Computational morphogenesis in architecture: the cost optimization of free form grid-shells

Abstract

In this paper an optimization problem related to the tessellation of a free form grid shell is presented. This kind of structures is generally composed by a supporting grid that defines the geometry of a large number of cladding elements always different one from another. From the constructive point of view it means that every single piece needs to be designed and produced "ad hoc", then marked and positioned with the aid of an assembling table. In order to reduce the heterogeneity of grid-shells elements, several optimization strategies referring both to evolutionary and gradient-based techniques, have been tested and compared. In view of future development, a multi-objective procedure that involves static analysis combined with the discussed geometrical optimization is finally proposed. All the free form geometries are defined and handled by means of a commercial NURBS based software. On the contrary, the development of all the presented optimization procedures has been possible thanks to the implemented VB based programming language of the same NURBS based software. Due to the smoothness of the solution domain of this specific problem, gradient based procedures seem to be the most efficient in the rapidity of convergence to the optimal solution.