Optimization Of Branching Structures For Free-Form Surfaces Using Force Density Method

Branching structures are mechanically efficient in supporting large-span structures, such as free-form roofs. To support a roof with a specified geometry, we present a novel shape and topology optimization method to find the optimal branching structure in this paper. In the proposed method, the branching structure is modelled as a cable-net, while the reaction forces from the roof are taken as external loads. The force densities of the members are the design variables. The optimal branching structure can be obtained by minimizing one of the several proposed objective functions. The shape of the branching structure represented by the nodal coordinates is determined by solving the linear equilibrium equations. The topology is optimized by removing the members with small axial forces and incorporating the closely spaced nodes. The cross-sectional areas can be easily calculated, if the allowable stress is assigned. Hence, it is very convenient to simultaneously optimize the cross-section, shape, and topology of a branching structure. Numerical examples show that this method can be easily applied to a 2D problem. For a 3D problem, the constraints on the reaction forces should be relaxed. Considering the roof supports as variables is also an effective solution for 3D problems

Application of Timber and Wood-based Materials in Architectural Design using Multi-objective Optimisation Tools

Digital fabrication leads architects and structural engineers to modify the design optimisation methodology. The designers, as never before, are facing new technologies developed in the search for new materials based, among others, on wood components and the improvement of manufacturing methods at the same time. In this process, the material and manufacturing technology adjustment to desired aesthetic outcomes is possible not only by the material used but also by the self-organisation of the structure's optimisation. New fabrication techniques linked with topology optimising software change traditional load-bearing systems designing using timber and wood-based materials. Multi-objective optimisation research indicates that timber might be a comprehensive material based on various applications from low-tech to cutting-edge contemporary fabrication technologies. The article presents new tools and methods for the optimisation of structural elements. A case study based on interdisciplinary architectural and structural optimisation suggests the possible effective research-based design. Comparing contemporary buildings with wood load-bearing structures explains timber usage's diversity and characteristics in modern design

The effect of geometry and topology on the mechanics of grid shells

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 128-131).The use of grid shell structures in architecture and structural engineering has risen in the past decade, yet fundamental research on the mechanics of such structures is lacking. Grid shells are long span structures comprised of a lattice of single layer members forming a curved surface. Grid shells can be made of a wide range of materials from steel to wood. They have potential to be used in readapting existing spaces or in new aesthetically pleasing structures. By studying their mechanics, engineers can be more effective at the schematic phase of design so that the potential of grid shells can be maximized. This research conducts a parametric study that varies the topology and topography of grid shells. The parametric space is framed around real-world design constraints including the grid spacing, panel shape, span-to-height ratio and the use of double curvature. In this thesis, the buckling capacity is evaluated using finite element analysis for two typical grid shell geometries: the spherical cap and the corrugated vault. First, a spherical cap is considered for which an analytical solution exists and therefore the accuracy of the numerical procedure is validated. Simple closed-form solutions are derived using the concept of the equivalent continuum and compared to the numerical models. Then, the parametric study of the spherical cap is performed including variations of the grid spacing, the span to height ratio and the panel shape (triangles and quadrilaterals). Having determined the efficiency of the computational tool the study is extended to the barrel vault. Here the new features of the analysis are the use of double curvature by introducing corrugation along the edge and the crown. By understanding the fundamental mechanical behavior of grid shells, design guidelines aimed to maximize their capacity and efficiency and intended to facilitate the discussion between architect and engineer are proposed.by Samar Rula Malek.Ph.D

Iterative geometric design for architecture

This work investigates on computer aided integrated architectural design and production. The aim is to provide integral solutions for the design and the production of geometrically complex free-form architecture. Investigations on computer aided geometric design and integrated manufacturing are carried out with equal importance. This research is considering an integral and interdisciplinary approach, including computer science, mathematics and architecture. Inspired by fractal geometry, the IFS formalism is studied with regards to discrete architectural geometric design. The geometric design method studied provides new shape control possibilities unifying two separate design paradigms of rough and smooth objects. Capable to design fractal geometric figures, the method also covers the generation of classical objects such as conics and NURBS-curves. Close attention has been paid to the design of iterative free-form surfaces, which are composed entirely out of planar elements. A surface method based on projected vector sums is proposed. The resulting geometric figures are expressed in a discrete form and can be easily translated into a coherent set of constructional elements. The studies for translation of the geometrical elements into constructional elements consider integrated manufacturing. Addressing and numbering of the elements by iterative geometric design are investigated and compared to lexicographically ordered addressing systems, in order to provide an adequate data structure for the design, production and assembly of the constructional elements. For the generation of the data describing constructional elements, problems related to thickening and offset meshes are discussed. Once the global geometry of the constructional part has been computed, parameters are defined for generic automated detailing. Hereby the entire description of the constructional elements is completed. These elements are mapped and packed with regards to the coordinate system of a CNC-machine and the properties and the dimensions of the raw material, providing the complete set of workshop plans needed for integrated manufacturing. For automated generation of machine instructions (G-code), machining strategies – depending on the type of machine used, tool and material properties – are elaborated. Finally, the integrated digital design methods studied within the scope of this thesis are tested and verified by the realization of different reduced scale prototypes. The studied applications range from bearing vault structures to fractal and smooth timber panel shell structures. The developed methods have shown to be efficient for the design and the realization of geometrically complex architectural objects. The required planning effort to handle and manipulate the design and the production data has been greatly reduced. Some of the proposed methods have proved to be robust and general enough to be applied on real world applications. Iterative geometric design provides high degree of design possibilities offering an efficient tool for the creation of smooth and rough free form objects. The possibility to incorporate successive folds in free-form objects allows structural applications

