40 research outputs found

    A triangular grid generation and optimization framework for the design of free-form gridshells

    Get PDF
    Gridshells have been widely used in various public buildings, and many of them are defined over complex free-form surfaces with complex boundaries. This emphasizes the importance of general grid generation and optimization methods in the initial design stage to achieve visually sound and easy-to-manufacture structure. In this paper, a framework is presented to generate uniform, well-shaped and fluency triangular grids for structural design over free-form surfaces, especially those with complex boundaries. The framework employs force-based algorithms and a connectivity-regularization algorithm to optimize grid quality. First, an appropriate distribution of internal points is randomly generated on the surface. Secondly, a bubble-packing method is employed to increase the uniformity of the initial point distribution, and the points are connected using Delaunay-based triangularization to produce an initial grid with rods of balanced length. Thirdly, the grid connectivity is optimized using a range of edge-operations including edge-flip, collapse and split. The optimization process features a grid relaxation objective which includes the degree of the vertices, leading to improved regularity. As a final step, the grid is relaxed to improve fluency using a net-like method. As part of its contribution, this paper, therefore, proposes a metric for fluency, which can be used to quantitatively evaluate the suitability of a given grid for architectural and structural expression. Two case-study examples are presented to demonstrate the effective execution of the grid generation and optimization framework. It is shown that by using the proposed framework, the fluency index of the grid can be improved by up to 157%

    Effects of different geometric patterns on free form gridshell structures

    Get PDF
    Gridshells are commonly known as structures with the shape and rigidity of a double curvature shell consisting of a grid, not a continuous surface. In recent decades, these structures have attracted significant attention. The impact of various geometric patterns on free form gridshell structures is investigated here to demonstrate the necessity of collaboration between structural and architectural characteristics in enhancing structure efficiency. To that goal, a framework is proposed where three shells are first designed, and then six geometric patterns are formed on them. The main factors for evaluation of gridshells are decreasing the steel weight as an economic index and decreasing the displacement as a structural index, also, finite element method is used for structurally analyzing the gridshells, and the generated gridshells are compared to each other based on the mentioned indices. For the optimization process, an approach is suggested to find the most optimum gridshell, then numerical results show the efficiency of the proposed alternative approach

    Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

    Get PDF
    © 2019 American Society of Civil Engineers. Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifests the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on guideline and surface-flattening methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete nonuniform rational basis spline (NURBS) surface is first divided into a number of patches, and a discrete free-form surface is formed by mapping dividing points onto the surface. The free-form surface is then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the two-dimensional (2D) surface, with grids formed by applying a guideline method. Subsequently, the intersections of the guidelines and the complex boundary are obtained, and the guidelines are divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the three-dimensional (3D) surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes by presenting realistic examples to demonstrate the practical effectiveness of the proposed method

    Isogonal moulding surfaces: A family of shapes for high node congruence in free-form structures

    Get PDF
    International audienceThe design of free-form structures is governed by structural and geometric considerations, the latter ones being closely linked to the costs of fabrication. If some construction constraints have been studied extensively, the question of the repeatability of nodes in free-form structures has rarely been addressed yet. In this paper, a family of surfaces that can be optimized regarding typical geometrical constraints and that exhibit high node congruence is proposed. They correspond to particular meshes of moulding surfaces and are called isogonal moulding surfaces by the authors. The geometrical properties of these surfaces are discussed. In particular, it is shown how to derive Edge Offset Mesh from them. It is also demonstrated that they represent all the possible meshes parallel to surfaces of revolution. Finally, the reader is introduced to some computational strategies linked to isogonal moulding surfaces

    Process analysis and improvments for production of engineered wood structures in an engineer-to-order system

