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Geodesic gridshells are shell structures made of continuous elements following geodesic lines. Their properties ease the use of beams with anisotropic cross-sections by avoiding bending about their strong axis. However, such bending may arise when flattening arbitrary geodesic grids, which forbids their initial assembly on the ground. This study provides a process to design elastic geodesic gridshells, that is, gridshells that minimise bending moments in both formed and near-flat configurations. The generation process first brings a target geodesic network onto a plane by maintaining arc lengths. The flat mesh is then relaxed to minimise its main curvatures and hence bending moments in its members. The result is an elastic geodesic gridshell that can be assembled flat on the ground and then lifted up into its target surface. The method is applied to the design of six geodesic gridshells made of reclaimed skis.

This paper presents a full life-cycle assessment study of a constructive system and addresses two following problematics: the impact of robotic fabrication and the performance of reuse solution for the end-of-life phase. As a case study a shell-nexorade hybrid constructive system is selected. The structure was designed computationally and fabricated robotically; a reuse scenario is developed for the end-of-life. The results point out an occurring of a significant impact transfer in system’s life-cycle caused by robotic construction technology. Concretely, the contribution of the last can represent over 40% of the overall environmental impact of the structure in climate change category and exceeds the impact related to construction materials production in categories of toxicity and eutrophication. Regarding the end-of-life phase, a method for reuse assessment was developed and a strategy for control of an environmental performance of reclaimed structures is formulated. The data for environmental evaluation of digitally fabricated systems is provided.

En este artículo se revisita la clásica cercha espacial de doble pared reemplazando las diagonales por módulos poliédricos curvos de paredes delgadas. Las mejoras esperadas son tanto tecnológicas como mecánicas. Los nodos complejos de 8 ramas se dividen en una conexión de dos miembros continuos superpuestos y una conexión lineal entre las barras y los bordes del poliedro. La curvatura en las caras y bordes de los módulos introduce resistencia por forma y estabiliza los miembros frente al pandeo. La optimización global de la estructura se realiza mediante un proceso de búsqueda de forma basado en la parametrización individual de los módulos.Finalmente, se lleva a cabo una validación experimental mediante la fabricación y prueba de un prototipo a escala real (de 6 x 6 m aproximadamente).

Curved envelope structural building envelopes have been quite popular in architecture in the past decades, and pose many challenges in their design, manufacturing and planning. In gridshells, a popular structural morphology for curved structure, designers will often strive to orient beams such that their top face is parallel to the envelope surface. However, this tends to induce geometrical torsion along the beam centerline, which complexifies significantly the manufacturing of the connection nodes or of the beams themselves. It is well known that such issue can be avoided by aligning beams with principal curvature directions of the envelope surface, thus yielding a quadrangular paneling. In this article, we study how other types of patterns (non-quadrangular) can be used to design torsion-free grid-shells. Based on asymptotic considerations, we derive a set of geometrical rules which, if fulfilled by a pattern, insure that a surface can be covered by this pattern with negligible torsion and limited deviation of beams from surface normals. A wide variety of patterns fulfill these rules, offering interesting possibilities for the design of curved architectural envelopes (Figure 1) is shown. As these rules are based on first order asymptotic analysis, we perform global validation on case studies. One main application is for structures in which face planarity is not necessary, for example ones cladded with ETFE cushions.

International audience; This work presents a generalized method for robotic mortar extrusion, allowing the fabrication of structural-insulating walls of novel performances. It involves two distinct steps that are to be simultaneously automated: extrusion of a specifically formulated mortar, and assembly of adequately shaped insulating blocks. Here, the layer by layer approach of concrete printing is renewed by using insulating blocks as support for the extrusion. The volumetric space of the wall is divided by an adequate space tessellation, dividing it in polyhedra. They become insulating blocks, on the edges of which mortar is extruded. The set of edges then forms a space truss, of great mechanical efficiency. “Printable” mortar is crucial to the system for the blocks could not withstand the hydrostatic pressure of fresh mortar without additional form-work features, once a few meters height has been reached. This approach renews traditional confined masonry, allowing for geometric complexity and automation.

