论文标题
砌体结构和电缆网中的障碍问题
The obstacle problem in masonry structures and cable nets
论文作者
论文摘要
我们考虑找到一个网络的问题，该网络支持在规定点上应用的规定力量，但避免了某些障碍，并且净压缩的所有元素（Strut Net）或张力下（有线网）。例如，在砌体结构的情况下，这包括找到支持力的支撑网，其中包含在物理结构中，并避免了可能无法到达的区域，例如，由于存在孔的存在。我们在二维情况下解决了这样一个问题，在二维情况下，规定的力是在凸多边形的顶点上应用的，并且我们处理了单个障碍和多个障碍的情况。通过通过多边形区域近似障碍物，该任务减少了在线性编程问题中识别可行域。对于一个单一的障碍，我们显示了如何将可用于障碍物的区域$γ$放大，从某种意义上说，如果没有其他支撑网，并且具有$γ_1\subsetγ$的区域$γ_1$。某些力是反应性，未经规定但对其他规定力的反应的情况，也得到了处理。它再次减少了在线性编程问题中识别可行的域。最后，一个人可能允许一个不在规定的点，而是在规定的线段上的任何点上允许一个反应力的子集。然后，任务减少了在二次编程问题中识别可行域。
We consider the problem of finding a net that supports prescribed forces applied at prescribed points, yet avoids certain obstacles, with all the elements of the net under compression (strut net) or under tension (cable web). In the case of masonry structures, for instance, this consists in finding a strut net that supports the forces, is contained within the physical structure, and avoids regions that may be not accessible due, for instance, to the presence of holes. 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 $Γ_1$ available to the obstacle with $Γ_1 \subsetΓ$. The case where some of the forces are reactive, unprescribed but reacting to the other prescribed forces, is also treated. It again reduces to identifying the feasible domain in a linear programming problem. Finally, one may allow a subset of the reactive forces to each act not at a prescribed point, but rather at any point on a prescribed line segment. Then the task reduces to identifying the feasible domain in a quadratic programming problem.
