a) (b) H1 H1 V1 V2 V1 (c) (d) H1 H1 V1 V2 H2 V2 H2 V1 V2 Fig. 8. H1 , H2 and V1 , V2 are the reaction forces in horizontal and vertical directions, respectively. , ns = 2. , nr = 0, rigid-body motions should be considered in the Maxwell’s rule to verify internal static indeterminacy. 57) nb = 2 from which nb is equal to 3 for a two-dimensional case, and it is equal to 6 for a three-dimensional case. 58) statically indeterminate. 9 Maxwell’s rule for the two-dimensional free-standing structure as shown in Fig.
Static indeterminacy of a structure enables it possess member forces (prestresses) in the members, even though no external load is involved. A structures is said to be kinematically indeterminate, if there exists a nodal motion, except for the rigid-body motions, keeping all member lengths unchanged. Such motion is called mechanism, including infinitesimal mechanism and finite mechanism. Infinitesimal mechanism implies that the motion (nodal displacement) is sufficiently small, while finite mechanism can have large displacements.
13) v = Cy + Cf yf = ⎜ ⎜ y2 − y5 ⎟ . ⎜ y2 − y6 ⎟ ⎜ ⎟ ⎝ y2 − y7 ⎠ y1 − y8 For free-standing structures, the terms Cf xf and Cf yf corresponding to fixed nodes in Eq. 11) vanish. Therefore, the coordinate difference vectors are u = Cx, v = Cy, w = Cz. 4 Coordinate difference vectors of the two-dimensional freestanding structure as shown in Fig. 2. The two-dimensional free-standing structure as shown in Fig. 2. All of its five nodes are free nodes. 22 2 Equilibrium The coordinate difference vector u ∈ R8 in x-direction of the twodimensional free-standing structure as shown in Fig.