Generating fractal space frames

Structures under compression load are less efficient than the same structures under tension load. Instead of material breaking, yielding which determines design of a structure, at compression structures - buckling occurs before mentioned events.

By replacing straight beam elements under compression, with a series of fractal space frames (two tetrahedra on both end, and a stack of polyhedra in between) and distributing the initial compression force into tension and compression members of the space frame, R.S.Farr and Y.Mao succeeded in lowering down the amount of required material tens, several hundred times[1].

From left to right: solid rod under compression (Generation 0), Generation 1, Generation 2 fractal space truss[2]

Critical Load Factors, for G1 structure on the verge of buckling failure

A generator for creating Generation 1 and Generation 2 structures based on upper mentioned papers, could be found below in two versions - Grasshopper component and Rhino button. On Generation 3 fractal space frames, they output only a report (force parameter, number of hierarchical octahedra, radii, number of members, its lengths ...) but do not generate it, as number of G3 frame members could reach couple of millions, billions.

Inputs: Length of the initial rod [in meters], compression Force [in kilonewtons], and Material.

a) grasshopper component:
Can generate both grasshopper geometry and bake it to Rhino to appropriate layers. Report in form of Grasshopper panel.


download

b) Rhino button:

Only generates Rhino geometry. Can export report to comma separated .txt file.

download it, and drop in onto your Rhino workspace.


Special thanks to R.S.Farr, for all the help gave me!

+ Fractal space frames featured on Big Bang Theory (Season 6, Episode 13)[3]

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[1] "Fractal space frames and metamaterials for high mechanical efficiency"
http://iopscience.iop.org/0295-5075/84/1/14001

[2] photo taken from "Fractals for Mechanical Efficiency" article
http://www.london-institute.org/people/farr/fractals.shtml

[3] photo taken from http://users.asci.aalto.fi/daniel