Using fractal, or self-similar, patterns to design the lightest possible load-bearing structures with new strength-to-mass scaling laws.
A fractal has the property that any part of it, when magnified, resembles the whole. Remarkably, biology employs fractal designs to achieve high efficiency: spongy bone for stiffness and self-similar spiral shells for pressure resistance. But in the man-made world, fractal designs are rarely used for mechanical efficiency. Transmission towers and the branching columns of Gaudi’s cathedral hint at fractal design principles; but the small amount of hierarchy and lack of quantitative understanding suggest these are heuristic.
In this project we mathematically prove the existence of a new class of light and strong structures based on fractal principles with new strength-to-mass scaling laws. Our fractal structures offer extraordinary mechanical efficiency because the advantage achieved at each generation can be passed on to the next generation, and so on down to the smallest scale. We also quantify the role of imperfections in creating potential failure modes.
Fractal structures can extend the limits of architecture and civil engineering. They can increase the range and payload capabilities of drones and planes. In space, where launching structures is weight-critial, they offer new opportunities for building space stations and exploring space.
Fractal structures need very little mass to support a load; but for current designs, this makes them vulnerable to manufacturing errors.
The most efficient load-bearing fractals are designed as big structures under gentle loads ... a situation common in aerospace applications.
A systematic way to vary the power-law scaling relations between loading parameters and volume of material aids the hierarchical design process.
The transition from solid to hollow beams changes the scaling of stability versus loading analogously to increasing the hierarchical order by one.