Les réseaux de Chebyshev sont des systèmes de coordonnées sur les surfaces que l'on obtient par cisaillement d'un domaine du plan. Ceux-ci sont utilisés en particulier pour modéliser les gridshells qui constituent une construction architecturale notamment reconnue pour son faible coût environnemental. La difficulté principale dans la conception des gridshells est le manque de diversité des formes accessibles. En effet, bien que toute surface admette localement en tout point un réseau de Chebyshev, l'existence globale de ce type de coordonnées n'est possible que sur un ensemble restreint de surfaces. La recherche de conditions suffisantes pour l'existence globale de réseaux de Chebyshev est toujours d'actualité. Un des résultats de cette thèse est l'amélioration de ces conditions. Les possibilités d'améliorations en ce sens étant néanmoins limitées, nous élargissons la perspective en considérant des réseaux de Chebyshev avec singularités. Notre résultat principal est l'existence de réseaux de Chebyshev avec singularités coniques, lisses par morceaux, sur toute surface dont la courbure totale positive est inférieure à $2pi$ et dont la courbure totale négative est finie. Notre preuve est constructive, ce qui permet de déterminer ces réseaux dans des cas pratiques. Nous avons implémenté un cas particulier de notre algorithme dans le logiciel Rhinoceros et nous présentons des exemples de réseaux construits par cette méthode / Chebyshev nets are coordinate systems on surfaces obtained by pure shearing of a planar domain.These nets are used in particular to model gridshells, an architectural construction which is well-known for its low environmental impact. The main issue when designing a gridshell is the lack of diversityof the accessible shapes. Indeed, although any surface admits locally a Chebyshev net at any point, the global existence for these coordinate systems is only possible for a restricted set of surfaces. The research for sufficient conditions ensuring the global existence of Chebyshev nets is still ongoing. A result achieved in this thesis is an improvement on these conditions. Since the improvement in this direction seems to be rather limited, we broaden the perspective by introducing Chebyshev nets with singularities. Our main result is the existence of a global Chebyshev net with conical singularities on any surface with total positive curvature less than $2pi$ and with finite total negative curvature. Our proof is constructive, so that this method can be applied to practical cases. We have implemented a special instance of this algorithm in the software Rhinoceros and some discrete Chebyshev nets constructed using this method are presented

Following a well-documented rise in the popularity of concrete shell application in the 20th century, thin concrete shells have experienced a global decline despite their potential as efficient structures with an economy of material use with aesthetics benefits. This phenomenon is subject to geographically determined socio-economic conditions and competition from other building solutions as a result of technological advancement in alternative construction systems. Importantly, their decline was attributed to limitations inherent to concrete shell formwork and construction methods. Being able to produce efficient shaping did not ensure that this method of construction is most cost efficient as it still remains difficult to construct double curved surfaces. The thesis addresses the limitations associated with past and present concrete shell building by proposing the use of actively-bent gridshells as re-configurable and reusable formwork for concrete shells to be designed and built. The hypothesis uses deployable scissor-jointed actively-bent gridshells as re-configurable and reusable formwork for concrete shell construction. This was developed from a series of Flash research (Benjamin, 2012) as student construction workshops to investigate the design and creation of actively-bent gridshells held between December 2008 and March 2011 in Sheffield. In this study, to understand this new system, scaled models of actively-bent gridshells were used as preliminary design aid. Deployed into three dimensional forms from a flexible flat grid mat, the structures were rigidized by bracing through triangulation restraints. The temporary rigid structure was subsequently enveloped with fabric onto which concrete was applied to create the concrete shell, thus acting as formwork. This formwork was then removed following the curing of the concrete cast to be reused repeatedly, or reconfigured into another concrete shell form. Hence, the thesis draws on the concepts, principles and ideas pertaining to three key architectural technologies: 1. concrete shell, 2. actively-bent gridshells and 3.fabric formwork. The thesis then presents a series of four prototype concrete shells constructed from different materials spanning between 1.3 meters and 2.45 meters in the workshops at the University of Edinburgh built between August 2014 and September 2015. For each experimental construction, the process of gridshell construction, fabric formwork preparation, concrete casting, gridshell formwork decentring and different design elements of openings, edges and anchorage abutments were analysed and discussed under the themes of construction, architectural tectonics and structure. The tectonic of process and material is understood and discussed based on the idea of stereogeneity (Manelius, 2012). Specifically, the relationship between gridshell as formwork and the concreting process was studied, analysed and assimilated in concrete shells built with progressive sophistication and elegance, culminating in a doubly-curved concrete shell that demonstrated both synclastic and anticlastic geometries, with further abutment simplification, edge leaning and physical openings incorporation. The study concludes with a physical concrete shell model formed by applying concrete onto fabric formwork to cover the Weald and Downland Jerwood gridshell. In the 1:20 scaled model, the proposed method is speculatively applied onto fabric stretched between pre-determined curvatures of the as-built gridshell. This formwork was subsequently removed for reuse, re-deployed and reconfigured. Using finite element analysis, the structural behaviour of the gridshell made of glass-fibre reinforced tubes and structural characteristics of the resultant concrete shell was checked. The interaction between the three technologies are discussed architectonically and structurally to inform guidelines for potential life-scale application. The thesis evidences the feasibility of the proposed system. It re-purposes a scaled model of a deployable gridshell as a physical modelling tool to facilitate concrete shell design, for both pure compression shells and "improper" shells, demonstrating its adaptability. It also promotes and reinvigorates concrete shells as possible architectural systems serving to instigate future research to revive concrete shell construction as an intelligent and intuitive way of creating structures with material economy, structural efficiency and visual elegance.

