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 supporta compressive force $F$, where $f=F/YL^2$ and $f\ll 1$. By taking into accountboth Euler and local buckling, we provide a hierarchical design for such astrut consisting of intersecting curved shells, which requires a volume ofmaterial proportional to the much smaller quantity $L^3 f\exp[2\sqrt{(\ln3)(\ln f^{-1})}]$.
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机译：由于欧拉屈曲，长度为$ L $且杨氏模量$ Y $的简单支杆需要与$ L ^ 3 f ^ {1/2} $成比例的材料体积，以支撑压缩力$ F $，其中f = F / YL ^ 2 $和$ f \ ll 1 $。通过同时考虑欧拉和局部屈曲，我们为由相交的弯曲壳体组成的铸件提供了分层设计，这需要与体积小得多的$ L ^ 3 f \ exp [2 \ sqrt {（\ ln3） （\ ln f ^ {-1}）}] $。
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