Christmas Tree Structural Optimization

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It’s Christmas time and here in the office we were wondering how the position and the weight of the decoration can affect the equilibrium of a Christmas Tree.

Problem: how to minimize the bending moment at the base of a Christmas Tree
Parameters: position of the decorations on the tree’s branches and branches length

We decided to optimize the moment that forms at the base of the trunk of a Christmas tree, by varying the length of the branches and the position of the Christmas balls.

The branches’ lengths can change within some limits (domain) as well as the position of the decorations. These parameters affect the equilibrium at the base of the tree: the lower the bending moment, the better the structural optimization. The better the structure, the lower the cost! The lower the cost, the happier the customer!

Some data to understand the complexity of the problem:

• 1 Christmas Tree with rigid connection at the base (support)
• 14 branches of variable length in L1, L2, L3 (beams)
• 14 Christmas decorations of equal weight can move along the length of the branches (point loads)

If you haven’t already realized it, the number of cases to be analyzed is so large that without an optimization algorithm it would impossible to be solved in short time.

ANALYSIS:

We have created a parametric model of the Christmas tree structure and then the algorithm that automatically changes the parameters mentioned above. So now both tree and parameters are just numbers and formulas, it not a simple drawing anymore.

With all these variables the only way to analyze and optimize the problem is to set up an iterative method that by changing the variables performs the simulation, analyzes the results and understands where the function converges to zero to find the best solution.
There are many software allowing you to perform these simulations and they are often categorized as Evolutionary Solver or Multi-Objective Evolutionary Optimizer.

Our Computational Design department decided to go for Rhino, Grasshopper, Galapagos and Octopus.

RESULTS:

During the simulations, it was possible to see “live” if the problem to solve has been set correctly, and therefore if the function converges to zero. It’s amazing to see how the algorithm can evolve step by step.
As you can see from the movie below, the iterative calculation works very well: analyzing and calculating thousands of solutions with traditional methods would be impossible and super time-consuming.

CONCLUSIONS:

This exercise shows the great potential of the integration between computational methods and structural analysis.
What about using these methods to optimize a full-scale structure like a mass timber multistorey building or a roof of a warehouse or a slab made of CLT and GLT beams?

How to get the most out of the “Computational design”? We believe that the best way is to add timber and DfMA because this is the only way to quickly move from the drawings to the production in a lossless way. It would be useless to optimize the structure if you had then to loose days to redraw thousands of complex elements with the risk of making some mistakes.

It is not easy but we at Ergodomus worked very hard to develop this workflow: structural analysis -> optimization -> production drawings. What You Draw Is What You Get®!

Contact us if you want to know more!