In a world of Computational Engineering we often use nature as inspiration. The logic is, if something works well in nature, after millions of years in evolution, then it’s probably not a bad engineering solution. This is why we use, for example, Differential Growth, which can be found in coral and many plants as surface-maximizing strategy, in heat exchangers (and famously in the Aerospike rocket engine). The majority, if not all, of these patterns follow algorithms and mathematical principles, the Fibonacci Sequence, for example, can be found in everything from snail shells to sunflowers.
There are mathematical patterns, however, that are not readily found in nature (at least not until the discovery of Quasicrystals), such as aperiodic tiles. Penrose Patterns and other tilings used to be a mere mathematical curiosity (a tiling that never repeats) and found their way into design (see islamic mosques and mosaics).
They do not just look beautiful, however, they have a stringent, underlying logic which could make them the next killer application for high-vibration environments like airframes for Hypersonics. The aperiodic nature of their structure means that it will have a much less dominant eigenfrequency when compared to periodic lattices. Why are space planes not reinforced using Penrose structures?
The caveat is that creating the tiling is easiest done through subdivision, which algorithms can do. If you try to place tiles manually (for example, if you are using CAD) it is just not feasible. This may be the main reason, why we have never seen aperiodic tiles in engineering applications before.
Since we would love to see this hypothesis being put up for physical testing and validation, we developed a computational model to automatically generate variations of such airframe panels.
The algorithm works like this:
- define a 3D-curved surface as the panel base (here a simple cylinder segment)
- generate the first 2D-Penrose pattern with a low degree of subdivision generations
- generate the second 2D-Penrose pattern with a higher degree of subdivision generation, that is 180 rotated 180º against the first one
- specify 3 regions with different heights that act as layers on top of the base panel surface
- map the coarse pattern onto the tallest layer
- map the finer pattern onto the medium layer
- combine the two patterns and map the result onto the lowest layer that connects directly to the base panel surface (the airframe skin)
- union all the layers together and add some screw holes on the sides of the panel
- The screw holes have a repetitive spacing, whereas the Penrose structure is aperiodic. So we adjusted the frames on the edges to pick up the screw spacing
One panel assembly (sub-scale) takes 1min to create on a regular MacBook.