HexDome 

Eden Fabric Stability

A light, sparse fabric

The Eden Project fabric has fewer struts than practically any other double-layer dome design. Its sparsenss saves weight, money - and allows in lots of sunlight.

However it does suffer from some structural issues as a result of its lack of stabilising struts.

Stability issues

If you've ever constructed a dome made using the same fabric as the Eden Project domes, you may have noticed that one of the ways in which is is most likely to move involves alternate tetrahedra in its truss rotating in opposite directions.

In fact the whole fabric is fundamentally a flexible one - and is free to move in two different ways - unless it is anchored down.

Diagrams

Some diagrams will help explain the idea. Firstly the following diagrams identify six tetrahedra in the truss:


Unit cell

Tetrahedra marked
The basic idea is that - on a small scale - the red tetrahedrda could rotate one way, while the green tetrahedrda could rotate the other way, while facing minimal resistance.

Next, consider this neodymium model of the Eden Project fabric:


Top side of the fabric
The view from underneath looks like this:


Underside of the fabric
...and if you try to twist alternating tetrahedra in opposite directions, the result looks like this:


Tetrahedra twisted in alternating directions
As the last picture illustrates, alternating tetrahedra in the truss are relatively free to rotate in opposite directions.

Rotating the tetrahedra in this way increases the overall curvature of the dome locally - but is not resisted by the fabric in any other way.

Linear stability analysis

Linear stability analysis suggests that the fabric acutally lacks linear stability in the face of this type of small perturbation of the tetrahedral layer - assuming that this is free to move at its edges.

Lack of linear stability can be associated with structures that are prone to vibration. Vibration in metal structures may increase the risk of metal fatigue. It seems like an undesirable characteristic for a structural fabric.

Implications

The fact that this fabric can be deformed in this way raises a few issues for dome builders.

Firstly, the lack of resistance of the fabric to this type of transformation is ameliorated when it is bent into a full dome - because the rotating elements no longer all link together in structures with an even number of elements.

Instead of forming rings of six tetrahedra, a dome throws in a few pentagons into the structure - where five tetrahedra are linked together.

The fact that five is an odd number means that the pentagons act to stabilise the resulting structure - since alternating tetrahdra around a pentagon is impossible.

Consequently, a dome built from this fabric gains stability from its pentagonal elements.

There's may also be a slight gain in stability as a result of the tetrahadra not all necessarily being exactly the same size.

Having a structure be stable because it is anchored intermittently is sometimes acceptable - provided the anchors occur regularly enough. If this type of fabric was used in a large enough dome, there would be areas which were far from any pentagonal anchor - and imperfections at the joints may accumulate and allow some resulting movement.

Remedies

Throwing in a few more struts in the internal layer seems like it would be effective at preventing these degrees of freedom. Additional structural elements could be placed at the points which are furthest from any pentagonal elements, to act as additional anchoring points.

Flexibility

In addition to the issue associated with lack of resistance to rotation of the tetrahedra forming the truss, the fabric is also flexible in another way.

In particular, it can be bent into anticlastic curved surfaces.

In this respect the fabric closely resembles a thin square section octet truss fabric.

The following photographs illustrate that transformation:


Fabric bent into an anticlastic surface

Fabric bent into an anticlastic surface
This type of flexibility presents other issues to dome designers - particularly during construction, when the dome shape is incomplete. In particular it makes additional elements - not present in the final structure - necessary.

These act as scaffolding during the construction process.

Tim Tyler | Contact | http://hexdome.com/