Fractal design for an efficient shell strut under gentle compressive loading

Abstract

Because of Euler buckling, a simple strut of length $L$ and Young modulus $Y$ requires a volume of material proportional to $L^3{f}^{1/2}$ in order to support a compressive force $F$, where $f=F/Y{L}^2$ and $f\ll 1$. 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 $L^{3}f\exp [2\sqrt{(\ln 3)(\ln f^{-1})}]$.

7 pages, 4 figures

Cited by in corpus (1)

• Fractal space frames and metamaterials for high mechanical efficiency