In 2007, I started my PhD working on the development of a GA for the structural optimisation of free-form structures. I first tested the GA on the crematorium of Kakamigahara, designed by Toyo Ito and Mutsuro Sasaki consultants. The geometrical data, as well as the optimisation procedure were directly developed in Rhinoscript, the simple programming environment implemented by Rhinoceros. Ansys was used as the FEM solver to calculate the maximum displacements of the roof structure. The structural model was prepared in Rhinoscript, and then transferred to the FEM solver via a *.txt file (that run in batch mode). The optimisation procedure was conceived to be entirely automated.

The mesh was a triangular grid of 2500 elements. The concrete columns were considered as the only supports (fixed joints, even if that was not the real condition, as explained in the book “From control to design”). Regarding applied loading, gravity and self-weight were considered. The design variables of the problem were the Z coordinates of the control points of the NURBS surface of the roof. This was my way to “see” – or better interpret – the crematorium, and it was an exercise in which such architecture was freely redesigned.

The results of this research work were published in: Pugnale A., Sassone M., Morphogenesis and Structural Optimization of Shell Structures with the Aid of a Genetic Algorithm, “Journal of the International Association for Shell and Spatial Structures”, Vol. 48, n. 155, December 2007, pp.161-66. The can also be found within my PhD thesis, which is published online here (in the appendix you can find the original algorithm used).

In the following years (2008-2010), similar GAs and relaxation algorithms were developed for the solution of other optimisation problems, related – for instance – to acoustics and planarity of gridshells.

Considering that Toyo Ito has been recently awarded of the Pritzker prize 2013, I am proposing here a “restored version” of the crematorium case study using Grasshopper, Karamba and Galapagos as design tools.

This time, the roof has been described with a NURBS surface, again using the Z coordinates of the control points as the design variables (vertical domain restricted to the range -10m/+10m). Karamba has been used as the FEM solver. The mesh has been simplified comparing to the previous calculation done in 2007 for speed reasons (now it is a 35×20 grid). Regarding the loads, a gravity load has been applied, as well as the self-weight and a live load of 6KN/m2. The shell material has been chosen as a conventional concrete C25/30 (defined by the Eurocode), and the shell thickness has been defined equal to 25cm. The algorithm has been run for 400 generations in Galapagos, and it has resulted in a structural form with maximum displacements of 3.3 cm. (the flat surface would give a max displacement of 67 cm).

The Rhinoceros and Grasshopper files of this exercise can be downloaded under Resources.

You will need a full license of Karamba to run the optimisation process. However, you could also use the trial version by reducing the number of shell elements used (max 50 elements).