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Structural explorations of fabrication-aware design spaces for non-standard architecture
Abstract and Figures
The last decades have seen the emergence of non-standard architectural shapes. Designers find often themselves helpless with the geometrical complexity of these objects. Furthermore, the available tools dissociate shape and structural behaviour, which adds another complication. This dissertation takes the point of view based on invariance under geometrical transformations, and studies several strategies for fabrication-aware shape modelling. Three technological constraints have been identified and correspond to three independent contributions of this thesis.
The repetition of nodes is studied via transformations by parallelism. They are used to generalise surfaces of revolution. A special parametrisation of moulding surfaces is found with this method. The resulting structure has a high node congruence.
Cyclidic nets are then used to model shapes parametrised by their lines of curvature. This guarantees meshing by planar panels and torsion-free beam layout. The contribution of this dissertation is the implementation of several improvements, like doubly-curved creases, a hole-filling strategy that allows the extension of cyclidic nets to complex topologies, and the generation of a generalisation of canal surfaces from two rail curves and one profile curves.
Finally, an innovative method inspired by descriptive geometry is proposed to generate doubly-curved shapes covered with planar facets. The method, called marionette technique, reduces the problem to a linear problem, which can be solved in real-time. A comparative study shows that this technique can be used to parametrise shape optimisation of shell structures without loss of performance compared to usual modelling technique. The handling of fabrication constraints in shape optimisation opens new possibilities for its practical application, like gridshells or plated shell structures. The relevance of those solutions is demonstrated through multiple case-studies.
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... Les méthodes sont nombreuses et dépendent de l'objectif constructif visé mais aussi des contraintes sur la solution initiale (surface et type de maillage imposés, surface imposé et maillage libre, etc.). Pour une revue détaillée des différentes méthodes existantes, nous invitons le lecteur à consulter les thèses de Mesnil [2017] et Tellier [2020] qui dressent toutes deux un panorama des techniques principales de morphogenèse, c'est-à-dire de création de forme sous contrainte de fabrication. ...
... Des noeuds sans torsion sont obtenues par exemple en alignant les éléments sur les lignes de courbures principales d'une surface [Tellier, 2020]. Les maillages coniques et circulaires garantissent aussi cette propriété [Mesnil, 2017]. ...
... En première approche, il est possible de réaliser une analyse de flambement global linéaire pour évaluer une charge critique (ou un facteur critique) de flambement correspondant à l'obtention de l'instabilité (divergence importante du déplacement à un niveau de force fini) de la structure. Le flambement linéaire souffre cependant de certaines limitations intrinsèques : le problème étant linéarisé, l'équilibre est toujours calculé sur la configuration initiale de la structure, de sorte que le flambement linéaire peut surestimer de façon importante la capacité résistante des structures soumises à de grands déplacements avant flambement [Mesnil, 2017]. C'est pourquoi une estimation plus précise de la charge critique exige généralement une analyse non-linéaire de la structure en prenant en compte un niveau d'imperfection géométrique initial de l'ouvrage. ...
