This thesis explores the use of small diameter, round timber in the construction of lightweight gridshell structures. The project intention is to develop a simple and accessible construction method, based on locally available material that embraces a diverse range of technology. The design is developed using a material based approach, which first explores the behavior and limits of the material through testing at full scale. This information is used in a rapid prototyping process of scale modeling which focuses on material and construction sequence to develop a structural system. Using available materials as a design parameter, the work is an exploration of how the gridshell system can be adapted to the specific context of rural Nova Scotia. This design method is explored through the design of a craft school at the Ross Creek Centre for the Arts in Ross Creek, Nova Scotia, Canada.

The bending of elastic strips and rods is a field of research that continues to offer new possibilities for exploration. This dissertation focuses on two distinct problems within this context. These are the search for the equilibrium shape of thin inextensible elastic strips, such as a M�öbius strip made out of paper, and the optimal shape of tapered columns that are stable against buckling. A theoretical approach based on the principle of virtual work is used to investigate both problems. This produces novel governing non-linear differential equations that describe both equilibrium and form. In order to discover the equilibrium shapes, numerical algorithms are developed that are based on Dynamic Relaxation. There are two ways in which they are used, one as an explicit form-finding tool, and the other as a way of solving differential equations. Results are provided that extend current theoretical models. The numerical schemes produce three-dimensional shapes for strips, going beyond the canonical Möbius strip, and solution shapes for tapered columns made from non-linear elastic materials. With the aid of analytical and numerical tools, finding the form of the M�öbius strip and the tallest possible column are interesting challenges in the search for new shapes that are driven by physical and material rules. These have applicability in structural engineering, architecture, nano-technology and even artistic endeavour.

学位授与大学：京都大学 ; 取得学位: 博士(工学) ; 学位授与年月日: 2007-09-25 ; 学位の種類: 新制・課程博士 ; 学位記番号: 工博第2856号 ; 請求記号: 新制/工/1420 ; 整理番号: 25541 / Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第13385号 / 工博第2856号 / 新制||工||1420(附属図書館) / 25541 / UT51-2007-Q786 / 京都大学大学院工学研究科建築学専攻 / (主査)教授 加藤 直樹, 教授 上谷 宏二, 准教授 大﨑 純 / 学位規則第4条第1項該当

The thesis project aims to investigate a Form Finding process as a design tool as well as the generator of a structural system, in this case a process of intersecting cones to create surface network logic, for a sailing school at Lidingö, Stockholm. Specifically the research aims at the blurring of the cone shape and the diffusion of a cellular logic by a process that increases the complexity and definition of the whole system. And as a result, a design method that generates and shapes the space.

Esta dissertação apresenta uma revisão histórica dos trabalhos acerca de superfícies minimais, ressaltando a pertinência da analogia entre a busca de superfícies de mínima área e a busca de formas de membranas estruturais sujeitas a um estado de tensões superficiais, homogêneo e isótropo. São colocados alguns conceitos geométricos das superfícies parametrizáveis, com base na geometria diferencial, a fim de realizar o equilíbrio diferencial de membranas e determinar as suas equações de equilíbrio. Além disso, é apresentada uma metodologia puramente geométrica para a determinação de superfícies minimais, baseada na minimização do funcional da área, dado pela soma das áreas das facetas triangulares nas quais a superfície é discretizada. O trabalho discute a formulação matemática do problema e apresenta resultados obtidos tanto por meio das rotinas implementadas no software MATLAB quanto por meio daquelas da biblioteca de otimização deste mesmo software. Finalmente, são realizados alguns exemplos e um teste de convergência, comparando as superfícies resultantes dos métodos numéricos com suas respectivas respostas analíticas. A geometria final de um dos exemplos é verificada por meio da analogia dos filmes de sabão, realizando-se uma análise não-linear de equilíbrio através do software Ansys. As soluções foram bastante satisfatórias, resultando em formas muito próximas das analíticas e com pequenos erros relativos das áreas. O teste de convergência também comprovou que o refinamento da discretização leva a uma solução mais próxima da desejada. Portanto, os procedimentos apresentados podem ser empregados no processo de busca da forma de membranas estruturais. / This dissertation presents a historical review on the theoretical developments on minimal surfaces, highlighting the important analogy between the problems of finding minimal area surfaces and finding membrane surfaces with homogeneous and isotropic stress fields. Some geometric concepts of the parametric surfaces are placed, on the basis of differential geometry, in order to do the differential equilibrium of membranes and to achieve its equilibrium equations. Moreover, a purely geometric methodology for the determination of minimal surfaces is presented, based on the minimization of the area functional, which is computed by the simple addition of a finite number of triangular facet areas in which the surface is divided. It discusses the mathematical formulation of the problem as well as some results obtained with the algorithms implemented in MATLAB and others obtained with the aid of MATLAB optimization routines. Finally, some examples and a convergence test are produced, comparing their analytical and numerical results. The final geometry of one of examples is verified by means of the soap film analogy, with a nonlinear equilibrium analysis through Ansys. The solutions have been sufficiently satisfactory, resulting forms very close to the analytical ones and with small areas relative errors. Convergence test also confirm that the method lead to numerical solutions as close to the analytical one as required, as long as the triangular facets mesh is refined. Therefore, the presented procedures can be used in structural membranes form finding.

