The set of forces that ideal trusses, or wire webs, under tension can support

Milton, Graeme W.

doi:10.1016/j.ijsolstr.2017.08.035

Cited by 4 publications

(24 citation statements)

References 13 publications

(25 reference statements)

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“…Specifically, we will give a positive answer in the following asymptotic sense: one can find a sequence of finite webs W n such that C Wn X approaches C as n → ∞. For two-dimensional webs where the points X are the vertices of a convex polygon, a similar question was addressed by Theorem 2 in [13], and the proof given here is similar.…”

Section: Channeling the Stresses In A Webmentioning

confidence: 90%

“…. , x N are vertices of a convex polygon, our condition (3) is a generalization of the condition (1) proved in [13].…”

Section: Theorem 11 In Two Dimensionsmentioning

confidence: 91%

“…In two dimensions the procedure for replacing a junction with M > 3 wires by a localized web in which at most three wires meet is straightforward and described in Section 3 of [13]. Briefly, and as illustrated in Figure 5, one finds the associated Airy stress function in the neighborhood of the junction.…”

Section: Reducing the Number Of Wires Meeting At A Pointmentioning

confidence: 99%

“…Here we seek answer to the question: given a convex cone C ⊂ A * X can one find a web W such that C W X = C? To proceed, as sketched in Figure 4 of [13], one approximates the convex cone C by a cone, that we will denote with C Wj X , having a finite number j of extreme rays F (j)m , m = 1, 2, . .…”

Section: Possible Loading Conesmentioning

confidence: 99%

“…The reader is referred to [5] for details. So the question now is: what happens when the points are not the vertices of a convex polygon or what happens in the three-dimensional case?…”

Section: Introductionmentioning

confidence: 99%

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On the forces that cable webs under tension can support and how to design cable webs to channel stresses

et al. 2019

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In many applications of Structural Engineering the following question arises: given a set of forces f1, f2, . . . , fN applied at prescribed points x1, x2, . . . , xN , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x1, x2, . . . , xN in the two-and three-dimensional case. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two-dimensions we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f1, f2, . . . , fN applied at points strictly within the convex hull of x1, x2, . . . , xN . In three-dimensions we show that, by slightly perturbing f1, f2, . . . , fN , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for distributing stress in desired ways.1 By "admissible stress state" we mean an equilibrium state in which all bars are either in tension, or carrying no load. Thus, by "supporting", we mean supporting with all bars either in tension, or carrying no load.2 Notice that we solve this problem within the context of infinitesimal elasticity: examples of applications of the finite deformation theory to describe the geometric nonlinearity are given, for instance, by [6,18,17].

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Section: Channeling the Stresses In A Webmentioning

confidence: 90%

“…. , x N are vertices of a convex polygon, our condition (3) is a generalization of the condition (1) proved in [13].…”

Section: Theorem 11 In Two Dimensionsmentioning

confidence: 91%

Section: Reducing the Number Of Wires Meeting At A Pointmentioning

confidence: 99%

Section: Possible Loading Conesmentioning

confidence: 99%

“…The reader is referred to [5] for details. So the question now is: what happens when the points are not the vertices of a convex polygon or what happens in the three-dimensional case?…”

Section: Introductionmentioning

confidence: 99%

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On the forces that cable webs under tension can support and how to design cable webs to channel stresses

et al. 2019

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The obstacle problem in no-tension structures and cable nets

et al. 2023

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We consider the problem of finding a net that supports prescribed point forces, yet avoids certain obstacles, with all the elements of the net being under compression (or all being under tension), and being confined within a suitable bounding box. In the case of masonry structures, when described through the simple, no-tension constitutive model, this consists, for instance, in finding a strut net that supports the forces, is contained within the physical structure, and avoids regions that may be not accessible. We solve such a problem in the two-dimensional case, where the prescribed forces are applied at the vertices of a convex polygon, and we treat the cases of both single and multiple obstacles. By approximating the obstacles by polygonal regions, the task reduces to identifying the feasible domain in a linear programming problem. For a single obstacle we show how the region Γ available to the obstacle can be enlarged as much as possible in the sense that there is no other strut net, having a region Γ ′ available to the obstacle with Γ ⊂ Γ ′ . The case where some of the forces are reactive is also treated.

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Limit analysis of strut nets

Amendola

Fortunato

Mattei

et al. 2022

Mathematics and Mechanics of Solids

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Truss structures composed of members that work exclusively in tension or in compression appear in several problems of science and engineering, e.g., in the study of the resisting mechanisms of masonry structures, as well as in the design of spider web-inspired web structures. This work generalizes previous results on the existence of cable webs that are able to support assigned sets of nodal forces under tension. We extend such a problem to the limit analysis of compression-only “strut nets” subjected to fixed and variable nodal loads. These systems provide discrete element models of masonry bodies, which lie inside the polygon/polyhedron with vertices at the points of application of the given forces (“underlying masonry structures”). It is assumed that fixed nodal forces are combined with variable forces growing proportionally to a scalar multiplier (load multiplier), and that the supporting strut net is subjected to kinematic constraints at given nodal positions.

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The set of forces that ideal trusses, or wire webs, under tension can support

Cited by 4 publications

References 13 publications

On the forces that cable webs under tension can support and how to design cable webs to channel stresses

On the forces that cable webs under tension can support and how to design cable webs to channel stresses

The obstacle problem in no-tension structures and cable nets

Limit analysis of strut nets

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