Fractal design for efficient brittle plates under gentle pressure loading

TL;DR

This paper proposes a fractal hierarchical design for brittle elastic plates that optimizes material use and enhances mechanical efficiency under pressure loading, based on physical approximations.

Contribution

It introduces a novel fractal structure for brittle plates that minimizes material while preventing failure, advancing design strategies for pressure-loaded brittle materials.

Findings

Fractal hierarchical structures improve material efficiency.

The proposed design withstands pressure with less material.

Hierarchical spars outperform uniform structures.

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.