From Historical and Theoretical Analysis of Representation and Geometry to Topology for Structural Optimization

To study Geometry and Representation from a theoretical point of view, it is certainly necessary to refer critically to the historical-anthropological climate of their genesis. This training approach allows to see and understand their evolution/impact for new approaches to the genesis of architectural/engineering artefacts, both from a configurative and structural point of view. On the other hand, if we consider the typical primitive/intuitive approaches of Representation, up to its rigorous elaborations based on a consistent knowledge of Optics and Geometry, it is possible to recognize the strong links between artistic experience, mathematical contribution and scientific elaboration. It is therefore possible to offer a broad overview of the "state of the art" relating to critical sector studies, conducted both in Italy and abroad, to underline:- how awareness in the multiple fields of Geometry is expressed in the methods and process of realization of architecture and engineering, from conception to its realization;- how Representation stands as a means between theory and construction.In this sense we focus on Topology and its genesis, as an area of Geometry that can be concretized in Structural Optimization, in order to verify the promising results that these procedures ensure in terms of reducing the use of material and design iterations, without neglecting the architectural/engineering quality, also in configurative terms. For this reason, one of the main factors in the growing popularity of this topic is the development, in computational terms, of modern computers, which allow to reliably solve complex analyzes based on FEM (Finite Element Analysis)