A unified solution for self-equilibrium and super-stability of rhombic truncated regular polyhedral tensegrities

Zhang, Li-Yuan; Li, Yue; Cao, Yanping; Feng, Xi‐Qiao

doi:10.1016/j.ijsolstr.2012.09.024

Cited by 29 publications

(14 citation statements)

References 35 publications

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“…By truncating uniformly each vertex of these regular polyhedra, the truncated regular polyhedra can be obtained [10]. Truncated forms of tetrahedron, dodecahedron and icosahedron are illustrated in Fig.…”

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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Section: Truncated Polyhedral Tensegritymentioning

confidence: 99%

Generalized Multiple Equilibrium Paths for a Truncated Polyhedral Tensegrity

2016

IJRCMCE

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“…where I e R^"^ denotes the three-dimensional identity matrix, and ® the Kronecker product symbol [30]; D is the reduced stress matrix [12], also referred to as the force density matrix [31,32], which can be obtained as [14] -qe(ij) if i 7^ j and / is connected with j by element e 0 if / 7^ j and i does not connect with j (8)…”

Section: Basic Equationsmentioning

confidence: 99%

“…The initial self-equilibrated configuration of the considered tensegrity before actuation is obtained via an analytical or a numerical form-finding method [7,32]. In each increment step, the Newton-Raphson iteration scheme is utilized to eliminate the outof-balance forces.…”

Section: Incremental Eq (19)ismentioning

confidence: 99%

“…At the initial self-equilibrated state of the expandable octahedron tensegrity, each string has the initial length of Ig = ^3/8, each pair of parallel bars (e.g., (5,6). and (7,8)) has the initial distance of i^fl = Syo = s-o = I /2, and the ratio of the prestress of the strings to the prestress of the bars is qso/qw = -2/3 [8,32].…”

Section: Expandable Octahedron Tensegrity Under Externalmentioning

confidence: 99%

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A Numerical Method for Simulating Nonlinear Mechanical Responses of Tensegrity Structures Under Large Deformations

Zhang

Cao³

et al. 2013

Journal of Applied Mechanics

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An efficient numerical method is developed to analyze the mechanical responses of tensegrity structures subjected to various actuations that lead to large and highly nonlinear (e.g., hardening or softening) deformations. The proposed method, whose accuracy and efficacy are demonstrated through a number of representative examples, holds promise for applications in design, analysis, and safety evaluations of large-scale tensegrity structures.

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“…Flexible structures with a diversity of structural forms, such as Geiger domes, Levy domes, Panta domes, and tensegrities, attract great attention from civil engineers to meet the design requirements of large-space, light-weight, and novel architectures (Eriksson and Tibert, 2006;Pai, 2011;Zhang et al, 2013). A crucial step of the structural design is the system identification, targeting a preliminary prediction for the mechanical performance.…”

Section: Introductionmentioning

confidence: 99%

Distributed indeterminacy evaluation of cable-strut structures: formulations and applications

Zhou

Chen

Zhao

et al. 2015

J. Zhejiang Univ. Sci. A

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Abstract:The indeterminacy evaluation is an effective method for system identification; it can predict the mechanical behaviors of flexible structures in the primary design. However, the conventional indeterminacy evaluation based solely on geometry and topology has neglected the influence of material properties on mechanical behavior and the contribution of each component to the total indeterminacy. To address these issues, a distributed indeterminacy evaluation taking account of the effect of component stiffness was carried out with a view to providing reasonable interpretations and feasible applications for two concepts, i.e., the distributed static indeterminacy (DSI) and the distributed kinematic indeterminacy (DKI). A unified method for the DSI is proposed, and a comparative analysis between this and an existing method revealed that the proposed method has a wider range of applicability and is essentially identical in the kinematically determinate case. It can be concluded that since the DSI is representative of symmetric properties, a simple but efficient grouping criterion can be established which can improve the efficiency of the specific force finding method entitled double singular value decomposition (DSVD). On the other side, an evaluable method for the DKI is proposed suggesting that DKI is a useful indicator for the assessment of nodal mobility and can provide a feasible solution to the form transforming study.

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A unified solution for self-equilibrium and super-stability of rhombic truncated regular polyhedral tensegrities

Cited by 29 publications

References 35 publications

Generalized Multiple Equilibrium Paths for a Truncated Polyhedral Tensegrity

Generalized Multiple Equilibrium Paths for a Truncated Polyhedral Tensegrity

A Numerical Method for Simulating Nonlinear Mechanical Responses of Tensegrity Structures Under Large Deformations

Distributed indeterminacy evaluation of cable-strut structures: formulations and applications

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