The patterns of many structural systems must fulfil a property of two-colourability to partition their elements into two groups. Such examples include top versus bottom layers of continuous beams in elastic gridshells, corrugated versus non-corrugated directions in corrugated shells or warp versus weft threads in woven structures. Complying with such constraints does not depend on the geometry but on the topology of the structure, and, more specifically, on its singularities. This paper presents a search strategy to obtain patterns that fulfil this topological requirement, which represent only a fraction of the general design space. Based on an algebra for the exploration of the topology of quad meshes, including a grammar and a distance, a topology-finding algorithm is proposed to find the closest two-colour quad-mesh patterns from an input quad-mesh pattern. This approach is expressed as the projection to the two-colourable subspace of the design space. The distance underlying the definition of the projection measures the similarity between designs as the minimum number of topological grammar rules to apply to modify one design into another. A design application illustrates how two-colour topology finding can complement workflows for the exploration of structural patterns with singularities informed by the system's topological requirements., Computer-Aided Design, 137, ISSN:0010-4485, ISSN:1879-2685

International audience; Funicular structures can resist a given load with pure axial forces, and therefore tend to use material very efficiently. One main challenge in their design is the form-finding, which often requires advanced numerical methods. In this article, we show analytically that a very common family of curves, conics, is funicular for a particular load case: a uniform radial load emanating from a focus (Figure 1). The result is a generalization of the well-known funicularity of parabolas and arcs of circles, respectively under uniform vertical load and constant normal pressure. It can be used to design self-stressed structures by hand without the need for calculations. Portions of conics can be combined to obtain original shapes.

International audience; Curved structural envelopes have been popular in architecture in the past decades. Their main limitation is their high cost, which is due in particular to the manufacturing complexity induced by curvature. This article introduces Caravel meshes, a new family of meshes that offers geometrical properties allowing a significant reduction of fabrication complexity. In particular, for gridshells, the most complicated fabrication aspect is usually the connection between the structural elements-beams and panels. In Caravel meshes, all these connections are rationalized. Beams are connected to panels without kinks, beams are connected top each other with repetitive which are also free of geometrical torsion. We show that a great variety of mesh combinatorics is possible with these properties. We study in particular quadrangular and hexagonal patterns. In each case, we estimate the possible shapes using differential geometry. We show that hexagonal Caravel meshes offer a significant design freedom, such that other geometrical properties simplifying fabrication can be obtained, such as edge offsets. Finally, we show that Caravel meshes offer many new ways to design curved structural systems, in which beams and panels may work together mechanically. We highlight one application for the fast prototyping of curved surfaces.

International audience; The fabrication of a freeform structural envelope is usually a highly complex task. The costliest aspect is often the connections between the constitutive parts. The Caravel heX-Mesh Pavilion is a prototype that demonstrates a new rationalization strategy. Its structure, composed of a hexagonal grid of beams and cladding panels, is based on a geometry that rationalizes connections at two levels: firstly, nodes are free of geometrical torsion and are repetitive: only two types of nodes are used. Secondly, panels can easily be connected to the support beams as they are orthogonal to each other. The mechanical behavior is validated by finite-element analysis. We generate these meshes by numerical optimization from a smooth target surface, with an initialization derived from the asymptotic case and surface theory. The pavilion shows an alternative way of rationalizing a gridshell beyond the popular planar-quad meshes and circular/conical meshes. It also demonstrates a way to generate hexagonal gridshells which are not necessarily synclastic, this limitation being typically imposed to achieve planarity of cladding panels.

International audience; This article proposes a new computational method for the form-finding of nexorades, also called reciprocal frames in the literature. The method is based on the translations of members forming the initial layout. It is shown that the two geometrical quantities defining nexorades-eccentricity and engagement length-depend linearly on the transformation parameters. The method introduced in this article is thus based on linear algebra, so that fitting problems can be formulated as simple quadratic optimisation problems under linear constraints. The proposed method is therefore fast, simple to implement, robust and can be applied to various grid patterns. Furthemore, the proposed framework preserves planar facets. This paper proposes thus a new structural system where the nexorade is braced by planar facets. The feasibility of this structural system and of the computational framework introduced in this article is demonstrated by the fabrication of a 50m 2 timber pavilion.