    Get PDF
    Augmenter la part de marché du bois dans la construction non résidentielle est un objectif important dans les pays où les produits forestiers et de bois d'ingénierie jouent un rôle fondamental. Afin de faciliter la production de structures en bois innovantes, il est nécessaire de mettre sur pied des procédures de réingénierie en termes d’analyse de marché et d’amélioration de la productivité. L'objectif principal de cette thèse est de faciliter la production de bois d'ingénierie (produits en lamellé-collé) destiné à être utilisé dans des structures en bois innovantes telles que les résilles en bois. Pour atteindre ce but, trois objectifs spécifiques sont définis. Le premier objectif est de déterminer les phases de production et les opportunités de marché pour la production de résilles en bois. À cet égard, une revue de la littérature académique et de la littérature grise a été réalisée, et vingt échantillons ont été identifiés et analysés à l'aide de diagrammes de processus et de catégorisations. Les résultats ont montré qu’une structure en résille de bois est utilisée dans l'industrie de la construction en Europe et qu'elle est moins connue en Amérique du Nord, ce qui offre une opportunité de marché pour sa production et sa construction. La catégorisation des échantillons étudiés dans les petites, moyennes et grandes structures et l'identification des acteurs pour chaque catégorie fournissent une vue d'ensemble pour les entreprises qui envisagent la production de cette structure. Le deuxième objectif de cette thèse est de fournir un modèle de simulation pour la production de bois lamellé-collé dans de petites usines et le processus d'application de techniques Lean pour apporter des améliorations. À cet égard, le système de production d’une entreprise québécoise a été analysé et un modèle de simulation créé. Afin d'éliminer chaque source de gaspillage, un outil Lean a été suggéré en fonction de la réalité du système à l’étude. Les résultats ont montré une amélioration notable du temps d’attente et de cycle suite à l’utilisation de techniques issues du Lean. Ils ont également contribué à souligner qu’une élimination du gaspillage limitée à 50% pouvait améliorer la considérablement la productivité pour les petites entreprises et s’avérer un premier pas important dans l’implantation du Lean. Le troisième objectif est de fournir un outil de planification et d'ordonnancement de la production dans un contexte de production multi-projets d’ingénierie sur commande (Engineer-to-Order) de bois lamellé-collé. À cet égard, des modèles d'optimisation ont été créés. Le premier modèle (modèle 1) concerne la minimisation du coût de production total, tandis que le modèle 2 vise la minimisation de la durée totale des projets. Le modèle 3 cherche plutôt à réduire le temps de mise en route sur la presse, le poste goulot du système de production considéré. Le modèle 4 intègre les trois objectifs de réduction des coûts, de durée et de temps de mise en route. Deux scénarios d’ajout de projets de grande et de moyenne envergure ont été conçus et testés. Le test des scénarios démontre qu'il y a une capacité suffisante pour l’ajout d’un projet de grande envergure ou de neuf projets de taille moyenne sans recourir à la sous-traitance. L'ajout d'un projet de grande envergure est plus sensible à la période d'insertion, pouvant exiger du temps supplémentaire selon la date de début du projet. Les travaux de cette thèse permettent donc de fournir des outils d'aide à la décision pour les entreprises œuvrant dans un milieu d'ingénierie sur commande afin d'améliorer leur productivité et la standardisation de leurs processus.Increasing the share of wood in non-residential construction is an important goal in countries with major forest and engineered wood products. In order to facilitate the production of innovative timber structures, procedures should be re-engineered in terms of market analysis and productivity improvement. The main objective of this thesis is to facilitate the production of engineered wood to be used in innovative wood structures such as timber gridshell. To achieve this goal, three specific objectives are defined. The first objective is to determine production phases and market opportunities for the production of timber gridshell. In this regard, a review of the academic and grey literature was conducted, and twenty samples were identified and analysed by making process charts and categorisations. The results showed that gridshell is used in the construction industry in Europe and is less recognised in North America, which provides a market opportunity for its production and construction. The categorisation of studied samples in small, medium and large structures provides an overview for the companies who consider the production of this structure. The second objective of this thesis is to provide a simulation model for the production of glued laminated timber in small factories and the process of applying lean techniques to make improvements. In this regard, the production system of a Small and medium-sized enterprise (SME) was analysed, and a simulation model was created. In order to eliminate each source of waste, a lean tool was suggested according to the reality of the system under investigation. The lean methods were applied in the simulation model to analyse the potential improvements. Results showed a noticeable improvement in waiting and cycle time. It also showed that applying even 50% elimination of the wastes is also a considerable solution to improve productivity as a beginning step for SMEs. The third objective is to provide a production planning and scheduling tool in the context of multi-project engineer-to-order production of glued laminated timber. In this regard, optimisation models were created. The first model (model 1) concerns the minimisation of total production cost while model 2 aims to minimise projects’ makespan. Model 3 introduces the set-up time reduction and model 4 integrates the three objectives of minimising cost, makespan and set-up time. Two scenarios of adding complex and medium projects were designed and tested. Testing the scenarios showed that there is enough capacity for adding one complex project or nine medium projects without the need to outsource. Adding a complex project is more sensitive to the insertion period and beginning the project in different weeks leads to different results in terms of the overtime requirement. As a result, the work of this thesis provides decision support tools for engineer-to-order environments which could help SMEs to improve their productivity and standardisation

