Fractal design for efficient brittle plates under gentle pressure loading.
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.
Farr
Robert S
RS
Unilever R&D, Olivier van Noortlaan 120, AT3133, Vlaardingen, Netherlands. robert.farr@unilever.com