Doppelt gekrümmte Schalen und Gitterschalen sind Tragsysteme, die, obwohl in Ihrer Wirkungsweise grundsätzlich verschieden, besonders für den Einsatz von Textilbeton geeignet sind. Aufgrund ihrer doppelten Krümmung weisen derartige Tragsysteme zahlreiche Besonderheiten hinsichtlich Formfindung, Lastabtrag und Herstellung auf. Anhand eines Ausführungsbeispiels von monolithischen Schirmschalen und Konstruktionsstudien zu Gitterschalen werden die Strukturkonzepte und ihre Auswirkungen auf das Tragverhalten, das Bewehrungskonzept und die Auswirkungen auf die Herstellung sowie die Bauteilfügung erläutert. / Structural systems based on double curved monolithic shells or gridshells are both characterised by their good load bearing behaviour depending on the chosen geometry. Although both systems are different regarding their functionality they are suitable applications for TRC while taking advantage of the main constructive and design characteristics of the material. In describing an execution example of an umbrella-shaped shell-structure and design studies on gridshells the relation between structural concept and load bearing behaviour and the relation between the reinforcement concept and production as well as joining are discussed.

Doppelt gekrümmte Schalen und Gitterschalen sind Tragsysteme, die, obwohl in Ihrer Wirkungsweise grundsätzlich verschieden, besonders für den Einsatz von Textilbeton geeignet sind. Aufgrund ihrer doppelten Krümmung weisen derartige Tragsysteme zahlreiche Besonderheiten hinsichtlich Formfindung, Lastabtrag und Herstellung auf. Anhand eines Ausführungsbeispiels von monolithischen Schirmschalen und Konstruktionsstudien zu Gitterschalen werden die Strukturkonzepte und ihre Auswirkungen auf das Tragverhalten, das Bewehrungskonzept und die Auswirkungen auf die Herstellung sowie die Bauteilfügung erläutert. / Structural systems based on double curved monolithic shells or gridshells are both characterised by their good load bearing behaviour depending on the chosen geometry. Although both systems are different regarding their functionality they are suitable applications for TRC while taking advantage of the main constructive and design characteristics of the material. In describing an execution example of an umbrella-shaped shell-structure and design studies on gridshells the relation between structural concept and load bearing behaviour and the relation between the reinforcement concept and production as well as joining are discussed.