CAAD e Criatividade, uma experiência com arquitetura fractal

Esta pesquisa resulta da experiência realizada com alunos de Arquitetura a partir da introdução de conceitos da geometria fractal na composição arquitetônica. Os autores elaboraram um conteúdo didático para o Ambiente Virtual de Aprendizagem em Arquitetura e Design, que aborda o potencial dos fractais como sistema generativo de formas no projeto arquitetônico assistido por computador (CAAD). A criação da disciplina" CAAD e criatividade" utiliza de estratégias pedagógicas específicas para o ensino de fractais na arquitetura e para o ensino a distância, que são explicadas neste artigo.Esta investigación es el producto del resultado de una experiencia hecha com alumnos de arquitectura con base en la introducción de conceptos de la geometría fractal en la composición arquitectónica. Los autores elaboraron un contenido de enseñanza para ser utilizado en el Ambiente Virtual de Aprendizaje en Arquitectura y Design, que aborda el potencial de los fractales como sistema generativo de formas en el proyecto arquitectónico a través del computador (CAAD). La creación de la asignatura 'CAAD y creatividad' es para utilizar estrategias pedagogicas especificas para la enseñanza de los fractales en la arquitectura y para la enseñanza a distancia, que se explican en el presente artículo.This research results from the experience held with architecture students starting from the introduction of fractal geometry concepts for architectural composition. The authors elaborated a didactic content for the Architecture and Design Virtual Learning Environment about the potential of the fractals as generative shape system in the computer-aided architectural design. The creation of the 'CAAD and Creativity' course uses specific pedagogical strategies in teaching fractals in the field of architecture as well as for distance teaching, which are explained in this article

Sobre dimensões fractais de ambientes construídos e naturais

In this study, fractal analysis is applied in the evaluation of the visual complexity of historic buildings and the surrounding natural environment. The fractal dimension and its approximations, quantified through the box-counting method, are used to define the general and local complexity of digital images of houses and landscapes. The essential properties of the box-counting method are discussed and an optimized version of the method is proposed. The hypothesis of the existence of a relationship between the complexity levels of built sites and natural landscapes is analyzed in the well-known case of the city of Amasya, and also for two historical cities in Brazil, Ouro Preto and Pelotas. The findings reveal a strong relationship between the spatial dynamics of fractal dimensions of built and natural environments.En este estudio, se aplica el análisis fractal para la evaluación de la complejidad visual de edificios históricos y ambientes naturales circundantes. La dimensión fractal y sus aproximaciones, encontradas por medio del método de conteo de cajas (“boxcounting method”), se utilizan para definir la complejidad general y local de imágenes digitalizadas de edificios y paisajes. Se discuten las propiedades esenciales del método de conteo de cajas, y se elabora una versión optimizada del método. La hipótesis de la existencia de relación entre el nivel de complejidad fractal de ambientes construidos y de paisajes naturales es analizada para el caso conocido de la ciudad de Amasya, en Turquía, y también para dos ciudades históricas brasileñas, Ouro Preto y Pelotas. Los resultados obtenidos revelan un fuerte vínculo entre la dinámica espacial de dimensiones fractales de los ambientes construidos y naturales. Neste estudo, a análise fractal é aplicada à avaliação da complexidade visual de edifícios históricos e ambientes naturais circundantes. A dimensão fractal e suas aproximações, encontradas via o método da contagem de caixas (“box-counting method”), são usadas para definir a complexidade geral e local de imagens digitalizadas de edifícios e paisagens. As propriedades essenciais do método da contagem de caixas são discutidas, e uma versão otimizada do método é elaborada. A hipótese da existência de relação entre o nível de complexidade fractal de ambientes construídos e de paisagens naturais é analisada para o caso conhecido da cidade de Amasya, na Turquia e, também, para duas cidades históricas brasileiras, Ouro Preto e Pelotas. Os resultados obtidos evidenciam uma ligação forte entre a dinâmica espacial de dimensões fractais de ambientes construídos e naturais

Discriminatory transient mass transfer through reticulated network geometries: a mechanism for integrating functionalities in the building envelope

In this thesis it is demonstrated how mass transfer can be induced within a network of reticulated channels through turbulent mixing, and how this mechanism can be applied as an integrated functional structure in a building envelope. The research is based on suggestions in literature that there are transient modes of mass transfer which are active in termite mounds of the species Macrotermes michaelseni and which do not rely on steady or cross flows: is the interaction of transient air flows, induced or natural, and the geometry found in the mounds – a complex reticulated network of tunnels with variable dimensions – conducive to controlled mass transfer? My original contribution is to show that such mass transfer is possible, to demonstrate the ways which geometry and input flow interact to create turbulent mixing, and to demonstrate how these parameters may be useful to control the flow within and across building elements. The research method is structured around a series of experiments where various geometries, based on the egress complex of termite mounds, are exposed to transient fluid flows, either a controlled, low amplitude oscillation or external turbulent flow. The resulting mass transfer is measured using tracer gas measurements and visualisations using planar laser and/or fluorescent dye. It is found that the oscillations in certain conditions, which involve a combination of geometry and oscillation properties, lead to the emergence of large scale turbulent convection which can increase the mass transfer rates with up to two orders of magnitude over an unperturbed system. It is concluded that such mechanisms are potentially useful to control the flows of heat and moisture within buildings and across building envelopes. The particular properties of the described flows can complement conventional steady flows and expands the repertoire available to the building designer, enabling new types of boundaries and functional integration in the building envelope