This thesis investigates minimal surfaces in design and researches their potential for constructability in concrete through the creation of physical prototypes with the design of two mold making processes, one being sacrificial and the other reusable. The study starts by acknowledging that minimal surfaces have been extensively explored in the field of differential geometry for decades. In spite of the availability of geometric definitions which provide the basic background for digital model generation (which in this text is assumed to be equal to design itself), minimal surfaces inspired very few people in their architectural design. This study attempts to look into the wider implications of minimal surfaces for architecture by taking up the challenge of designing and realizing various processes of mold making for the fabrication of such surfaces in concrete. Throughout this study, a gradient of complexity in the definition and digital modeling of minimal surfaces will be included as well as a variety of production methods in a research and fabrication based process, in order to investigate the correlation between what can be designed and what can be produced. I shall begin with a historical survey of the constructability of surfaces in thin shell concrete to provide background information for the reader. This chapter on the evolution of concrete structures presents a compilation of selected projects to illustrate the progress of thin shell construction throughout the history of architecture. It is here that I review what happened, why, and who made it possible. I draw heavily on published scholarly studies as most of the selected projects are cornerstones of the evolution of architecture and have been discussed by many others. Here, I simply attempt to remind the reader of the achievements of these projects in order to justify why investigation of the constructability of minimal surfaces may be the next step in the evolutionary process. After this section, the mathematics of surfaces in the complex plane is discussed based on information retrieved from many excellent resources. Here, the intention is to acquire information related to descriptions of various minimal surface types in differential geometry in order to be able to generate their representations in the digital environment. It would have been impossible to generate digital representations of minimal surfaces without the knowledge acquired through these descriptions. The last section provides a comparison of ruled surfaces and minimal surfaces meant to reveal the similarities and differences of such surfaces with regard to the principles of digital representation and fabrication. It provides insight into various fabrication techniques and materials to illuminate the design of a making process in which the goal is to know and control every parameter regarding both the design and fabrication of an object. The discussion of the design of a making process for a complexly shaped object provided in this part is followed by discussion of casting prototypes in concrete. In that section, the subject matter is the design and testing of various mold making techniques for the production of concrete prototypes of a selected minimal surface geometry. This section presents an increasing complexity of mold making from a sacrificial mold to a reusable mold.

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.