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International audience; The present work addresses the problem of maximizing a structure load-bearing capacity subject to given material strength properties and a material volume constraint. This problem can be viewed as an extension to limit analysis problems which consist in finding the maximum load capacity for a fixed geometry. We show that it is also closely linked to the problem of minimizing the total volume under the constraint of carrying a fixed loading. Formulating these topology optimization problems using a continuous field representing a fictitious material density yields convex optimization problems which can be solved efficiently using stateof-the-art solvers used for limit analysis problems. We further analyze these problems by discussing the choice of the material strength criterion, especially when considering materials with asymmetric tensile/compressive strengths. In particular, we advocate the use of a L 1-Rankine criterion which tends to promote uniaxial stress fields as in truss-like structures. We show that the considered problem is equivalent to a constrained Michell truss problem. Finally, following the idea of the SIMP method, the obtained continuous topology is post-processed by an iterative procedure penalizing intermediate densities. Benchmark examples are first considered to illustrate the method overall efficiency while final examples focus more particularly on no-tension materials, illustrating how the method is able to reproduce known structural patterns of masonry-like structures. This paper is accompanied by a Python package based on the FEniCS finite-element software library.

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; This work aims at proposing a strategy for 3D-printing geopolymer composite structures at a half-meter scale, without using organic additives. An original printing device based on cartridges is developed and adapted to a 6-axis robot. The yield stress, working time and apparent Young modulus of the extruded material are measured. A devoted software, procedure and printing path are set up, leading to the fabrication of a structure without height limitation, without major geometrical defects or instabilities. The working time ensures the consolidation of the material during printing and good adhesion between layers. As an example, four successive cartridges have been successfully used to elaborate a hollow cylinder (Φ = 35 cm, H = 45 cm).

International audience; The embodied energy of a building is not only but essentially due to the quantity of material in its structure. Current fabrication techniques of optimised reinforced concrete (RC) structural elements have not proved sufficient economic competitiveness to be broadly accepted by the construction industry. This partly explains why the construction industry has not yet been able to reduce the embodied energy of newly-constructed buildings or civil works. However, most of the researches driven in the academic world on digital fabrication with concrete are focused on the construction of non-standard structures. Application of digital fabrication to standard structures could help bridge the gap between the need for lower-carbon structures and the economic interest of players in the construction industry. This paper questions the compatibility of existing building codes with digital manufacturing techniques and presents a novel method for the fabrication of sustainable optimised reinforced concrete beams, compliant with EN 1992-1-1 design requirements.

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; Important developments in additive manufacturing with concrete have been achieved in the past decades. Yet, printed components usually do not comply with building standards or basic reliability principles, and are not commonly used as load-bearing components. A gap between research and practice exists and despite several attempts, off-the-shelf commercial solutions for the reinforcement of the 3D printed structural components seem always expected. This article presents an alternative (pending for patent [1]) for reinforcement of 3D printed structures. This technology inspired by the composite industry is called Flow-Based Pultrusion for additive manufacturing (FBP). A strict control of the rheological behaviour of the cementitious matrix ensures the routing and impregnation of continuous rovings of thin fibres (glass, basalt, etc.) without any motorization. The resulting material, Anisotropic Concrete, homogeneously reinforced in a single direction, provides new possibilities, may enhance strength and ductility for hardened material but also help to a better handling of the fresh laces during the deposition, permitting inclined or cantilever paths. This paper describes the process, its constraints, first experimental achievements and first investigations about the mechanical performances of such a material.

This paper introduces a novel rheological technique allowing for the assessment of printable materials yield stress at nozzle exit in the case of extrusion-based 3D printing. This technique is derived from the analysis of the specific gravity-induced non-Newtonian flow that takes place at nozzle exit, which is at the origin of the formation of material drops or so-called slugs. A simple connected balance located below the nozzle gives access to the slugs mass distribution, the average value and the variability of which allow for the computation of the yield stress and, in parallel, for the assessment of the material homogeneity. In this paper, this method is first experimentally validated on simple materials in simple extruders before it is applied to a real printing system. The equations allowing for the yield stress computation are derived. The accuracy of the technique and its range of applicability are discussed.

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.

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.

