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 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 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.

International Photo Contest - Third Prize.

Photo and short image description published in "Structural Engineering International", November 2009.

Footbridges designed by Calatrava are famous landmarks all over the world: perspective views and lights are an integral part of his structural design, emphasized in this picture with a night shot that allows a better reading of all structural lines, outlined by the lights and reflected into the water. Palm fronds in the foreground, in relationship with the footbridge, accentuate also the interesting tension between a natural contest and its wonderful artificial addiction.

This paper presents a critical study of the church of Longuelo, Italy, designed in 1966 by Giuseppe (Pino) Pizzigoni (1901–1967), an Italian architect who lived and worked in the city of Bergamo. He began his studies on shell structures in the Fifties and many of his buildings show outstanding skills in conceiving and handling complex structures. The church is one of his most interesting works: it is divided in four identical free parts, each composed by four shells joined by a fifth one, supported by twenty one bars which realize an statically-determinate spatial frame resulting in an outstanding inner space.

The Force density Method [FDM] has been well known - since Linkwitz and Schek's first development in 1970's - as a powerful tool for analytical form-finding and static analysis of self-stressed structures like tensile membranes and cable networks. Actually, force density is always associated to a real stress state of the structure under a field of applied forces that, combined with other boundary conditions (constraints, etc.), allows the shape to evolve and improve). The approach proposed in this paper enables the technique to become more versatile so that it is possible to extend its application to different kinds of problems. In particular, changing the connection matrix and introducing virtual forces, morphogenesis can be related to general spatial frame structures looking at geometrical requirements as form and function irrespective of the applied stress field. As a demonstration of the capabilities of this tool, three different applications on current issues in free-form architecture are tested by means of a commercial NURBS based software and a VB based algorithm. One of these applications concerns the preliminary design of the roof structure of the Ponte Parodi project, by UNStudio Amsterdam, a multifunctional building to be located on the waterfront of Genoa, Italy.

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.

In this paper, we present two different optimization procedures, developed and implemented to deal with economic and constructive problems of free form grid shells. This kind of structures is generally composed by a supporting grid that defines the geometry of a large number of cladding glass 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 laid with the aid of an assembling table. Moreover if the grid is defined by four or more sides elements the realization of curve glass slabs turns out to be very expensive because of the carving process, forcing very often designers to try to avoid it by triangulating the grid where the shape results more complex. In order to reduce the cost of complex glass grid shells by limiting the number of element typologies and, if we have quadrilateral elements, defining at the same time a plane panels configuration, two optimization procedures have been developed. Starting with an analytic approach, it is impossible to define a set of rules that are able to generate efficiently a mesh corresponding to the previously set goals. For this reason, gradient based methods, such as the Force Density Method, as well as evolutionary methods, such as Genetic Algorithms, have been applied separately to benchmark shapes and a real case study, in order to compare their efficiency. All the free form surfaces are defined and handled by means of a commercial NURBS based software. Instead, its implemented VB based programming language has allowed to develop all the presented optimization procedures. Due to the smoothness of the solution domain of these specific problems, gradient based procedures seem to be the most efficient in the rapidity of convergence to the optimal or sub-optimal solution.