When topology optimizers go mad 3

[GregLocock]

The above are 4 different runs of the amazing 99 line matlab topology optimizer. get it here . The load case is just a vertical load at the tip, all the points on the lhs are fixed. top left run is a 30x10 matrix, top right is 60x20, bottom left is 90x30, the other one is 300x100. I have not delved into the code to find out what is happening, but thought it was interesting that the design gets less sensible between the top right and bottom left, for a fairly small increment in model resolution. I am gently wondering if a better method might be to start with coarse resolution and then use that to define the solution space for the next run at finer resolution.

Cheers

Greg Locock


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[Mustaine3]

Other optimizer like Tosca offer constraints like "Minimum member size" or other manufacturing constraints to avoid impractical solutions.

 

[FEA way]

Here's the same case, with the same number of elements but solved using Abaqus (Tosca optimization module):

The algorithm will propose such solutions unless you specify some particular restrictions, like symmetry, moldability and so on.

 

[GregLocock]

The similarity of features in the 300x100 cases is very interesting. Thank you. The differences throughout are also interesting! Mustaine3, yes, but I was interested in the emergent complexity.


Cheers

Greg Locock


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[jhardy1]

Just a quick philosophical comment:

I don't think it's fair to say that the optimised geometries for the finest meshes are "less sensible".

If you think about the internal structure of sea sponges, animal and bird bones, etc, you will find very similar structures. These are very much "optimised" by evolution and natural selection - driven mainly by "minimum energy / material" required. Evolution doesn't include factors such as "simplicity" or "minimum thickness" or "assembly from straight elements" or "assembly from a catalogue of standard cross-sections" or "simplicity of connections" as constraints. (What looks like unnecessary complexity to us can still be a very efficient biological solution.)

If you add these constraints to your optimisation algorithm, you will very likely see the geometry converge towards a classic truss solution.

(I assume the OP's optimisation model is a simple plane-stress analysis; simply converting to a 3D analysis, and including buckling behaviour, will likely change the resulting optimised geometries significantly, as this will create a de-facto "minimum slenderness" constraint.)

http://julianh72.blogspot.com