Team uses fractal geometry to build lighter structures

Dec 03, 2012 by Bob Yirka report
Fractal frame. This construction shows the similarity of different scales (“self-similarity”) in a generation-2 hierarchical structure. Due to manufacturing limitations, the scaffolding here is made of solid rather than hollow beams (inset). Credit: D. Rayneau-Kirkhope et al., Phys. Rev. Lett. (2012)

(—A team made up of members from several European countries has published a paper in Physical Review Letters describing a technique they've developed for using fractal geometry to build structures that maintain their strength despite weighing significantly less.

The researchers began their study by noting that many structures in the world already demonstrate some degree of fractal . The Eifel Tower for example, they note was essentially built using a single type of metal rod that is replicated in different sizes throughout the tower to minimize weight. What's not been the case however, they add is a predefined way to implement fractal geometry into structures in general. To rectify that, they have come up with a process that allows for creating metal beams that take advantage of .

The first step is to create a hollow metal beam of the size desired for a given project. Next, reengineer the beam by changing its and thickness such that the beam weighs as little as possible but is still able to withstand the weight or pressure it will be subjected to as a final . Once that is achieved, label it generation-0. The next step is to create a larger beam made out of generation-0 beams arranged using triangular subdivisions. This next beam is labeled a generation-1 beam. Generation-2 beams would be constructed by replacing all of the generation-1 beams with full scale versions of itself, only in a larger construct. Theoretically, the process can be repeated as many times as is desired or is possible, depending on scale.

The resulting structures weigh less than those made with solid steal because they contain less of it – the more generations used, the lighter the structure becomes proportionally to one made of solid steel. As an example the researchers suggest that a made with a solid metal 100 meter boom (not that anyone is proposing that) could be made to be 10,000 times lighter if a generation-3 beam were used instead.

The overall idea the team reiterates, is that it appears possible to use a standard methodology that includes fractal elements in building new structures, rather than borrowing fractal ideas and adding them in an ad hoc fashion, to achieve lighter weight constructs.

Explore further: And so they beat on, flagella against the cantilever

More information: Ultralight Fractal Structures from Hollow Tubes, Phys. Rev. Lett. 109, 204301 (2012) DOI: 10.1103/PhysRevLett.109.204301

A fractal design is shown to be highly efficient both as a load bearing structure and as a general metamaterial. Through changing the hierarchical order of the structure, the scaling of material required for stability against loading can be manipulated. We show that the transition from solid to hollow beams changes the scaling in a manner analogous to increasing the hierarchical order by one. An example second order solid beam frame is constructed using rapid prototyping techniques. The optimal hierarchical order of the structure is found for different values of loading. Possible fabrication methods and applications are then discussed.

Physics Focus

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4.7 / 5 (3) Dec 03, 2012
So, I'm going to ask the silly question that everybody might have in mind but nobody dares to ask:
space elevator?
not rated yet Dec 03, 2012
So, I'm going to ask the silly question that everybody might have in mind but nobody dares to ask:
space elevator?

I was thinking a buoyant dome city as envisioned by Buckminster Fuller. Perhaps on Venus.
5 / 5 (4) Dec 03, 2012
A Space Elevator really needs more tensile strength than structural support strength, at least once you get off the ground a few 100 meters. All proposed designs I have seen seem to prefer a tether, or cable of some type that links from the earth to a platform in geosyncronous orbit. Trying to build a structure from earth out into space without a tether seems almost impossible, the base of the structure would have to be miles wide.
1 / 5 (2) Dec 15, 2012
What about a craft that contains a bunch of 3D printers, that we launch into space. Then they start printing up massive solar sails ?

Or, here's a good one: we could use this technology to build a telescope in space that is far bigger than the Hubble. In this design the 'reflector' (light collector) would be far from perfect (smooth surface normally being required), but we could use two magnetically levitated (i.e. separated) disks of mirrors counter-rotating to collect the light in such a telescope, and over the large exposure times it seems like the rotation would cause the 'errors' to cancel out, and end up rendering a perfect image onto the camera's chip. Actually for that matter, you could use two counter-rotating mirrors shaped like curved helicopter blades 100 yards long, that would rotate, reflecting to the camera, and over time, the photons collected would STILL end up rendering a perfect image. Imagine the kind of quality image we would get from a 100 yard telescope!
not rated yet Dec 16, 2012
And what about Shimizu's Mega-City Pyramid?