International audience; In this paper phenomenological observations of the creep rupture under maintained combined traction and torsion loading are first presented. They show the importance of the matrix’s behavior in the long-term durability of the material. Understanding and foreseeing creep rupture of unidirectional fiber reinforced polymers (UD FRP) involves comprehension at the fibers’ scale of various time-dependent interactions among the fibers and between the matrix and the fibers. Shear-lag models have been successfully applied in the modeling at the micro-scale of these interactions, some of them even introducing time dependence. Long-term durability of macro-scale structure demand further developments of such models to be able to predict the macro-damage cluster and their evolution. The aim of the present contribution that is an extension from existing models is to investigate the progressive damage of a 0o UD composite material subjected to combined shear-traction loading including a high number of interacting fibers, with a viscoelastic matrix, debondings and random distribution of fiber flaws. Results of simulations including different loadings and matrix viscoelastic properties will be shown and discussed for a better comprehension of the role of composite’s components in the creep rupture phenomenon. In particular, the long-term influence of matrix’s shear stiffness on the material’s lifespan is shown, and the impact of an additional uniform shear stress is studied. This combined shear-traction loading is of interest in real-scale structures where shear stress can result from torsion or shear forces (such as those due to anchor points, misalignment and coupling). Moreover, this model is a first step to approach the long term failure of 0o composites subjected to torsion-bending loading, what is shown decisive in the second section of this work. Further experimental works in combined traction-torsion loadings are needed to validate this simulations with a specific attention on the identification of required parameters.

Face à la diminution des ressources et afin de réduire l’impact carbone du secteur de la construction, il est important d’envisager la fin de vie des bâtiments. Il faut considérer les constructions et leur structure comme des éléments pouvant être démontés ou désassemblés pour être recyclés ou réutilisés. Cette recherche s’intéresse aux assemblages non-séquentiels, permettant une réversibilité pour répondre à ces enjeux. Pour démontrer l’intérêt de ces assemblages, un prototype de Nexorade échelle 1 a été construit et illustre l’article. La première partie définit l’assemblage non-séquentiel et ses cinématiques possibles. La recherche du pavage et de la géométrie sont évoquées dans la seconde partie. L’article continue sur la génération de la nexorade et son analyse mécanique mettant en évidence l'intérêt d’incliner les poutres de la nexorade, pour réduire la flèche de 35%. La séquence d’assemblage est développée dans la partie 5. Enfin, la construction du pavillon est détaillée, permettant le passage d’un modèle numérique à la fabrication du prototype. Pour conclure cet article, les auteurs discutent des résultats obtenus sur les assemblages non-séquentiels et sur l’inclinaison des poutres. Des extensions possibles et futures recherches sont suggérées.

La construction de coques minces en béton est coûteuse en matériaux et en main d’œuvre à cause de la fabrication du coffrage qui génère une vaste quantité de déchets. Ces éléments non réutilisables ont un impact négatif sur l’ACV de la construction. Ces difficultés expliquent en partie pourquoi la construction de coques minces est devenue rare à la fin du XXème siècle malgré l’indéniable qualité architecturale qu’elles confèrent aux espaces créés. Cette recherche a pour objectif de modéliser et concevoir un nouveau système de coffrage économe en moyens, pour préfabriquer des éléments surfaciques en béton à partir de structures gonflables. Contrairement à des exemples historiques proposant des gonflables à simple peau, nous proposons de liaisonner deux membranes selon un motif. Composé de courbes, le motif est conçu afin qu’une fois les membranes gonflées, la métrique du plan varie de manière non uniforme et génère une surface en trois dimensions selon le theorema egregium de Gauss. Le dessin du motif d’assemblage est guidé par un outil numérique capable de simuler précisément une forme gonflée en 3D à partir d’un motif de soudure en 2D. Cette méthode de fabrication serait automatisable et transposable à plus grande échelle. L’article décrira les principes géométriques et l’outil de simulation numérique. Nous présenterons une application, la fabrication d’un coffrage gonflable et la construction d’une coque mince en béton.