It is believed that structures and actuation systems should be tightly integrated together in the future to create fast moving, efficient, lightweight dynamic machines. Such actuated structures could be used for morphing aircraft wings, lightweight actuated space structures, or in robotics. This requires actuators to be distributed through the structure. A tensegrity structure is a very promising candidate for this future integration due to its potentially excellent stiffness and strength-to-weight ratio, and the inherent advantage of being a multi-element structure into which actuators can be embedded. Development of these machines will utilise expertise in several fields, involving kinematics, dynamics, actuation and multi-axis motion control. The research presented in this thesis concerns the study of multi-axis actuated tensegrity structures. A form-finding method has been developed to find stable geometries and determine stiffness properties of the type of tensegrity structure proposed. It has been shown that a tensegrity structure, with practical nodes of finite size, can be designed with actuated members to give shape-changing properties while potentially allowing a good stiffness to mass ratio. An antagonistic multi-axis control scheme has been developed for the tensegrity structure. The describing function technique has been used to analyse the dead band controller in the control scheme, giving a stability criterion. An experimental actuated tensegrity system has been designed and built incorporating pneumatic muscles controlled by switching valves. Mathematical models for the experimental actuated tensegrity system have been developed in detail, including the pneumatic actuation system and the structure geometry. The dynamic behaviour of the tensegrity system has been investigated via several simulation studies, using the developed models and the proposed control scheme. Experimental validation has been successfully conducted. The multi-axis control scheme can accurately control the tensegrity structure to achieve shape changes while maintaining a desired level of internal pre-load. The mathematical models can be used as a basis for further development.

Form-finding in Architecture looks at processes in nature to discover a more correct way in which to organize building. It is a study into the capability of discovering optimum form, dynamic adaptability, and exposes a set of unique relationships not relevant to Architecture previously. The beauty of these objects does not have to be designed. It is an emergent property of natural form. However, the wonder lies not in aesthetics, but in the manner in which natural forms come into being seemingly without a plan, at a multitude of scales, and in a vast array of materials. Alone, pattern in nature opens a vast array of potentialities for the study into new methods of architectural design. It is important to note that this inquiry will not be into the aesthetics of self-organized pattern, but the mathematical and procedural processes of formation itself. This study forms a set of principles, methodologies and tools for structuring a full-scale form-finding inquiry through the self-organization of pattern in nature. Following this inquiry one should be able to apply the organizational principles of patterning in nature, specifically breakdown patterns, to inform the programmatic design and layout of shopping malls. The rules set forth outline the formation of breakdown patterns, and the ordering of shopping malls. Through the use of parametric modeling software and computer programming language, sets of digital models efficiently explore of the vast number of potential pattern organizations by mimicking their formation in digital space. Through computational scripting, digital models also reveal formation changes due to the adaptation to site, circulatory loads, and spatial distribution, while still maintaining the laws of pattern formation.