    Applications of Mathematical Models in Engineering

    Get PDF
    The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools

    Process analysis and improvments for production of engineered wood structures in an engineer-to-order system

    Get PDF
    Augmenter la part de marché du bois dans la construction non résidentielle est un objectif important dans les pays où les produits forestiers et de bois d'ingénierie jouent un rôle fondamental. Afin de faciliter la production de structures en bois innovantes, il est nécessaire de mettre sur pied des procédures de réingénierie en termes d’analyse de marché et d’amélioration de la productivité. L'objectif principal de cette thèse est de faciliter la production de bois d'ingénierie (produits en lamellé-collé) destiné à être utilisé dans des structures en bois innovantes telles que les résilles en bois. Pour atteindre ce but, trois objectifs spécifiques sont définis. Le premier objectif est de déterminer les phases de production et les opportunités de marché pour la production de résilles en bois. À cet égard, une revue de la littérature académique et de la littérature grise a été réalisée, et vingt échantillons ont été identifiés et analysés à l'aide de diagrammes de processus et de catégorisations. Les résultats ont montré qu’une structure en résille de bois est utilisée dans l'industrie de la construction en Europe et qu'elle est moins connue en Amérique du Nord, ce qui offre une opportunité de marché pour sa production et sa construction. La catégorisation des échantillons étudiés dans les petites, moyennes et grandes structures et l'identification des acteurs pour chaque catégorie fournissent une vue d'ensemble pour les entreprises qui envisagent la production de cette structure. Le deuxième objectif de cette thèse est de fournir un modèle de simulation pour la production de bois lamellé-collé dans de petites usines et le processus d'application de techniques Lean pour apporter des améliorations. À cet égard, le système de production d’une entreprise québécoise a été analysé et un modèle de simulation créé. Afin d'éliminer chaque source de gaspillage, un outil Lean a été suggéré en fonction de la réalité du système à l’étude. Les résultats ont montré une amélioration notable du temps d’attente et de cycle suite à l’utilisation de techniques issues du Lean. Ils ont également contribué à souligner qu’une élimination du gaspillage limitée à 50% pouvait améliorer la considérablement la productivité pour les petites entreprises et s’avérer un premier pas important dans l’implantation du Lean. Le troisième objectif est de fournir un outil de planification et d'ordonnancement de la production dans un contexte de production multi-projets d’ingénierie sur commande (Engineer-to-Order) de bois lamellé-collé. À cet égard, des modèles d'optimisation ont été créés. Le premier modèle (modèle 1) concerne la minimisation du coût de production total, tandis que le modèle 2 vise la minimisation de la durée totale des projets. Le modèle 3 cherche plutôt à réduire le temps de mise en route sur la presse, le poste goulot du système de production considéré. Le modèle 4 intègre les trois objectifs de réduction des coûts, de durée et de temps de mise en route. Deux scénarios d’ajout de projets de grande et de moyenne envergure ont été conçus et testés. Le test des scénarios démontre qu'il y a une capacité suffisante pour l’ajout d’un projet de grande envergure ou de