The stiffness of prestressed frameworks: A unifying approach

Guest, Simon D.

doi:10.1016/j.ijsolstr.2005.03.008

Cited by 222 publications

(132 citation statements)

References 11 publications

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“…Matrix K s is the tangent stiffness matrix that consists of the stress matrix (or geometric stiffness matrix) Z and the material stiffness matrix AĜA T with Ĝ=diag(g 1 , g 2 , …, g i , …, g b ), where g i is the modified axial stiffness of element i (Guest, 2006;Sultan, 2013;Zhang et al, 2014). As cable slacking is beyond the scope of this study, matrix Z is presumed to be invertible for simplicity.…”

Section: Mathematical Formula For Dkimentioning

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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Section: Mathematical Formula For Dkimentioning

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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show abstract

“…In the literature it is possible to find both, a mathematical definition, [19], or a more intuitive physical derivation [32]. Its non-diagonal elements are the stress, with changed sign, between any two adjacent nodes, and the elements of the main diagonal are the sum of the corresponding row (column) as shown in eq.…”

Section: Definitionsmentioning

confidence: 99%

“…Vassart et al [77] further characterized first and higher order mechanisms, and proposed a method to find out the order of a given mechanism based on geometrical considerations. More recently, Sultan et al [71] has provided analytical solutions for particular structures, and Guest [32] has presented a comparison between different existing formulations for the problem of analyzing prestressed structures.…”

Section: Static Analysismentioning

confidence: 99%

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Tensegrity frameworks: Static analysis review

Juan

Tur

2008

Mechanism and Machine Theory

218

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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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“…Tibert and Pellegrino (2003) reviewed form-finding methods. Several studies have included the derivation of tangent stiffness matrix for a pre-stressed framework (Argyris and Scharpf 1972, Murakami 2001and Guest 2006. Skelton et al (2014) proposed a topology optimization method for minimum mass design of tensegrity bridges and showed that the optimized design has a multi-scale character.…”

Section: Introductionmentioning

confidence: 99%

Deployment of a Tensegrity Footbridge

2015

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Deployable structures are structures that transform their shape from a compact state to an extended in-service position. Structures composed of tension elements that surround compression elements in equilibrium are called tensegrity structures. Tensegrities are good candidates for deployable structures since shape transformations occur by changing lengths of elements at low energy costs. Although the tensegrity concept was first introduced in 1948, few full-scale tensegrity-based structures have been built. Previous work has demonstrated that a tensegrity-ring topology is potentially a viable system for a deployable footbridge. This paper describes a study of a near-full-scale deployable tensegrity footbridge. The study has been carried out both numerically and experimentally. The deployment of two modules (one half of the footbridge) is achieved through changing the length of five active cables. Deployment is aided by energy stored in low stiffness spring elements. Self-weight significantly influences deployment, and deployment is not reproducible using the same sequence of cable-length changes. Active control is thus required for accurate positioning of front nodes in order to complete deployment through joining both sides at center span. Additionally, testing and numerical analyses have revealed that the deployment behavior of the structure is non-linear with respect to cable-length changes. Finally, modelling the behavior of the structure cannot be done accurately using friction-free and dimensionless joints. Similar deployable tensegrity structures of class two and higher are expected to require simulation models that include joint dimensions for accurate prediction of nodal positions.

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The stiffness of prestressed frameworks: A unifying approach

Abstract: A simple derivation of the tangent stiffness matrix for a prestressed pin-jointed structure is given, and is used to compare the diverse formulations that can be found in the literature for finding the structural response of prestressed structures.

Cited by 222 publications

References 11 publications

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

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

Tensegrity frameworks: Static analysis review

Deployment of a Tensegrity Footbridge

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