Esta dissertação apresenta uma revisão histórica dos trabalhos acerca de superfícies minimais, ressaltando a pertinência da analogia entre a busca de superfícies de mínima área e a busca de formas de membranas estruturais sujeitas a um estado de tensões superficiais, homogêneo e isótropo. São colocados alguns conceitos geométricos das superfícies parametrizáveis, com base na geometria diferencial, a fim de realizar o equilíbrio diferencial de membranas e determinar as suas equações de equilíbrio. Além disso, é apresentada uma metodologia puramente geométrica para a determinação de superfícies minimais, baseada na minimização do funcional da área, dado pela soma das áreas das facetas triangulares nas quais a superfície é discretizada. O trabalho discute a formulação matemática do problema e apresenta resultados obtidos tanto por meio das rotinas implementadas no software MATLAB quanto por meio daquelas da biblioteca de otimização deste mesmo software. Finalmente, são realizados alguns exemplos e um teste de convergência, comparando as superfícies resultantes dos métodos numéricos com suas respectivas respostas analíticas. A geometria final de um dos exemplos é verificada por meio da analogia dos filmes de sabão, realizando-se uma análise não-linear de equilíbrio através do software Ansys. As soluções foram bastante satisfatórias, resultando em formas muito próximas das analíticas e com pequenos erros relativos das áreas. O teste de convergência também comprovou que o refinamento da discretização leva a uma solução mais próxima da desejada. Portanto, os procedimentos apresentados podem ser empregados no processo de busca da forma de membranas estruturais. / This dissertation presents a historical review on the theoretical developments on minimal surfaces, highlighting the important analogy between the problems of finding minimal area surfaces and finding membrane surfaces with homogeneous and isotropic stress fields. Some geometric concepts of the parametric surfaces are placed, on the basis of differential geometry, in order to do the differential equilibrium of membranes and to achieve its equilibrium equations. Moreover, a purely geometric methodology for the determination of minimal surfaces is presented, based on the minimization of the area functional, which is computed by the simple addition of a finite number of triangular facet areas in which the surface is divided. It discusses the mathematical formulation of the problem as well as some results obtained with the algorithms implemented in MATLAB and others obtained with the aid of MATLAB optimization routines. Finally, some examples and a convergence test are produced, comparing their analytical and numerical results. The final geometry of one of examples is verified by means of the soap film analogy, with a nonlinear equilibrium analysis through Ansys. The solutions have been sufficiently satisfactory, resulting forms very close to the analytical ones and with small areas relative errors. Convergence test also confirm that the method lead to numerical solutions as close to the analytical one as required, as long as the triangular facets mesh is refined. Therefore, the presented procedures can be used in structural membranes form finding.

This diploma thesis deals with problem of design and calculation of membrane structure. Design proces of light and airy structure was demonstrated on conical shaped roof in the finite element analysis program RFEM. The structure was loaded in the virtual wind tunnel in the program RWIND. Results were compared with the values given in the literature. A comprehensive guide for the design of membrane structures has been created. Subsequently, the influence of design stages on the internal forces was demonstrated. Membrane structures are very sensitive to construction stages, because it is not possible to prestress all membrane surfaces at once. Program by DLUBAL software s.r.o. was used for form-finding analysis during construction stages.

The thesis project wants to research the concept of Mongrel Geometries, the development of a spatial system that considering the processes of Form Finding as a design tool and their tight relationship with the model of efficiency and structural optimization, start questioning their problem/solving based procedure with the purpose of understanding which are the potentials of these methods to introduce within the built environment new atmospheric and programmatic qualities. / The intervention consists in the re-design of the Train Station and of the incorporated Bus Terminal, resolving the general connective tissue, and stimulating the public activity towards the sea side. The Terminal wants to be intended not only as a place of departure but also as an attractive place itself.