neuf projets de taille moyenne sans recourir à la sous-traitance. L'ajout d'un projet de grande envergure est plus sensible à la période d'insertion, pouvant exiger du temps supplémentaire selon la date de début du projet. Les travaux de cette thèse permettent donc de fournir des outils d'aide à la décision pour les entreprises œuvrant dans un milieu d'ingénierie sur commande afin d'améliorer leur productivité et la standardisation de leurs processus.Increasing the share of wood in non-residential construction is an important goal in countries with major forest and engineered wood products. In order to facilitate the production of innovative timber structures, procedures should be re-engineered in terms of market analysis and productivity improvement. The main objective of this thesis is to facilitate the production of engineered wood to be used in innovative wood structures such as timber gridshell. To achieve this goal, three specific objectives are defined. The first objective is to determine production phases and market opportunities for the production of timber gridshell. In this regard, a review of the academic and grey literature was conducted, and twenty samples were identified and analysed by making process charts and categorisations. The results showed that gridshell is used in the construction industry in Europe and is less recognised in North America, which provides a market opportunity for its production and construction. The categorisation of studied samples in small, medium and large structures provides an overview for the companies who consider the production of this structure. The second objective of this thesis is to provide a simulation model for the production of glued laminated timber in small factories and the process of applying lean techniques to make improvements. In this regard, the production system of a Small and medium-sized enterprise (SME) was analysed, and a simulation model was created. In order to eliminate each source of waste, a lean tool was suggested according to the reality of the system under investigation. The lean methods were applied in the simulation model to analyse the potential improvements. Results showed a noticeable improvement in waiting and cycle time. It also showed that applying even 50% elimination of the wastes is also a considerable solution to improve productivity as a beginning step for SMEs. The third objective is to provide a production planning and scheduling tool in the context of multi-project engineer-to-order production of glued laminated timber. In this regard, optimisation models were created. The first model (model 1) concerns the minimisation of total production cost while model 2 aims to minimise projects’ makespan. Model 3 introduces the set-up time reduction and model 4 integrates the three objectives of minimising cost, makespan and set-up time. Two scenarios of adding complex and medium projects were designed and tested. Testing the scenarios showed that there is enough capacity for adding one complex project or nine medium projects without the need to outsource. Adding a complex project is more sensitive to the insertion period and beginning the project in different weeks leads to different results in terms of the overtime requirement. As a result, the work of this thesis provides decision support tools for engineer-to-order environments which could help SMEs to improve their productivity and standardisation.Résumé en espagno

