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Parametric Design and Construction Optimization of a Freeform Roof Structure

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Abstract

The pioneering works by Poleni, Rondelet and especially Gaudì, shows how some structural principles related to the field of shape-resistant structures has been well-known for centuries. The design of structural shape has been approached differently; the more analytical way of engineering, such as the works of Dyckeroff and Widmann or the intuitive approach of engineering referring to the works of Torroja. The focus for the new structures was lightweight, large spans, functionality, efficiency and economy. This brought new developments of form-findings structures, i.e. a set of tools and strategies to find the form of ’structural minimum’ - in shells where the surface is mainly stressed in the plane with compression, tension and shear. The research started with the development of experimental tools, or physical models, reaching a high point with the work of Heinz Isler [2]. However, this prosperous period has been concluded in about 20 years, since the rigid generative rules of shape-resistant structures brought to the rapid exploration of the complete family of potential shapes of shells during the 60ies.
... First, it allows an indepth exploration of solutions using a metaheuristic search method that can be easily followed by the designer. It also gives inspiration and direct feedback during the optimization process [8]. In this situation the goal is not to find an optimal solution, but to define a sub-optimal solution that is the best compromise following an in-depth evaluation of design criteria. ...
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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.
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Full-text available
The optimization problem related to the tessellation of free-form grid shells is presented in this paper. This kind of structure is generally composed of a supporting grid that defines the geometry of a large number of cladding elements that are always different from each other. From the construction point of view this means that each 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 shell elements, several optimization strategies, referring both to evolutionary and gradient-based techniques, have been tested and compared. All the free-form geometries are defined and handled with a commercial NURBS based software, while the development of all the optimization procedures has been made thanks to the VB based programming language implemented inside the NURBS based software. Due to the smoothness of the solution domain of this specific problem, gradient based procedures seem to be the most efficient for the rapid convergence to the optimal solution. Finally a multiobjective procedure, that involves static analysis combined with the discussed geometrical optimization, is proposed in view of future developments.
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Philosophy of structures
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Evolutionary Principles applied to Problem Solving
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