Remember fractals? Those incredible structures that arise from the apparent random variability of both the mathematical and the real universe. A few years after prof. Mandelbrot published his work on what he defined as fractals, swarms of ideas exploded in the minds of scientist: they turned out to be an astonishing revelation in understanding the structure of the universe – from the cosmological scale down to the patterns of biological organisms. The technology applications soon followed. To name a few famous examples: the image and sound compression algorithms that we nowadays use more than we can imagine to applications like fractal antennas used in mobile phones today are just two of the many places where fractals are embedded in our modern world.
Yong Mao, a lecturer at the University of Nottingham, UK and his colleagues have developed new kinds of load bearing structures that use fractal patterns. The advantage of such structures is that they turn out to be both very strong and very light.
They begin constructing such a structure by building what they call the “generation-0” element – a hollow beam with the right radii and thickness parameters that are optimised for an optimum ratio of strength versus amount of material used. They test this beam by applying loads along two of its axis to see where failures develop and then they optimise the the fractal structure that will sustain these loads accordingly.
Similar to the way a fractal is generated, in the next step, this first segment is replaced by multiple beams according to a specific fractal rule, thus creating a “generation-1” structure. For the “generation-2” element, a further iteration is implemented, by repeating the fractal rule: each individual segment of the first generation is replaced by a smaller scale replica of the generation-1 model. As you can observe in the image below, this is what scientists refer to when speaking about the self-similar nature of fractals.
The iterations can be repeated further as long as the manufacturing limitations permit such a thing – the advantage being, the calculations show, that with each generation, less material is needed to support a given load.Trying to quantify the advantages of this type of structures, the team calculated that if they were to replace for example a beam made from solid steel from a crane boom with a generation-1 model, the fractal pattern would turn out to be 100 times lighter than the initial simple beam. The amazing thing is that with each further generation, such a fractal design gains another two orders of magnitude in the strength versus mass ratio, making the range of possibilities really interesting.
Then, you might ask yourself – if these structures are so efficient, why haven’t we seen more of its applications in the world around ? Well..it’s because the resources used in manufacturing such intricate patterns outweigh the potential benefits..at least that was the case until high quality 3D printing came along. And because 3D printing is just beginning to improve itself, we might find very soon that printing such strong and lightweight objects would turn out to be quite useful and efficient. As Yong Mao puts it, “we could just upload our different designs to a program and people could download and print off the structures at home.”
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Copyright 2012 ZME Science
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