ACSA Presentation - PPT slides

Webinterface of dome generations

click HERE to see the evolution process of the domes!!

GC - set-up

I decided after some discussion and thinking, to use the right support configuration for the model. Since cellular structures in nature, tend to arrange perpendicular to stiffer surfaces. This is the most optimal way to distribute forces within a structure. This phenomenon is also seen within radiolarian skeletons.


40 rings model with higher densities of points

This image illustrates the way the points are projected onto the dome in GC.

Projection

Symmetric or almost symmetric?
Either symmetric or total a-symmetric...? For our topic, it might be best to use symmetric, because we decided not to focus too deeply on wind forces for now.


Perfect Symmetric configuration of 40 ring model

To explore the possibilities of having the rings regulated, I added some images of different amounts of rings below. each set is a screen shot of a different GC model. Within one model, the rings are limited to a specific amount. (5,7,10,10,20,40)

I still hope to find a way to integrate them into one GC model.


random results of configurations based on different ring densities.



It would be best to control the density of the rings in the same GC model. But until this point we cannot integrate this into one script.together with the point distribution variables. I hope we can manage to solve this. but we might will test different models for specific ring densities.


This is an example of a possible configuration of points based on a 40 ring model. This would be the most dense ring-density possible within the model. We defined 41 different variables to define independent point distribution along each ring. .


This image shows a model with different densities of points per ring (20 rings)
voronoi on top & delaunay below (based on same points)



Voronoi (above) vs Delaunay (below) GC


Voronoi Dome GC

Test Run

This homogeneous hexagon dome is ready for a test run. The maximal values are illustrated in the pic below, all values in between are part of the "solution space"



test run

Comparing different tessellations for a dome shape

What happens if you construct the three tessellations based on the same set of points?

Below you find 2 combined drawings. The hexagonal part is devided in two ways, the lower one comes closer in comparisation with the voronoi and delaunay part.
In these two dwawings the amount of points are chosen by using factors of 2. Thats why the structure is more regular. The second one is the best. Because the density of the hexagonal structure is more equal to the others.


For the research it would be interesting to test the three types of structures and compare them. In the next scheme, I defined a try-out set up of the comparisation.

These domes are all constructed based on the same set of points. The amount of points per ring are random. Thats why the Delaunay and Voronoi version are a bit irregular. The errors in the hexagon sample are because it took too long to draw all lines manually and I arrayed one quarter. but it gives an idea. The size of the dome can be a parameter as well!! (unlike i noted on this picture) But to compare them, the size should be the same for all 3 domes.

How to define the circels and points (in GC), which define the tesselations?

In the picture below is illustrated how a plane is projected onto the dome. the set-up size of the plane has a diameter of 32 m, while the dome itselves has a diameter of 20.37 m. I defined the plane first, in order to get a regular division of rings possible.
The overal size can be changed afterwards by adjusting the diameter of the projection plane.

RULES RINGS
The rings can vary in number. They are always linear distributed on the plane.
Number of rings: n_ring
Diameter of projection plane: d_plane
The max distance between the rings is 4 meter.
The min distance between the rings is 0.5 meter.
The formula which defines this relation is: 1/2 = smaller than: (0.25*pi*d_plane)/n_ring = smaller than: 4

RULES POINTS
The points on each ring can vary in number. They are always linear distributed along the ring.
A similar system rules the division of points onto the rings
Number of points: n_point
Diameter of ring: d_ring
The max distance between the points is 4 meter.
The min distance between the points is 0.5 meter.
The formula which defines this relation is: 1/2 = smaller than: (d_ring*pi)/n_point = smaller than: 4.




definition of the projection plane & rings


Diagram of GC hierarchy.

Proposal; More Details

An other tessellation which is worth taking a closer look at, is the previous used hexagon diagram. In the version below, its a bit more compicated, in the sense that the density of the hexagonal structure varies between the circles. In this case, the radial division is set to 132 points in all sections. The circular division varies in density between the different rings.

other options of this one are:
- varying also the radial density between the rings.
- inserting a random factor when defining the points, to get a more unsteady look of the structure.


An other configuration, Hexagon Structure
The parameters are in this case:
n_c (number of main circels)
p_cALL (density of points along all circles)
n_cSEC_1 (circular density of secondary circles in between the 1st and 2nd circel)
n_cSEC_2 (circular density of secondary circles in between the 2nd and 3rd circel)
n_cSEC_n (etc)



The folowing image illustrates what happens if we construct the Voronoi Diagram, based on the same configuration of the model as in previous image of the Delaunay triangulation.


Same configuration, but Voronoi Diagram

Proposal

Okay, here is my proposal: Since the wind trajectories are not steady enough to use as a starting point, I decided to keep the basic set-up a bit more general in order to have some freedom in the model it selves to develop during the optimization. In the way i propose now, I kept a few things in mind:
1. the aesthetic quality of the tessellation
2. the variabiliy of the model set-up
3. the basic structural needs of a dome structure (rings & ribs)
4. the basal connections to the ground

Since rings are one of the basic needs for a dome structure, I take circular distribution of points as a starting point in this proposal.
The bars defined by the Delaunay triangulation will automatically generate sets of "ribs" which will lead the vertical forces to the ground, the idea is that all irregular ribs will work together as a network of ribs.
The density of distributed points along the outer (lower) ring (not drawn in this picture yet), will define the amount of basal supports the dome will have.


Fig. Drawing of possible configuration Delaunay Triangulation:
amount of points circle1:20 (d_c1:20)
d_c2:40
d_c3:20
d_c4:15
d_c5:50
d_c6:80
d_c7:75
d_c8: invisible in this drawing


The setup is arranged in this way:
1. definition of the rings. they are based on regular vertical divisions of the dome, as pointed out in the drawing.
2. along each circle we set a variable amount of points. (Parameters in GC will be: point density circle1, d_c2, d_c3, ..., d_c9).
3. The points will be connected by a Delaunay triangulation. This will create a closed lattice structure. Each possible structure will look different and perform different.
4. We can optimize this model according to different load cases or even different dome shapes.

note: we can try the Voronoi diagram applied on this model as well, I want to keep this open as an option.
we can also try to play a bit with the amount of circels and distances between the circles, but this seems like a proper starting point.

I post some clear images of stresses in a dome structure caused by wind forces, below. This information made me, together with Peter's comments, decide to jump of the idea of using the stress trajectories, as i proposed before. Because it doesn't make too much sense, in a simplified way. It could make sense to try to work out how to adapt a building perfectly to wind forces, but that could be a complete study on its own.


Principle stresses by simple horizontal load - Staad plot


Dynamic stressed due to different speeds of wind