Cette thèse explore les leviers d’optimisation des structures en bois de grande portée tant sur le plan des critères usuels de conception des structures, que sur le plan des impacts environnementaux. L’essor actuel de la construction bois encourage en effet les ingénieurs à s’interroger en profondeur sur les typologies structurelles et les principes constructifs adaptés à ce matériau, notamment autour du comportement mécanique, des moyens de mise en œuvre et du coût des assemblages.Nous proposons dans un premier temps de développer un modèle statistique permettant d’obtenir une loi de comportement simplifiée des raideurs et de la masse d’un assemblage par broches à partir d’un nombre restreint de variables d’entrée (torseur (N,V,M) et facteur de forme de la section) et pouvant être utilisé facilement dans des modèles de calcul de structure. Puis, nous illustrons comment la simple prise en compte du comportement semi-rigide des assemblages peut directement influencer la géométrie et la topologie optimale d’un exosquelette en bois.Par ailleurs, les assemblages, qui concentrent les procédés d'usinage les plus complexes de l'ouvrage, ne peuvent pas être négligés dans le bilan économique et environnemental d'une structure en bois. Dans la suite nous présentons un cadre d'évaluation des impacts environnementaux des structures en bois, intégrant les assemblages et adapté aux premières phases de la conception, là où se font les choix les plus fondamentaux. Ce travail nous conduira à introduire des méthodes de sélection et de réduction du nombre d’indicateurs. L’utilisation des métriques de type endpoint permet tout d’abord d’évaluer sur une échelle commune la contribution de différentes catégories à l’impact total d’un système, et ainsi d’en sélectionner les plus pertinentes. Puis, nous proposons l’utilisation d’un indice de corrélation en classement et en étendue afin de sélectionner les indicateurs non corrélés pour un ensemble de scénarios donné.Finalement, à l’aune de cette sélection d’indicateurs et du modèle d’assemblage simplifié développé dans ce travail, cette thèse explore dans la dernière partie les voies d’optimisation structurelle et environnementale des ouvrages en bois de grande portée. Au travers de l’étude de deux types de structure, le treillis et le gridshell, nous illustrons l’importance de la conception et du comportement des assemblages en lien avec la continuité des éléments, la densité des connexions ou encore le choix des matériaux.
... New computational tools [1] made possible interactive design based on graphic statics resulting in non-standard and efficient shell shapes. Even if the analysis of such non-standard structures became possible, their shapes challenge fabricators and builders making these structures non-affordable or hard to build [8]. In this paper, interactive design and analysis method are used to conceive a funicular prototype having its manufacturing method addressed to reduce waste of material and to simplicity of construction. ...
... From the Thrust Network (G) of Figure 2, a smooth surface was created to materialize the structure ( Figure 3). The fabrication of complex surfaces has been studied by several authors [8,9,10] showing that the constructive strategy can dramatically reduce waste and simplify installation. Many strategies could have been adopted to discretize the structure into smaller elements for fabrication and assembling. ...
This paper presents the steps of design, fabrication and installation of a Styrofoam masonry vault, produced in 2018 at the Polytechnic School at the University of São Paulo (POLI-USP), in the context of a graduate course on Light Structures. The challenge of the project was to design and deliver an innovative structural prototype, in a relevant scale. The project selected by the students was a funicular, three-legged masonry vault laying within a 3.0m diameter circle. The structure was form-found using graphic statics. Then it was discretized into 45 irregular bricks cut out from 10cm thick Styrofoam bulk blocks, with the aid of a CNC hot wire router machine. An efficient stereotomy technique was applied to ensure that adjacent bricks could be fabricated with minimum waste of material and high precision in the final shape. The structure was nicknamed 'Stereodome I' and resulted in an eye-catching curved complex surface that was exhibited for months at the Civil Engineering Building of POLI-USP.
... Free form structures challenge involved planners and fabricators by the complexity of their forms as the repetition of building components is no longer guaranteed. Agreeing with Mesnil (2017), both, the loss of repetition and difficulty in manufacturing, makes the design of free-form architecture tedious and distinguishes them essentially from the design of conventional structures. ...
... There are multiple solutions to assemble/disassemble a non-sequential assembly according to the orientations of the slides. Thanks to Combescure transformations, in Mesnil [5], also known as parallel transformations, preserving angles, we can deform the OCG to obtain the desired kinematic. The kinematic can have an isovelocity, with each part having the same relative velocity of the other parts as in figure 5(a). ...
This paper proposes a method to design non-sequential assembly for construction. Unlike interlocking assemblies, a non-sequential joint can be assembled with simultaneous movement of all parts and blocked only by its kinematic. Thanks to robotic manufacturing and advances in digital fabrication, we can produce complex joints which can be easily assembled together. Non-sequential assembly can be a solution to build more sustainable construction by anticipating their end of life and their disassembly, reusing or recycling rather than their demolition. The paper will firstly introduce the non-sequential assembly. Secondly, a design method will be proposed showing that the oriented connectivity graph can be interpreted in the same manner as a force diagram where Maxwell equations can be applied. Then, a method to define the velocities is explained. An elementary non-sequential assembly generation table that enumerates the assembly according to their valence and connections in between each element of the assembly is then proposed. Finally, the construction of a wooden prototype demonstrates the efficiency of the method.
