Fractal design for efficient brittle plates under gentle pressure loading

摘要

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.