What I did in SFO (SG’09) truss optimization

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This was my first time in an SmartGeometry, and I was impressed level of all participants and tutors.

Truss Optimization Trough Excel

Mi proposal for the workshop (4 days) consisted in optimize a steel truss, reducing the total weight of the steel. The search process consisted in modify the geometry of the truss moving some nodes of the structure, and “blocking” others. The original idea was use Genetic Algorithms but for timescale I used the excel plugin “SOLVE”.  So the main problem to face was evaluate the structure in excel and connect GC with excel as a feedback loop.

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Problem Explanation.

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This Image above explains the interoperability between GC and Excel and how operates the feedback loop. Also explains the goal, the number to reduce. The load in the truss is decomposed node by node using the trigonometric function Sin and Cos.

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The freedom nodes degree is defined by areas. Inside that areas the nodes are free to move.   the areas are defined graphically in GC and numerically in Excel. Although the code in GC is very short performs the right tasks.

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The image is a capture of Excel plugin Solver. The parameters in the windows Solver define the search space, the performs of the algorithm, number of iterations, the optimization type, the precision and others parameters.

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The above images shows the truss before the optimization. The rectangle colored represents the area of freedom for nodes. if a node is not inside of one of these areas then is block. For this example only 5 nodes have some degree of freedom. I choose the option to block some nodes in order to obtain unpredictable results.

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This print screen shows the truss and the degree of freedom per each node. The width in tubes representation is according to the compression and the load to support.  The Red colour represents that all the tubes are working in compression.

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The truss is  Re-calculated and new loads are defined. The blue colors represent that these tubes support slenderness.  A new optimization iteration is executed.

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After the optimization. Solver is quite fast and results are almost immediately.

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Sketches

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Here the constraints for each node.

the video shows different optimizations for different loads applied to the truss.

Deeply thanks to Matthew Clark from Arup New York and Steven Downing from Arup Australia.

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