Bending-active structures produce efficiently complex curved shapes made of flat or straight elements . To this purpose, these are brought into a deformation state of elastic bending. In the past, such structural systems were empirically explored and adopted in vernacular architecture contexts because of their efficiency. For instance arches and domes were produced by curving branches or reeds. After being neglected for years, nowadays the availability of simulation techniques, which gives control of form-finding and verification processes, renews the appeal of such lightweight and efficient structures [2,3,4,5,6,7]. While in the past the main advantage was to have a cheap technology to build even doubly curved surfaces, nowadays the main reason to adopt this technique lies in the reduced weight and the economy of producing flat panes regardless of the curvature they will have once installed .
The bending-active technology characterizes different structural types such as plate shells , hybrids composed of membranes with elastically bent battens , and various types of adaptive and elastic kinetic structures .
The workflow adopted for the FlexMaps Pavilion (Fig. 1) uses a fully automated approach for the definition and the control of the mesostructures (base geometry) and consequently of the material behavior. In the present work, an existing optimization method  is being utilized in a novel application domain of architectural-scale objects. Similar to other architectural-scale bending-active methods [8, 11], the present method allows for controlling the shape by means of a numerical form-finding. Hence, the load-bearing elements are altered in search for their best configuration, so that once assembled the obtained shape results as close as possible to an input target geometry. This is a step towards a designer/artist-oriented tool.
Compared to other architectural methods used for bending-active structures, another novelty of the present approach lies in the assembly. In post-restrained structures where the components are bent and fixed to the ground, a common approach is to post-tension the overall shape that initially lies in the flat position. This procedure requires external facilities, a large work area and usually requires the whole shape to be developable. Conversely, the FlexMaps approach is based on bending and assembling the single mesostructured element, which lays flat in the rest configuration. Eventually, the final shape of the structure results from internal elastic forces that redistribute among the elements once they are all connected. The construction sequence consists in bending the panels, one at a time, and progressively connecting them to the neighboring ones. This procedure has the advantage of requiring only a minimal amount of bending energy and can be performed by hand. The two cost-saving characteristics of the FlexMaps Pavilion originate from the easy fabrication that is obtained by producing a flat segmented array of panels, and from the simple assembly procedures that does not require any specialized manpower nor other tools. In FlexMaps examples, active-bending should be regarded in a broader sense of either bending and torsion deformations.
The main issue of bending-active structures is that the elastic bending causes initial stress. This lowers the stress reserves that the structure may attain due to external loading. The spiral geometry, which is the main idea behind the present project, tackles this point. Having a spiral path instead of a linear path brings to minor bending stress for the same curvature. This phenomenon can be well observed from the example in Fig. 2, in which it is reported the stress obtained through FEA for three different panels that are deformed with the same given curvature.
Moreover, the spiraling geometry can be favorably modified to obtain bespoke FlexMaps panels in order to accommodate local curvature demands. A modification in the geometry consequently varies the bending stiffness, which in turn affects the bent shape, since all the panels tend to preserve a uniform stress once assembled. This approach corresponds to designing custom mechanical properties without changing the material but only by acting on the geometric parameters of spirals.
The objective of this work is to apply and validate the algorithm  for architectural design intents. The opportunity of testing the feasibility and extending this work from small objects to large scale objects has been provided by the call for “Competition and exhibition of innovative lightweight structures” organized in 2019 by the IASS Working Group 21 “Advanced manufacturing and materials” . The competition posed as a limit for the experimental structure to fit a maximum volume of 4.00x4.00x4.00 meters. Moreover, all the components should have fit into a maximum of six boxes up to 1.00x0.75x0.65 m and \(32\ kg\) each in order to be transportable by airplane.
We designed a non-trivial shape of a non-developable twisted arch with varying curvature demand, which has been later segmented in patches of the dimensions required for shipping. Special attention has been given to the plywood material selection, whose properties have been used to inform the reduced model that is embedded in the optimization routine, and for a subsequent FE validation of the design. In this pipeline, this latter step is fundamental to verify the real structural behavior of the Pavilion and to check its safety.