Tuesday, July 14, 2009

more tessellations

I tried to combine some different types of tessellations for the dome, in order to respond to the wind forces and gravity acting on the structure.

The first three images are the combination of the wind trajectories, as discussed before, and "vertical" ribs to lead the self weight to the ground.

Vertical ribs

Compression ribs following trajectories and connected to get a Delaunay triangulation

Tension side added.

If we want to split the domes into a double layered dome, only vertical ribs won't be sufficient for the part of the dome that supports the weight of the structure, therefore I added rings. The rings are following the cross sections of the stress trajectories of the other dome. I also added a quick sketch of how a cross section could look like.
I want to note here, that I'm not sure if this option is do-able within the time span we have for this research. I expect that the connection of two domes, is quite complex. The connection part it selves probably needs a lot of study in order to get it reasonable realistic and working.
Solution could be to make a simple connection between both structures, by reducing the distance between both. (I'm not so sure about the aesthetic consequenses in this case).
Integrating both options in one shell also might work.

The next three images show the wind trajectories combined with a Delaunay triangulation. I think that a fine triangulation could work to transfer the self weight to the ground, as it acts like a homogenic shell.. only lighter, and optimized by the genetic algorithm.
In the first 3 images are created in this way: marked points on crossings of wind trajectories, added random points, drew the Delaunay triangulation, added the trajectories again.

If we want to integrate these two tesselations into a single dome structure, it would be better to try to create the trajectory lines, within the Delaunay, instead of "on top". I tried this in the next image. BUT it appeared not really possible in this way. You can see that the green marked triangulation is a correct Delaunay pattern. The red part, which I based on the trajectories, are messy and not correct. This system might work if the tesselation is more dense. In that case, the trajectories will be the main beams. In between this beams, will be a secondary and much denser structure created based on Delaunay triangulation. (I'll sketch it in next post).

This one is just a sketch of Voronoi diagram based on the same trajectories. In the right side I added some vertical ribs. The Voronoi adapts to it in a nice way.
But this doesn't seem to be an optimal structure to bear both loads. Since the lines are not following the stress trajectories any more. I expect that this will create unneccessary moments in the structure.