Numerical form-finding of tensegrity structures

Estrada, Giovani; Bungartz, Hans‐Joachim; Mohrdieck, Camilla

doi:10.1016/j.ijsolstr.2006.02.012

Cited by 157 publications

(89 citation statements)

References 20 publications

(32 reference statements)

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“…Finally, Estrada et al [25] presented an algorithm which only needs information about the type of each edge and about the topology, but does not account for external forces. Then, the equilibrium geometry and force densities for each edge are iteratively calculated using rank constraints on both the stress matrix (Ω) and the rigidity matrix (R(p)).…”

Section: Formfinding Methodsmentioning

confidence: 99%

Tensegrity frameworks: Static analysis review

Juan

Tur

2008

Mechanism and Machine Theory

216

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This paper hands in a review of the basic issues about the statics of tensegrity structures. Definitions and notation for the most important concepts, borrowed from the vast existing literature, are summarized. All of these concepts and definitions provide a complete mathematical framework to analyze the rigidity and stability properties of tensegrity structures from three different, but related, points of view: motions, forces and energy approaches. Several rigidity and stability definitions are presented in this paper and hierarchically ordered, from the strongest condition of infinitesimal rigidity to the more wide concept of simple rigidity, so extending some previous classifications already available.Important theorems regarding the relationship between these definitions are also put together to complete the static overview of tensegrity structures. Examples of different tensegrity structures belonging to each of the rigidity and stability categories presented are described and analyzed. Concluding the static analysis of tensegrity structures, a review of existing form-finding methods is presented.

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Section: Formfinding Methodsmentioning

confidence: 99%

Tensegrity frameworks: Static analysis review

Juan

Tur

2008

Mechanism and Machine Theory

216

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“…Moreover, due to the principle that the struts withstand pressure and cables bear tension, if v b does not satisfy tension-compression symbols, it is necessary to add orthogonal vectors to reconstruct the force density ζ [7].…”

Section: Solution Of Elemental Self-stressmentioning

confidence: 99%

“…However, the procedure needs so many search steps that it requires much more computation time. It should be noted that Estrada et al [7], Tran and Lee [8] introduced a form-finding algorithm based on the iterative computation of force density and coordinate. The algorithm merely needs to provide the connections of cables and struts, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Accordingly, the form-finding results were mainly regular tensegrity structures, attaching little emphasis upon geometrical configuration. In recent decades, with the increasingly deeper researches, relevant scholars have made some improvements based on the classic algorithms and created several novel form-finding algorithms [5][6][7][8][9]. The irregular tensegrity and its geometrical configuration have achieved attention gradually.…”

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confidence: 99%

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Form-Finding Analysis of Irregular Tensegrity Structures by Matrix Iteration

Lu¹,

Li²,

Shu³

2015

Volume 11 Number 4

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This paper proposed a novel form-finding method for irregular tensegrity structures base on matrix iteration. On the basis of two different forms of structural equilibrium equations, the estimated elemental self-stresses and nodal coordinates were constructed via the singular value decomposition of equilibrium matrix and eigenvalue decomposition of force density matrix, respectively. The configuration of tensegrity that satisfies the specified coordinates was determined through the iterative computation of self-stresses and nodal coordinates, and the constraint condition was introduced in the construction of the estimated nodal coordinates simultaneously. The detailed algorithm procedure was listed and the convergent criterion was also defined. In the end, several illustrated examples were given to prove the validity of the algorithm. Numerical examples and physical models showed that the proposed form-finding method was correct and efficient. The form-finding algorithm could be applied to find tensegrity structures that satisfied the given geometrical forms, and the creation of novel irregular tensegrity, as long as the topological relation and several known coordinate of nodes were given． Keywords: Irregular tensegrity, Form-finding, Equilibrium matrix, Force density matrix, Numerical method DOI: 10.18057/IJASC.2015.11.4.7 INTRODUCTIONTensegrity, a kind of self-balancing system where the cables are in continuous tensional status and a few of struts are located among the cables, is light-weight but efficient, in that they could be stiffened by specified inner prestressing. Tensegrity structures have been already applied to several research fields [1,2], such as mechanical control, aerospace, biology, etc.. In addition, an alternative form of tensegrity, i.e. cable dome, has been widely used in the large span structures in contemporary architecture.As a sort of form-sensitive structure, the superior mechanical property of tensegrity comes from its reasonable geometrical configuration. The topology, geometry and the prestressing both affect its stability and stiffness. Hence, form finding is the core of tensegrity researches [3]. The form-finding algorithms were divided into two categories by Tibert and Pellegrino [4], respectively static method and dynamic method, ranging from analytic method to force density method proposed by Schek and Linkwitz, and to dynamic relaxation method introduced earlier by Motro and Belkacem. These early form-finding algorithm gave more prominence to the research of reasonable topological relations. Accordingly, the form-finding results were mainly regular tensegrity structures, attaching little emphasis upon geometrical configuration. In recent decades, with the increasingly deeper researches, relevant scholars have made some improvements based on the classic algorithms and created several novel form-finding algorithms [5][6][7][8][9]. The irregular tensegrity and its geometrical configuration have achieved attention gradually. Meanwhile, the evolution theory began to be i...

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“…Tensegrities have applications in a range of fields such as sculpture, architecture, aerospace engineering, civil engineering, marine engineering and biology [7]. Most studies found in the literature investigated form-finding [8][9][10][11][12] and design characteristics of tensegrity structures [13][14][15][16]. Statics and dynamics of simple tensegrity modules have also been investigated [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Determining control strategies for damage tolerance of an active tensegrity structure

Korkmaz

Ali

Smith

2011

Engineering Structures

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Tensegrity structures are spatial, reticulate and lightweight systems composed of struts and cables. Stability is provided by a self-stress state between tensioned and compressed elements. Tensegrities have received interest among scientists and engineers in fields such as architecture, civil and aerospace engineering. Flexibility and ease of tuning make these systems attractive for controllable and adaptive structures. However, tensegrities are often prone to difficulties associated with meeting serviceability criteria and with providing adequate damage tolerance when used as civil engineering structures. This paper extends research on active control of tensegrity structures to study self-repair of a tensegrity pedestrian bridge that is damaged. Selfrepair is intended to meet safety and serviceability requirements in case of cable damage in the pedestrian bridge. Intelligent control methodologies that implement stochastic search with active member grouping are proposed. Case studies for several damage scenarios are presented to show the effectiveness of the methodology. Results from simulated damage scenarios show that self-repair can be successfully performed with a minimum number of active members leading to reductions in control complexity.

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Numerical form-finding of tensegrity structures

Cited by 157 publications

References 20 publications

Tensegrity frameworks: Static analysis review

Tensegrity frameworks: Static analysis review

Form-Finding Analysis of Irregular Tensegrity Structures by Matrix Iteration

Determining control strategies for damage tolerance of an active tensegrity structure

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