... The profound understanding of membrane structures is owed to Pritzker Prize laureate Frei Otto, an architect who has been studying these structures morphologically [46]. His first structures (from 1955) were form-found with the use of physical methods such as soap films and stockings. ...
Temporary pavilions play an important role as experimental fields for architects, designers, and engineers, in addition to providing exhibition spaces. Novel structural and formal solutions applied in pavilions also can give them an unusual appearance that attracts the eyesight of spectators. In this article, the authors explore the possibility of combining structural novelty, visual attractiveness, and low cost in the design and construction of a temporary pavilion. For that purpose, an innovative structural system and design approach was applied, i.e., a membrane structure was designed in Rhino and Grasshopper environments with the use of the Kiwi!3D IsoGeometric analysis tool. The designed pavilion, named Obverse/Reverse, was built in Opole, Poland, for the occasion of World Architecture Day in July 2019. The design and the construction were performed by the authors in cooperation with students belonging to the Humanization of Urban Environment organization from the Faculty of Architecture Wroclaw University of Science and Technology. The resultant pavilion proved the potential of obtaining a low-budget but visually attractive architectural solution with the adaption of parametrical design tools and some scientific background with innovative structural systems.
... The profound understanding of membrane structures is owed to Pritzker Prize laureate Frei Otto, an architect who has been studying these structures morphologically [46]. His first structures (from 1955) were form-found with the use of physical methods such as soap films and stockings. ...
Temporary pavilions play an important role as experimental fields for architects, designers and engineers, apart from providing exhibition spaces. Novel structural and formal solutions applied in pavilions also can give them unusual appearance that attracts eyesight of spectators. In this article authors explore the possibility of combination of structural novelty, visual attractiveness and low-cost by a design and construction of a temporary pavilion. For that purpose, an innovative structural system and design approach was applied, i.e. membrane structure designed in Rhino and Grasshopper environments with the use of Kiwi!3D IsoGeometric analysis tool. The designed pavilion, named Obverse/Reverse, was built in Opole, Poland, for the occasion of World Architecture Day in July 2019. Design and construction was performed by the authors in cooperation with students’ organisation Humanisation of Urban Environment from the Faculty of Architecture Wroclaw University of Science and Technology. The Rresultant pavilion proved the possibility of obtaining a low-budgets but visually attractive architectural solution with the adaption of parametrical design tools and some scientific background with innovative structural systems.
... Due to symmetry, the shape is parameterized with 9 degrees of freedom for the NURBS model and 8 degrees of freedom for the Marionette model. A more detailed discussion on this parameterization for the shape optimization of shell structures is proposed in [20]. The beams are rectangular hollow sections with b/h=3 and t=1cm. ...
The design of gridshells is subject to strong mechanical and fabrication constraints, which remain largely
unexplored for non-regular patterns. The main technological constraints for glazed gridshells are related to the planarity of facets and the existence of torsion-free offsets. The authors propose indicators to evaluate a priori the quality of design space of gridshells covered with different patterns for these fabrication constraints. By comparing these metrics, the kagome grid pattern is identified as a pattern with a complexity similar to the ubiquitous quadrilateral pattern. Finally, the authors propose to generate gridshells with planar facets with the marionette technique and to explore the resulting design space by the means of multi-objective optimization. The results of the study show that our framework for shape modeling has similar performances as more usual frameworks, like NURBS modeling, while maintaining the facet planarity
We introduce an intuitive method, called Marionette by the authors, for the modelling of free-form architecture with planar facets. The method takes inspiration from descriptive geometry and allows to design complex shapes with one projection and the control of elevation curves. The proposed framework achieves exact facet planarity in real-time, and considerably enriches previous geometrically-constrained methods for free-form architecture. A discussion on the design of quadrilateral meshes with a fixed horizontal projection is first proposed, and the method is then extended to various projections and patterns.
The method used is a discrete solution of a continuous problem. This relation between smooth and continuous problem is discussed and shows how to combine the marionette method with modelling tools for smooth surfaces, like NURBS or T-splines. The result is a versatile tool for shape modelling, suited to engineering problems related to free-form architecture.
