The obstacle problem in no-tension structures and cable nets

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 gamma available to the obstacle can be enlarged as much as possible in the sense that there is no other strut net, having a region gamma ' available to the obstacle with gamma subset of gamma '. The case where some of the forces are reactive is also treated.

Automated summary

This paper discusses how to design suitable support structures in masonry structures to support specified point forces and avoid certain obstacles. By approximating the obstacles, the problem can be reduced to a linear programming problem. The paper focuses on the two-dimensional case, studying the forces at the vertices of convex polygons and considering both single and multiple obstacles, as well as the case of reactive forces.