Volume 93, Number 3, February 2011
|Number of page(s)||5|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||10 February 2011|
Fractal-like dependence in the designs of efficient pressure-bearing structures
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
Accepted: 17 January 2011
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).
PACS: 46.25.Cc – Theoretical studies / 46.32.+x – Static buckling and instability / 46.70.De – Beams, plates, and shells
© EPLA, 2011
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.