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

## Sunday, July 19, 2009

### 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

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

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