Stress Trajectories Wind on Dome

As discussed in my report on rads, this image shows the schematic stress trajectories of wind in a dome shaped structure:


Source: Structures, D.L. Schodek

To explore the possibilities of adjusting the structure to the specific wind trajectories, i've made some sketches as seen below.

In the first sketch, I took one side of the trajectories (could be tension or compression). I distributed 9 points evenly along each line. I connected the points and created a Delaunay triangulation (red lines upper part). The lowerpart is the Voronoi diagram, based on the Delaunay triangulation. By connecting the points, we see that two additional line-sets are created. They look like the two sides of stress trajectories, but are not the same. This is because I distributed the points evenly and not accourding to the other side of the stress trajectories.



To check how this tesselation would work in 3d, I sketched the same lines onto a plastic dome shape. But distributed the points at the crossings of the two sides of stress trajectories. This causes a symmetrical image again. except that the thicker lines should resist to compression and the other set, to tension. I elongated the lines in order to get an enclosing structure. The way to close the structure can be more dense or adjusted in an other way.



Then I copied this line-set into illustrator, to get it more clear. The green lines, which appear when connecting the points, become clear ellipses.



I'm curious how this set-up would respond to forces at this point. Since I'm doubting if they can transfer the self weight of the building. We probably need to add an other line-set..