International audience; Elastic gridshells are structures made of flat two-way grids which are deformed elastically before they are braced and which afterwards mechanically behave like continuous shells. Gridshells present some advantages in terms of manufacturing, lightness and time of assembly. Their covering remains however a technical issue. The present article proposes hence an alternative method to cover them by planar quadrilateral facets, which could also be used as natural bracing if connected properly. It relies on the duality between a certain family of circular meshes with a unique radius and some Tchebycheff nets. The approach is versatile and allows for the design of a large variety of shapes from two curves in space. Real time numerical tools are developed for open and closed curves as well as a strategy for umbilical points. The relaxation of the Tchebycheff net shows finally that an equilibrium configuration can be found in the vicinity of the planar quadrilateral mesh (PQ-Mesh) which confirm the practical feasibility of elastic gridshells covered with planar facets.

We introduce an intuitive method, called Marionette, 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 non-uniform rational basis spline or T-splines. The result is a versatile tool for shape modelling, suited to engineering problems related to free-form architecture.

This paper presents an environmental assessment of a 6-Axis robotic Arm for extrusion-based 3D Concrete Printing technology using Life Cycle Assessment method. In addition, the other components of a printing cell are assembled within a life cycle model and the relative contribution of the cell to the printing process is evaluated. The results show that, per one hour of printing, an environmental impact coming from the production phase of robotic printing cell would represent 2,2 kg CO2 Eq for the category of Climate Change. Hourly contributions are also calculated for the rest of environmental indicators.

International audience; This paper proposes a specific extrusion method for 3D printing of mortar called free deposition by the authors. It consists in letting a fine mortar flow through a moving nozzle above a support, here EPS foam. The aim is to obtain a regular lace, thus to avoid instability phenomena like coiling, and ensure a regular diameter, without stretching the lace. A rheological characterisation is proposed and is experimentally tested. This work takes place in the context of the building of space trusses in 3D printed concrete thanks to progressively assembled EPS foam blocks acting as support.

International audience; The paper presents new results about the geometry of topological interlocking masonries and some possibilities they present to build without formwork. Construction without the use of formwork may be an important issue concerning both productivity increase and decreasing of waste generated on a construction site. Due to the development of computational design and robotics in the construction industry, it makes sense to (re)explore innovative design and process of complex masonry structures. The design of this kind of masonry is standard for planar structures, and in this paper, a generalization is proposed for the parametric design of curved structures. To achieve this, a criterion for translationally interlocked structure based on quadrilateral meshes is exhibited. The application of this criterion is then extended to masonry structures derived from other patterns. Physical prototypes of topological interlocking masonry are also presented. One of these designs seems to allow construction without formwork.

International audience; 3d printing of cementitious material by pressing layers during the extrusion is a strategy that requires a rather low initial yield stress so the material can deform without cracking. It allows to perfectly control the height of the layer and gives freedom in the orientation of the printing head and of the layer allowing for a wider range of printable geometry than the classic so-called "infinite brick" extrusion. This strategy has however some drawbacks as pressing the material on the previous layers may lead to a deformation of the sub-layers and even failure of the structure. In this work; we make a first step into understanding forces involved in such a process and measure their dependency on material fresh properties and printing parameters.

International audience; This article discusses design strategies to improve the mechanical behavior of elastic gridshells with singularities. The advantage of meshing with one or more singularity is to allow a wider range of surfaces to be meshed with equal-length, quadrilateral meshes, known as Chebyshev nets. However, the application of this meshing process will influence the fabrication and the mechanical behavior of the structures. The erection process is simulated by means of the dynamic relaxation method, bending the bars to their final position. This simulation shows that a facetted shape is found instead of a smooth surface. This deformed shape makes the structure softer under applied gravity load. Two strategies are investigated in this paper to enable the construction of gridshells with singularities. The first consists in extending the bars close to the singularities edge-lines to have a smother gridshell after the erection process. The second strategy applies post-tension cables to the patches to increase the local curvature in the faceted zones. Both strategies increase the stiffness and buckling load of the final structure.

The ongoing development of digital design and fabrication techniques has explicitly changed the way architecture is thought, designed and produced. 3D Concrete Printing Technology personifies best the long-lasting pursuit of non-standard production in architecture. A recently established tendency of systematic recourse to optimization algorithms for formal design fashioned a general belief into the sustainable character of those forms as well as the potential of digital technologies in field of environmental performance of construction sector.

