Fractal-like dependence in the designs of efficient pressure-bearing structures

¹ School of Physics and Astronomy, University of Nottingham - Nottingham, UK, EU
² Unilever R&D - Olivier van Noortlaan 120, AT3133, Vlaardingen, The Netherlands, EU
³ London Institute for Mathematical Sciences - 22 South Audley Street, Mayfair, London, UK, EU

Received: 7 September 2010
Accepted: 17 January 2011

Abstract

By analysing the possible failure modes at each level, we propose a hierarchical design for highly efficient mechanical structures to withstand hydrostatic crush pressure, which becomes fractal in the limit of zero pressure. We deduce the Hausdorff dimension of these designs (over the range of length scales where this applies), and show that through changing the number of hierarchical levels, the power law scaling relation between applied external pressure and volume of material required can be altered in a systematic way. The design can be applied to arbitrary shapes, but for clarity we present two examples (cylinder and sphere).