The aim of this paper is to present some innovative strategies for the design of plated shell structures.
Fabrication constraints are carefully considered, as the obtained shapes are covered with planar quadrilateral
facets only. Different corrugation strategies are investigated, and our method guarantees extension of the shape generation to complex topologies. Few parameters control the amplitude of corrugations, which also gives us the opportunity to perform a sensitivity analysis on the influence of corrugations on the structural performance of folded-plate structures. The study focuses on the influence of the mechanical attachment between plates on the overall structural performance as well as fabrication rationality.
The aim of this paper is to introduce a bottom-up methodology for the modelling of free-form shapes in architecture that meet fabrication constraints. To this day, two frameworks are commonly used for surface modelling in architecture: NURBS modelling and mesh-based approaches. The authors propose an alternative framework callled generalised cyclidic nets that automatically yields optimal geometrical properties for the envelope and the structural layout, like the covering with planar quadrilaterals or hexagons. This framework uses a base circular mesh and Dupin cyclides, which are natural objects of the geometry of circles in space, also known as Möbius geometry. This paper illustrates how complex curved shapes can be generated from generalised cyclidic nets. It addresses the extension of cyclidic nets to arbitrary topologies with the implementation of a 'hole-filling' strategy and demonstrates also that this framework gives a simple method to generate corrugated shells.
The design of gridshells is subject to strong mechanical and fabrication constraints, which remain largely unexplored for non-regular patterns. The aim of this article is to compare the structural performance of two kind of gridshells. The first one is the kagome gridshell and it is derived from a non-regular pattern constituted of triangles and hexagons. The second one results from a regular pattern of quadrangles unbraced by diagonal elements. A method is proposed to cover kagome gridshells with planar facets, which reduces considerably the cost of fabrication of the cladding.
The sensitivity of kagome gridshells to geometrical imperfections is discussed. The linearised buckling load of kagome gridshells is then compared to the one of quadrilateral gridshells. The most relevant design variables are considered in the parametric study. Two building typologies are studied for symmetrical and non-symmetrical load cases: dome and barrel vault. It reveals that the kagome gridshell outperforms quadrilateral gridshell for a very similar construction cost.
In architectural design, parametric models often include numeric parameters that can be adjusted during design exploration. The resulting design space can be easily displayed to the user if the number of parameters is low, for example, using a simple 2- or 3-dimensional plot. However, visualising the design space of models defined by multiple parameters is not straightforward. In this paper it is shown how dimensionality reduction can assist in this task whilst retaining associations between input designs at a high-dimensional parameter space. A self-organising map (SOM), a type of unsupervised artificial neural network, is used in combination with Rhino Grasshopper in order to demonstrate the potential benefits for design exploration.
This paper describes the design and construction of the TRADA (Timber Research and Development Association) Pavilion by Ramboll Computational Design. The design process combined a zero-length spring funicular form-finding approach with a planar polygon discretisation method, thus enabling the final structurally efficient but complex geometric form to be realised with low-cost materials. The timber plate shell is fully demountable and has been assembled at several separate locations since being completed in September 2012. To the authors’ knowledge, the structure is one of the largest free-form facetted thin shell structures ever to be constructed. It is hoped that the project inspires a new approach in realising complex funicular shapes with low-cost materials and fabrication methods.
Inspired by freeform designs in architecture which involve circles and spheres, we introduce a new kind of triangle mesh whose faces' incircles form a packing. As it turns out, such meshes have a rich geometry and allow us to cover surfaces with circle patterns, sphere packings, approximate circle packings, hexagonal meshes which carry a torsion-free support structure, hybrid tri-hex meshes, and others. We show how triangle meshes can be optimized so as to have the incircle packing property. We explain their relation to conformal geometry and implications on solvability of optimization. The examples we give confirm that this kind of meshes is a rich source of geometric structures relevant to architectural geometry.
We present a method for the global parametrization of meshes that preserves alignment to a cross field in input while obtaining a parametric domain made of few coarse axis-aligned rectangular patches, which form an abstract base complex without T-junctions. The method is based on the topological simplification of the cross field in input, followed by global smoothing.
