# Optimization of fractal space frames under gentle compressive load

The most efficient load-bearing fractals are designed as big structures under gentle loads ... a situation common in aerospace applications.

*Physical Review E* 87, 63204 (2013)

D. Rayneau-Kirkhope, Y. Mao, R. Farr

The principle of hierarchical design is a prominent theme in many natural systems where mechanical efficiency is of importance. Here we establish the properties of a particular hierarchical structure, showing that high mechanical efficiency is found in certain loading regimes. We show that in the limit of gentle loading, the optimal hierarchical order increases without bound. We show that the scaling of material required for stability against loading to be withstood can be altered in a systematic, beneficial manner through manipulation of the number of structural length scales optimized upon. We establish the relationship between the Hausdorff dimension of the optimal structure and loading for which the structure is optimized. Practicalities of fabrication are discussed and examples of hierarchical frames of the same geometry constructed from solid beams are shown.

#### More in Fractal structures

### Hierarchical space frames

A systematic way to vary the power-law scaling relations between loading parameters and volume of material aids the hierarchical design process.

### Towers of strength

The Eiffel tower is now a longstanding example of hierarchical design due to its non-trivial internal structure spanning many length scales.

### Structural imperfections

Fractal structures need very little mass to support a load; but for current designs, this makes them vulnerable to manufacturing errors.

### Ultralight fractal structures

The transition from solid to hollow beams changes the scaling of stability versus loading analogously to increasing the hierarchical order by one.