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

Fractal design for efficient brittle plates under gentle pressure loading