Volume 84, Number 1, October 2008
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||16 September 2008|
Fractal space frames and metamaterials for high mechanical efficiency
Unilever R&D - Olivier van Noortlaan 120, AT3133, Vlaardingen, The Netherlands, EU
2 School of Physics and Astronomy, University of Nottingham - Nottingham, UK, EU
Corresponding author: email@example.com
Accepted: 19 August 2008
A solid slender beam of length L, made from a material of Young's modulus Y and subject to a gentle compressive force F, requires a volume of material proportional to (where f ≡ ≪ 1) in order to be stable against Euler buckling. By constructing a hierarchical space frame, we are able to systematically change the scaling of the required material with f so that it is proportional to , through changing the number of hierarchical levels G present in the structure. Based on simple choices for the geometry of the space frames, we provide expressions specifying in detail the optimal structures (in this class) for different values of the loading parameter f. These structures may then be used to create effective materials which are elastically isotropic and have the combination of low density and high crush strength. Such a material could be used to make light-weight components of arbitrary shape.
PACS: 46.32.+x – Static buckling and instability / 46.25.Cc – Static elasticity: Theoretical studies / 46.70.Hg – Membranes, rods, and strings
© EPLA, 2008
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