Underconstrained structural systems

Kuznetsov, E. N.

doi:10.1016/0020-7683(88)90026-1

Cited by 52 publications

(30 citation statements)

References 8 publications

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“…It is interesting that in the paper [28], most examples have a one-dimensional space of equilibrium flexes. See [5] for corrections, as well as [22][23][24][25][26] for a discussion of the problem of how to do the second-order analysis.…”

mentioning

confidence: 99%

Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks

Connelly¹,

Whiteley²

1996

SIAM J. Discrete Math.

248

280

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Abstract. This paper defines two concepts of rigidity for tensegrity frameworks (frameworks with cables, bars, and struts): prestress stability and second-order rigidity. We demonstrate a hierarchy of rigidity--first-order rigidity implies prestress stability implies second-order rigidity implies rigiditymfor any framework. Examples show that none of these implications are reversible, even for bar frameworks. Other examples illustrate how these results can be used to create rigid tensegrity frameworks.This paper also develops a duality for second-order rigidity, leading to a test which combines information on the self stresses and the first-order flexes of a framework to detect second-order rigidity.Using this test, the following conjecture of Roth is proven: a plane tensegrity framework, in which the vertices and bars form a strictly convex polygon with additional cables across the interior, is rigid if and only if it is first-order rigid.

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mentioning

confidence: 99%

Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks

Connelly¹,

Whiteley²

1996

SIAM J. Discrete Math.

248

280

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“…It is shown here that, besides geometry and topology, prestressing greatly influences on optimal design of the system. As noted in [1], "singular" (instantly-movable or instantly-rigid) constructions [18], whose prestressing state is stable, are always relative to geometrically hardening systems, regardless of the direction of loads acting on them. The similar conclusion would hold true both for "tensegrity systems" [19][20] and for their combination with geometrically "neutral" or all the more strengthening elements.…”

Section: Problems Of Finding Optimum Limits Of Repeatedly Variable Lomentioning

confidence: 99%

“…In any case, it is recommended to take such constant load with preloading, which is the "equilibrium" for the basic mechanism of the failure of the system. The term "equilibrium" load is known in the theory of geometrically changed suspension and cable-stayed structures [18]; it's a load that does not cause the kinematic displacements of such systems. For arbitrary constructions the "equilibrium" load does not cause the system's kinematic displacements in the state of limit equilibrium.…”

Section: Problems Of Finding Minimal Cost And/or Optimum Limits Of Prmentioning

confidence: 99%

Limit Analysis of Geometrically Hardening Composite Steel-Concrete Systems / Stany Graniczne Geometrycznie Wzmacniających Się Konstrukcji Zespolonych

Alawdin¹,

Urbańska²

2023

Civil and Environmental Engineering Reports

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The paper considers some results of creating load-carrying composite systems that have uprated strength, rigidity and safety, and therefore are called geometrically (self-) hardening systems. The optimization mathematic models of structures as discrete mechanical systems withstanding dead load, monotonic or low cyclic static and kinematic actions are proposed. To find limit parameters of these actions the extreme energetic principle is suggested what result in the bilevel mathematic programming problem statement. The limit parameters of load actions are found on the first level of optimization. On the second level the power of the constant load with equilibrium preloading is maximized and/or system cost is minimized. The examples of using the proposed methods are presented and geometrically hardening composite steel-concrete system are taken into account.

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“…Similar work was parallely developed by Kuznetsov [40,42,41]. His methods are based on the decomposition of the system in several subsystems and it also make extensive use of linear algebra techniques.…”

Section: Static Analysismentioning

confidence: 99%

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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Underconstrained structural systems

Cited by 52 publications

References 8 publications

Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks

Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks

Limit Analysis of Geometrically Hardening Composite Steel-Concrete Systems / Stany Graniczne Geometrycznie Wzmacniających Się Konstrukcji Zespolonych

Tensegrity frameworks: Static analysis review

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