International audience; This paper introduces topology finding of patterns for shell structures such as beam grids for gridshells or voussoir tessellations for vaults, among others. The authors refer to topology finding, by analogy and in complement to form finding, as the design of the connectivity of these patterns in order to follow architectural, structural and construction requirements. This paper presents a computational approach relying on a specific design space and data structures based on singularity meshes, which encode the information about the singularities in patterns. The designed patterns are structured, i.e. with a low number of singularities, can include high-valency pole points, and respect alignment to surfaces, curves and points. A feature-based exploration approach is introduced with a generation procedure for singularity meshes following the boundaries of a surface as well as point and curve features, using a topological skeleton or medial axis. These features can stem from statics heuristics, whose efficiency is assessed in a case study. A rule-based editing approach for singularity meshes supplements feature-based topology finding, using a grammar of strip rules as parameters to further explore the singularity design space. This conceptual design approach and its algorithms are an aid for topological exploration of patterns for shell-like structures by architects and engineers.

International audience; 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.

International audience; L'éclosion de l'impression 3d en béton se reflète aujourd'hui dans la recherche académique où des sujets comme la rhéologie du matériau extrudé, la cohésion entre couches ou encore les stratégies de renforcement sont largement étudiés [1]. Peu de publications en revanche traitent de la recherche de forme pour des structures obtenues grâce à ce nouveau procédé (tel que [2] ou [3]). Les caractéristiques du matériau frais venant d'être imprimé (ne reprenant pas ou très peu de traction), la maîtrise de sa rhéologie ou encore la barrière technologique (difficulté de définitir des trajectoires complexes des robots) peuvent être des facteurs limitant aujourd'hui presque essentiellement l'impression 3d à la réalisation de murs verticaux. Pour essayer d'élargir le champs des géométries imprimables, l'approche proposée est de s'in-téresser à une autre technique de fabrication additive bien plus ancienne : la maçonnerie. La maçonnerie comme l'impression 3d en béton consiste à empiler des couches successives d'un matériau présentant une très faible résistance en traction en cherchant à obtenir une structure finale travaillant principalement en compression (la recherche sur l'impression de structures armées n'étant qu'à ses débuts). Le rapprochement semble donc naturel et il a d'ailleurs été évoqué dès les débuts de l'impression 3d en béton par Pegna dans [4] en 1997. La comparaison entre les deux procédés peut être poussée jusque dans leurs éléments constitutifs propres : brique et cordon, appareillage et parcours d'outil (trajectoire du robot), maçon et robot.

International audience; With the improvement of the 3D printing industry, the interest in additive manufacturing of large-scale structures (AMLS) is rapidly increasing. Recent attempts of seeking solutions for 3D printing of large-scale buildings demonstrate that the transition from conventional construction systems to automated robotic manufacturing workflows is evident. The usage of formwork plays a crucial role in accelerating the progress of AMLS domination in construction industries. Other advantages of supportless printing have been seen in NASA's research for in-situ 3D printing of habitats on Mars. Investigations of large-scale 3d printing of concrete structures are mostly related to robotics, rheology and material mechanics. There is little research done on the application of architecture and form-finding in this field. This paper discusses solutions for supportless 3D printing of large-scale compression shells with the focus on In-situ concrete 3D printing. The aid of special form finding and robotic trajectory generation is also reverse engineered ancient brick-laying techniques recognized in international vaulting precedents lacking formwork. Finally, a strategy for the generation of robotic printing tool-path to span any convex inscribed quadrilateral based boundary with no temporary support is yielded and tested with the simulation of 1:20 (15×15 cm) scale construction practice by a "3Doodler" pro pen as extrusion head (child) and ABB IRB_120 six-axis arm as a parent.

International audience; Motivated by architectural applications, we propose a method to generate circular and conical meshes with planar curvature lines in both directions. The method is based on the discretization of the Gauss map of surfaces with planar curvatures lines. It allows generation of meshes in real-time via two planar guide curves. The resulting meshes can be used as a geometric base to build gridshells with flat panels, torsion free-nodes, node offset and planar arches. A particular technological application is for gridshells built with curved members: those can be built with planar piecewise-circular beams, and identical nodes if beams have circular cross-section.