Fractal design for an efficient shell strut under gentle compressive loading

Because of Euler buckling, a simple strut of length L and Young modulus Y requires a volume of material proportional to L3f12} in order to support a compressive force F, where f=F/YL2 and f<<1. By taking into account both Euler and local buckling, we provide a hierarchical design for such a strut consisting of intersecting curved shells, which requires a volume of material proportional to the much smaller quantity L3f exp[2 square root(ln 3)(ln f-1)].