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.

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..

Focus on the Continued Research

I mentioned in the report a number of ideas for possible proposals. For this particular research subject, as described in the previously posted abstract, my interest goes out to one main directions:

"IDEA: If a column free dome is the starting point, we could divide the dome structure in two shells, one resisting the wind loads, and one taking the deadweight of the structure. We could design the “deadweight shell” by distributing points onto the dome shape, and connect the points applying a Voronoi algorithm, in order to get a framework as light as possible, while at the same time being one integrated entity. The wind-shell could be constructed out of a frame following the stress trajectories due to wind loads (one main direction). The one shell should be connected to the other in a way, which is parametrically predefined."

To discuss this a bit further, I want to comment that, wind load is a tricky load case to use as a shape giver. Since it moves around and the force flow caused by the wind on the structure, very much depends on the shape of the structure itselves. To use this principle, we should at least stay to one type of shape of the structure.

Let's assume that we use a dome structure as a model. Based on the adaptive qualities of rads to their loadcases, we could consider to optimize the dome to one main wind direction. And make the dome able to rotate towards the wind direction. Other wise, the structure would collapse, as soon as the wind changes its direction. An other solution could be to over-dimension the structure of the dome in order to make it strong enough to stand wind form all directions, but in this case,this is not our aim, since we want to create a light structure which is as much optimized as possible to its surroundings.

The issue of two cooperating shells: In radiolarians we see that they have to deal with 2 kinds of load cases in general: 1) the distibuted pressure of the water surrounding them, and 2)Impact loads caused my predators or other objects in their environment. This way of dealing with both different types of forces, made them able to develop efficiently. The fine tesselation of their shells withstand the evenly distibuted pressure of the water. While the Impact forces are counter acted by the arm of spines connected to the shells.

If we want to translate this principle to a dome shaped structure, we first have to define our load case. The distributed loading acting on a building is it's selfweight, magnified by gravity. The impact force encountered by a building structure is wind force, although its partly distibuted.

The big question is: How can we integrate this into one structure?


Impact forces and distributed loads acting on radiolarian shell

Deeper Research Radiolarians

I've been working to get a bit deeper in the radiolarian principles.. Via this link you can find a report of my work done. This report is my way to archive my findings for my own process. And its also a way to share it with my colleagues Michela and Peter and all others who are interested in the subject.

you can download the radiolaria report via THIS link

Abstract 2009 ACSA Conference

STRUCTURAL DNA: Genetic Exploration of Biological Micro Structures for Architectural Applications

Abstract:
Complex biological structures, designed by forces of nature, frequently serve as inspiration for new developments in the field of building technology and architecture. Well know examples in the work of Gaudi, Paxton, Otto, le Ricolais and others demonstrate the inspiration of natural morphology and patterns for structural design. The use of digital technologies to investigate the translation of natural micro structures into architectural macrostructures offers a valuable exploration tool for both designers and engineers working in the field of architecture.
The approach demonstrated in this paper uses Evolutionary Computation (EC) to enhance and modify structural form based on biological micro structures. The forms are modified to conform to new boundary conditions associated with architectural structures. The process is based on a Genetic Algorithm (GA) which uncovers for the designer a range of good performing solutions within the design space. The application of the GA is combined with parametric software, in this case Generative Components (GC), to allow the designer to navigate through a range of solutions which follow morphological patterns taken from the biological form. The method, referred to in this paper as a GC-GA, uses a finite element analysis to determine the structural performance of the forms. This allows the designer to manipulate and optimize a parametrically defined model based on predefined criteria and parameters.
The opportunities and limitations of this design process are explored and evaluated based on an experimental case study using the forms of radiolarian skeletons. Radiolarians are a group of marine protozoa found in the open ocean which have ornate siliceous skeletons. The Radiolarians are analyzed in relation to their environment and special qualities. Based on these findings, a parametric model of an architectural, space enclosing structure is defined and used in the GC-GA exploration loop, taking into consideration new boundary conditions and load cases. The paper demonstrates how the GC-GA cycle of selection, recombination, and evaluation is used to optimize and explore a large range of solutions. Finally, there is a discussion of the quality of solutions found based on both structural and architectural performance. In conclusion, comments are made regarding the general application of design exploration methods like the GC-GA as design tools both in the context of practice and studio.

Keywords: radiolarians, nature, structure, genetic optimization, structural analysis, morphology.

First test in STAAD

To explore the set up of the new process, we tested a basic hexagon dome structure, parametrically built in GC, on structural performance in STAAD. The results are clear.

the tension is obvious caused by the horizontal thrust, which would be most efficiently translated into vertical forces bij tension ring(s) in regular dome structures.. So the hexagonal grid automatically divides these forces among its members on the spot where its needed.
blue: compression
red: tension
supprt/load conditions: simple pinned supports and a 1 N/m2 load





the deflection is very clearly demonstrated in this movie:



next steps:

• exploring radiolarian skeletons (relation between their shape and forces acting on them)
• defining approach
• modelling a new parametric model according to approach
• testing, analysing different configurations
• genetic optimization loop

get back to you soon..

One step back. Research Approach

I looked back into the radiolarians in order to decide on a renewed approach for the dome project. Please check the image below for some key observations.


Radiolarian dome shape principles

If we want to use the dome shape for architectural purposes, it could be of interest to integrate some features in the parametric model as seen in radiolarians as well. Taking in consideration, the dead load, the gravity, and the supports,we already know that a combination of radial vertical beams in combination with rings and diagonal beams for stability will work in architecture (Geodesic dome Buckminster Fuller). what seems interesting to me, learning from radiolarians, is: In which ways would some of their basis principles work for architectural purposes? The first option is, to take one homogenic grid and manipulate the density and the overall shape. The second option focusses on dividing the dome in horizontal strokes, devided by rings while manipulating the different grids in between.

objective: achieve a structure which is as light as possible and at the same time stiff enough to stand the load cases.

Approach option 1:
use a fixed grid structure for example the combined hexagonal en pentagonal grid. (this principle based on the buckyball/c60 molecule is considered as an optimal manner to devide a sphere into planars or straight beams). What the interesting part could be in this case, is that while optimizing the overall shape of the dome, its environment can be taken into consideration. That could be the support of the structure (straight ground, inclined ground) and the load case, focussing on wind from one main direction. An homogenic structure has a high potential of being able to be fabricated out of a limited range of prefab elements.

parameters: shape of dome, density of homogenic grid
fixed: material, grid type, constraints and load cases
criteria: lightness of structure
results: different dome shapes with certain density of grid. Optimized for a specific situation. (i.e. an inclined site at the sea side).

Approach option 2:

Taking the applications of rings in the dome as a starting point, we could divide the grid into multiple horizontal strokes, as seen in radiolarian skeletons (see image 6th example). Generate separate grids structures in between the rings. In this case its an option to design the grid based on some well known mechanical behaviours of architectural shells and domes. (i.e. small density in top, mainly vertical beams in base, etc. )

parameters: density of each grid stroke, type of grid per stroke (! GC might could exchange grid types)
fixed: material, overall shape of dome, constraints and load cases.
criteria: lightness of structure
results: Different combinations of grid configurations within one dome shape.

I will do some more research of dome structures and discuss it with my tutors Peter and Michela, in order to decide.