Before the introduction of NURBS-based CAD software and optimisation, the design of form-resistant structures was based on the use of either experimental tools (physical form-finding) or analytical surfaces, and architects were challenged in the articulation of spaces from the intrinsic characteristics/rules of structural forms. An outstanding example of this kind is provided by the Church of Longuelo, which was built by architect Pino Pizzigoni in Italy, between 1961-1966. It was conceived as composed by two major elements – an irregular frame and a set of shells suspended to it. The entire design process was based on the calculation of the frame on which the shells have been just added as a dead load. This paper presents one possible way to redesign the church parametrically. Comparison with the original design is not performed at the final formal level, which can logically differ, but around the concepts behind the project. The aim is to show how current digital design and optimisation tools are affecting the way architects design. But, at a higher level, the purpose is also to highlight where conceptual design is now taking place in the process.

In book: "AAD Algorithms-Aided Design. Parametric strategies using grasshopper", (pp.352-359). Publisher: Le Penseur. Editor: Arturo Tedeschi.

In architecture and structural engineering, ‘form-finding’ identifies the process of designing optimal structural shapes by using experimental tools and strategies, i.e. physical models, to simulate a specific mechanical behaviour.

The reverse hanging method is the oldest and probably most diffused form-finding technique for arches, vaults and shells – a physical model, made with elastic cables or membranes with no rotational stiffness, is first subject to gravitational forces to obtain a structural state of pure tension; such a form, which is called “funicular”, is then inverted to identify the mechanical compression-only situation.

This principle was first mentioned in a publication by Robert Hooke in 1675 . With a Latin anagram, only solved in 1701, he proposed to reverse the curve which was generated by a hanging chain, under self-weight and supported only at its ends, in order to define the optimal structural form of an arch. Such a curve is called “catenary” when the chain presents a constant distribution of weight . Initially confused with a parabola by Galileo Galilei, the catenary was then mathematically described by David Gregory in 1697.

Reciprocal systems based on superimposition joints, i.e. where un-notched bars sits on the top or in the bottom of each other, could be regarded as being intrinsically three-dimensional because of their natural out-of plane development. This paper presents seven of these three-dimensional configurations, conceived and built by the students of the Master of Science in ‘‘Architectural Design’’ at Aalborg University. They have been developed as an integral part of a 2-week workshop, organized and run by the authors during the fall semester 2011. Since physical models are instruments that trigger the exploration of new typologies because of the direct interaction they provide with the designer the students were called to deal with the issue of three-dimensionality in reciprocal systems through scale models and actual scale prototypes.

The concept of transferring forces in a reciprocal way has always been related to the use of timber beams, that is, elongated elements. However, planar components can also be considered; circular tiles, squares, triangles and more articulated or irregular geometrical shapes are all valid alternatives. This report proposes an initial exploration of reciprocal systems based on planar elements in order to guide further morphological studies. It also presents some prototypes, which were developed by the students of the Ecole des Ponts in Paris during two design workshops run in 2012 and 2013.

The construction of concrete shells has always been a difficult and expensive procedure. Preparation of complex formworks, as well as placement of curved reinforcing rods require experience and increase the overall cost. Building concrete shells is even more of concern within the Australian context, where the use of simple and rapid technologies has always been a priority. In the Sixties, Italian architect Dante Bini developed and patented a form-finding and construction technique that aimed to solve this issue, the so-called “Binishells”. This paper investigates Dante Bini’s system, from its conception within the Italian environment until the international success which was reached in the USA and Australia.

In book: "Shell Structures for Architecture - Form finding and optimization", (pp.290-294). Chapter: Appendix C. Publisher: Routledge. Editors: Sigrid Adriaenssens, Philippe Block, Diederik Veenendaal, Chris Williams.

Genetic algorithms are a subclass of evolutionary algorithms. A genetic algorithm (GA) is defined by Goldberg as a “search algorithm based on the mechanics of natural selection and natural genetics”, but another definition, more focused on its way of functioning, is provided by John R. Koza in his 1992 book, “Genetic programming: On the Programming of Computers by Means of Natural Selection”: “The GA is a highly parallel mathematical algorithm that transforms a set (population) of individual mathematical objects [...], each with an associated fitness value, into a new population (i.e. the next generation) using operations patterned after the Darwinian principle of reproduction and survival of the fittest and after naturally occurring genetic operations (notably sexual recombination)”. In other words, in a random population of potential solutions, the best individuals are favoured and combined in order to create better individuals at the nextgeneration.

In book: "Shell Structures for Architecture - Form finding and optimization", (pp.224-236). Chapter: 18. Publisher: Routledge. Editors: Sigrid Adriaenssens, Philippe Block, Diederik Veenendaal, Chris Williams.

Since the introduction of digital technologies, computational design and optimization has been gradually replacing practice based on physical models. Even if born as a set of mere solution strategies, architectural and structural design optimization seems also to be effective in supporting conceptual design. This aspect is highlighted through two design exercises of computational morphogenesis using genetic algorithm (GA). Two key aspects emerge from such processes: the possibility of freely formulating objective functions apart from structural performances, and the opportunity for designers to actively interact throughout the computational process.

Reciprocity is a structural principle that has fascinated designers and builders throughout the world since ancient times. Despite the topic's having been studied by various academics, designers and researchers, a critical overview of the references is still missing, as is an outline and discussion of the current and future promising research/design issues. Further, no single text provides an exhaustive definition of the principle of structural reciprocity and it must be critically reconstructed from several different sources. This paper aims to fill in these gaps, providing a complete and annotated list of references, in which historical examples, as well as patents, research articles and terminological issues are discussed. A consistent definition of structural reciprocity is also proposed, and the promising developments of such a principle are outlined in order to guide designers and researchers in the future.