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arXiv · 0912.3383

Fractal design for efficient brittle plates under gentle pressure loading

R. S. Farr
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Abstract

We consider a plate made from an isotropic but brittle elastic material, which is used to span a rigid aperture, across which a small pressure difference is applied. The problem we address is to find the structure which uses the least amount of material without breaking. Under a simple set of physical approximations and for a certain region of the pressure-brittleness parameter space, we find that a fractal structure in which the plate consists of thicker spars supporting thinner spars in an hierarchical arrangement gives a design of high mechanical efficiency.

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R. S. Farr. 2009-12-17. Fractal design for efficient brittle plates under gentle pressure loading. https://doi.org/10.1103/physreve.76.046601

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