The set of forces that ideal trusses, or wire webs, under tension can support
The set of forces that ideal trusses, or wire webs, under tension can support
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理想的桁架或钢丝网在张力下可以承受的一组力
DOI：
10.1016/j.ijsolstr.2017.08.035
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
G. Milton
中科院分区：
文献类型：
--
作者：
G. Milton
确定这些多重的力，或组的力多重，作用在一组点的问题，这样就存在一个桁架结构，或线网，可以支持这些力多重与桁架或线网的所有元素下的张力，被认为是。基本上解决了点位于凸多边形顶点的二维问题：每个力的多重态必须使得围绕任意顶点顺时针方向任意多个连续点的力的和的净抗扭力矩必须非负;人们可以找到一个桁架结构，它在张力下支撑，并且只支撑，力多重峰的凸多面体中的那些力多重峰，所述力多重峰由有限数量的力多重峰产生，每个力多重峰满足转矩条件。对于凸多边形中只有一部分点在顶点上，其余点在内部的问题也取得了进展。特别是，在只有一个点的情况下，内，一个明确的程序描述了一个合适的桁架，如果存在。Guevara Vasquez等人提供的替代配方。（2011），基于Camar-Eddine和Seppecher（2003）的早期工作，给出了构造桁架结构的方法，该桁架结构具有受压或受拉元件，支持凸多边形顶点处的任意平衡力集合。最后给出了三维桁架或钢丝网在张力作用下必须满足的力的一些约束条件。
The problem of determining those multiplets of forces, or sets of force multiplets, acting at a set of points, such that there exists a truss structure, or wire web, that can support these force multiplets with all the elements of the truss or wire web being under tension, is considered. The two-dimensional problem where the points are at the vertices of a convex polygon is essentially solved: each multiplet of forces must be such that the net anticlockwise torque around any vertex of the forces summed over any number of consecutive points clockwise past the vertex must be non-negative; and one can find a truss structure that supports under tension, and only supports, those force multiplets in a convex polyhedron of force multiplets that is generated by a finite number of force multiplets each satisfying the torque condition. Progress is also made on the problem where only a subset of the points are at the vertices of a convex polygon, and the other points are inside. In particular, in the case where only one point is inside, an explicit procedure is described for constructing a suitable truss, if one exists. An alternative recipe to that provided by Guevara Vasquez et al. (2011), based on earlier work of Camar-Eddine and Seppecher (2003), is given for constructing a truss structure, with elements under either compression or tension, that supports an arbitrary collection of balanced forces at the vertices of a convex polygon. Finally some constraints are given on the forces that a three-dimension truss, or wire web, under tension must satisfy.