Fractal design for efficient brittle plates under gentle pressure loading
arXiv:0912.3383 · doi:10.1103/PhysRevE.76.046601
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.
10 pages, 5 figures