    Elastic timber gridshells. from the finding form process to the erection of efficient lightweight structures

    Get PDF
    Doctoral Thesis (International Doctoral Programme in Sustainable Built Environment)Elastic timber gridshells emerged in the last century, essentially related to ephemeral buildings, setting a ‘new’ benchmark for lightweight, cost-effective, sustainable and temporary constructions. Timber gridshells are adaptable and can be used in rehabilitated buildings as well as, new buildings, new systems like roofs, or as small additions in nonstructural elements and act as a simple partition. However, the main feature is not its use, but its shape and how it allows some freedom in its design; an attractive characteristic for designers due to its structural behaviour. Based on the advantages of the structural system, it should be expected that timber gridshells have a wider presence in contemporary architecture. However, this is not the case, there are very few examples being built. One reason why this happens, is because of the difficulty to reach the desired design since there is a lack of information about the tools that can help to define such complex systems. Until today, the design and construction of elastic, or post-formed timber gridshells, have only been based on a case to case basis and have not been studied or used as a type of structure that can be repeated in several different applications. The aim of this thesis is to contribute to answer this difficulty, i.e. working on overcoming the lack of design guidelines, by presenting a state of the knowledge on elastic timber gridshells and by case studies analysing the process involved in building this kind of a structures. The thesis is addressing elastic timber gridshells, from the design phase to the construction phase. The results obtained show that this type of structure can be very interesting at a functional level with numerous tectonics characteristics that make elastic timber gridshells attractive as a structural solution in contemporary architecture.As malhas elásticas de madeira surgiram no século passado, essencialmente relacionadas com construções temporárias, estabelecendo uma "nova" referência para construções leves, econômicas, sustentáveis e efêmeras. As malhas de madeira são adaptáveis e podem ser usadas em edifícios a reabilitar, bem como, novos edifícios, coberturas, ou em pequenas modificações como elementos não estruturais. No entanto, a principal característica não é seu uso, mas sua geometria e como isso permite uma enorme liberdade formal torna-se uma característica atraente para todos os projetistas. Com base nas vantagens deste sistema estrutural, é de esperar que as malhas elásticas de madeira tivessem uma presença mais ampla na arquitetura contemporânea. Contudo, não é o caso, existem poucos exemplos construídos. Um motivo para isso acontecer é a dificuldade em projetar as formas desejadas, pois existe uma lacuna de informação sobre as ferramentas que podem ajudar a definir estas geometrias complexas. Por exemplo, as ferramentas baseadas em softwares computacionais têm um grande potencial para o processo de projeção das malhas de madeira nas fases de projeto e construção, onde a localização da malha e a otimização ocorrem, seguidas por um processo de produção industrial. Até hoje, o projeto e a construção destas estruturas, foram estudados apenas de caso a caso e não foram estudados ou usados como um tipo de solução que pode ser repetida em várias aplicações diferentes. O objetivo desta dissertação é contribuir para a resolução desse problema, ou seja, trabalhar na superação da falta de diretrizes de projeto, apresentando um estado do conhecimento sobre as malhas elásticas de madeira e analisando e explicando o processo envolvido na construção deste tipo de estruturas. Esta tese aborda as malhas elásticas de madeira, desde a fase de projeto até à fase de construção. Os resultados obtidos mostram que este tipo de estrutura pode ser muito interessante a um nível funcional, com numerosas características com valor tectônico que tornam as malhas elásticas de madeira atrativas como uma solução estrutural na arquitetura contemporânea.This work it was financed by FEDER funds through the Competitively Factors Operational Programme - COMPETE and by national funds through FCT – Foundation for Science and Technology within the scope of the project POCI-01-0145-FEDER-007633. The support of the Foundation for Science and Technology (FCT) through doctoral fellowship SFRH/BD/104677/2014 is grateful

    A framework for structural shape optimization based on automatic differentiation, the adjoint method and accelerated linear algebra

    Full text link
    Shape optimization is of great significance in structural engineering, as an efficient geometry leads to better performance of structures. However, the application of gradient-based shape optimization for structural and architectural design is limited, which is partly due to the difficulty and the complexity in gradient evaluation. In this work, an efficient framework based on automatic differentiation (AD), the adjoint method and accelerated linear algebra (XLA) is proposed to promote the implementation of gradient-based shape optimization. The framework is realized by the implementation of the high-performance computing (HPC) library JAX. We leverage AD for gradient evaluation in the sensitivity analysis stage. Compared to numerical differentiation, AD is more accurate; compared to analytical and symbolic differentiation, AD is more efficient and easier to apply. In addition, the adjoint method is used to reduce the complexity of computation of the sensitivity. The XLA feature is exploited by an efficient programming architecture that we proposed, which can boost gradient evaluation. The proposed framework also supports hardware acceleration such as GPUs. The framework is applied to the form finding of arches and different free-form gridshells: gridshell inspired by Mannheim Multihalle, four-point supported gridshell, and canopy-like structures. Two geometric descriptive methods are used: non-parametric and parametric description via B\'ezier surface. Non-constrained and constrained shape optimization problems are considered, where the former is solved by gradient descent and the latter is solved by sequential quadratic programming (SQP). Through these examples, the proposed framework is shown to be able to provide structural engineers with a more efficient tool for shape optimization, enabling better design for the built environment
    corecore