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p. 1163-1174, The Force density Method [FDM], since Linkwitz and Schek¿s first development [8] in 1970¿s, has been well known as a powerful tool for analytical form-finding and static analysis of self-stressed structures like tensile membranes and cable networks [12]. 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 Ponte Parodi project, by UNStudio Amsterdam, a multifunctional building to be located on the waterfront of Genoa, Italy.

p. 1154-1162, 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.

p. 1163-1174, The Force density Method [FDM], since Linkwitz and Schek¿s first development [8] in 1970¿s, has been well known as a powerful tool for analytical form-finding and static analysis of self-stressed structures like tensile membranes and cable networks [12]. 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 Ponte Parodi project, by UNStudio Amsterdam, a multifunctional building to be located on the waterfront of Genoa, Italy.

p. 1154-1162, 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.

p. 1154-1162, 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.