Orthogonal Voronoi
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3d Cellular Automata that either die out, run amok ad infinitum or freeze (class II behaviour). In the latter case, the fact that the system is equilibrium means that certain rules have been met, which in this case, refer to the adjacency rules of different building cells.

The TRADA Shell is a collaborative effort by the Ramboll Computational Design team: Andreas Bak (grasshopper model & structural analysis), Harri Lewis (surface discretisation into flat polygons), Stephen Melville (connection details & design advice), Emily Scoones (model making and all round excellence) and myself (initial design and funicular form-finding). The shell is a trade fair stand for the Timber Research and Development Association and was recently shown at the Timber Expo event in the UK (25-26th September).
Initial design
We began thinking up ideas the structure in early April 2012, and like the funnel we were keen to use some of the form-finding methods used in creating forms that had a certain structural logic. We decided upon an hexagonal shell structure, inspired by Frei Otto’s design for the Council of Ministers, Majlis al Shura, Riyadh, Saudi Arabia, 1979:
The design of the form was conducted using a particle-spring system similar to that used in our foyer sculpture last year. This time, we utilised the statically determinate nature of a hexagonal mesh (3-valancy) along with dynamic masses (updating at each time step depending on a shape function) to find a stable compressive shell structure. Free edges exist in order to make the shell more accessible to the public, and therefore suitable edge stiffeners were required similar to Heinz Isler’s up-turned cloth edge approach to counter accidental load cases.
Interestingly, during the process, areas of negative curvature developed around the centre area similar to Frei Otto’s Stuttgart21 project. This was unexpected but we ran with it due to the interesting form that was generated and the need for a central focus for the stand. For me, ‘designing’ code that at some meta-level designs a shell for you is very interesting, because you are never quite sure what the final result will be, and that is what design should be about whether just sketching, physical model making or working with computing machines.
Planar re-meshing
Once the doubly curved form was found and the client was happy, Harri Lewis wrote some nice code to replicate the process used by Cutler and Whiting in their excellent 2006 paper: ‘Constrained Planar Re-meshing for Architecture’. We think this is the largest structure to date that uses the method which goes beyond thinking about only planar quads (PQ) for doubly curved surface discretisation. Having a 3-valency (3 incident edges per node) mesh is also much more stable than a quad or triangular mesh (our initial design). The negatively curved areas around the centre give rise to the ‘bow-tie’ shaped concave facets, with the positively curved areas generating convex ones.
The resent rise in BSpline surfaces that bear no relation to structural logic have given prominence to post-rationalising methods to force designs to become buildable. It’s much more interesting when such methods are used to enable the construction of structurally efficient designs that are not necessarily regular in shape, but at least have a good reason for being so.


Materials & Detail
The shell is realised in flat pieces of CNC milled birch plywood which are joined by standard door hinges. The doubly curved nature of the shell provides enough geometric restraint to allow a completely hinged connection to be used at each edge, something we found very interesting to analyse and perhaps something of a first for this type of structure. Some very nice detailing by Andreas meant each hinge was recessed and a constant width gap between each panel was established. In effect, no single piece of timber touches any other in the structure, including the hinges that meet the base plates at ground level.
Unfortunately, the shell has now been dismantled, however it should make an outing at next year’s Ecobuild event in London so please come along to see it then. Many thanks to everyone at TRADA for inviting us to design their stand, and helping Harri and I build it over a single weekend!
As a final thought, economics meant that the sudden boom in concrete shells in the 70s hd to come to an abrupt end, but developments in computing and digital tools mean that the potential exists again to create such structures out of low cost materials that require no complex doubly curved formwork and that are relatively cheap to construct with standardised off the shelf materials. We therefore hope that there will be a kind of renaissance in shell structures in the coming years due to advances in the design computing community.
Finally, here is what the shell looks like before and after construction, with a comparison to the amount of plywood used on the foyer sculpture from last year… they’re getting bigger… 50 sheets next time!
A cellular automata with a rule set that finds equilibrium after a finite time period. You can make out the class IV behaviour patches occurring as the system becomes neither random or static (until the end). In terms of application to design, the process is an interesting way of satisfying all local conditions with neighbours in an emergent way. I’ve been thinking about this for a couple of years now, but still haven’t find the time to pursue the idea further.
Last week we constructed a successful test leg for our upcoming Trada shell sculpture. The plywood structure combines shell form-finding techniques with irregular flat polygon re-meshing and is being constructed in a month’s time here: http://www.timber-expo.co.uk/