Successful and efficient fabrication using robotic extrusion of cementitious materials mainly relies on the mastering of the printable material fresh state behavior. This paper tackles this aspect by introducing a novel rheological apparatus dedicated to the yield stress measurement at nozzle exit in extrusion-based manufacturing. It is based on the analysis of the specific gravity-induced flow that takes place at nozzle exit, which is at the origin of the formation of material drops or so-called “slugs”. Using a simple connected balance with a high measurement frequency gives access to these slugs average mass and, in turn, to the yield stress. Due to its convenience, the protocol is appropriate for setting the printing parameters according to the yield stress measurement at the nozzle exit in order to ensure successful fabrication.

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 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.

The vast majority of applications of extrusion-based concrete additive manufacturing deal with unreinforced mortar. The lack of reinforcement is a serious limitation for the industrial development of 3d printed concrete, because of the brittleness and lack of tensile strength of unreinforced mortar. In this paper, a new reinforcement method inspired by pultruded composite manufacturing, called flow-based pultrusion (FBP), is described and used. The principle is that continuous fiber rovings are impregnated and pulled by the matrix flow, avoiding motorisation, and increasing the apparent yield stress of the mortar and consequently its usability. The hardened resulting material, called anisotropic concrete, is unidirectionally and homogenously reinforced. For such composite material, the reinforcement ratio is an important material parameter that relates to specific process variables: roving type, roving count, and output diameter. This article further investigates the effect of the percentage of reinforcement on the process. It also highlights technical requirements to provide the first specifications for flow-based pultrusion.

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.

In a context of intense environmental pressure where the construction sector has the greatest impact on several indicators, the reuse of load-bearing elements is the most promising by avoiding the production of waste, preserving natural resources and reducing greenhouse gas emissions by decreasing embodied energy. This study proposes a methodology based on a chain of tools to enable structural engineers to anticipate future reuse. This methodology describes the design of reversible assemblies, the addition of complementary information in the building information modeling (BIM), reinforced traceability, and the development of a material bank. At the same time, controlling the environmental impacts of reuse is planned by carrying out a life cycle assessment (LCA) at all stages of the project. Two scenarios for reuse design are applied with the toolchain proposed. A. &ldquo, design from a stock&rdquo, scenario, which leads to 100% of elements being reused, using only elements from stock. B. &ldquo, design with a stock&rdquo, scenario, which seeks to integrate as many reused elements available in the stock as possible. The case study of a high-rise building deconstructed to rebuild a medium-rise building demonstrated that the developed toolchain allowed the inclusion of all reuse elements in a new structural calculation model.

International audience; The aim of this article is to propose parameterization with planar facets of dome structures. The technique introduced in this paper starts from an input parameterization and creates a dual pattern with planar quadrilateral facets. The derivation of the analytical solution allows to link the method with the creation of meshes with planar hexagonal facets and of circle packing on spheres. The method can be used in various contexts and allows designers to design with two superimposed parameterizations, which allows for a potential decoupling between structure and envelope.

International audience; This article presents a methodology to generate surfaces with planar lines of curvature from two or three curves and tailored for architectural design. Meshing with planar quadrilateral facets and optimal offset properties for the structural layout are guaranteed. The methodology relies on the invariance of circular meshes by spherical inversion and discrete Combescure transformations, and uses parametrisation of surfaces with cyclidic patches. The shapes resulting from our methodology are called super-canal surfaces by the authors, as they are an extension of canal surfaces. An interesting connection to shell theory is recalled, as the shapes proposed in this paper are at equilibrium under uniform normal loading. Some applications of these shapes to architecture are shown.

International audience; The difficulty to construct mechanically optimal shells may limit the use of structural optimisation in practice. The objective of this paper is to propose a new parametric representation of doubly curved shapes suited for structural optimisation of architectural shells that inherently considers fabrication constraints. We focus on a common construction constraint: the covering of building envelopes with planar facets. This paper proposes to implement the so-called marionette technique as a Computer-Aided-Design tool that guarantees covering of free-form shapes with planar quad-rilateral facets. General considerations on the size and nature of the optimisation space created with this method are made. It is demonstrated through different case-studies that the quality of the parametrisation for shape optimisation of shell structures is similar to the one offered by Bézier surfaces, an ubiquitous modelling technique. The proposed method conciliates thus fabrication and structural performance.

The aim of this article 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: non-uniform rational basis spline modelling and mesh-based approaches. The authors propose an alternative framework called generalised cyclidic nets that automatically yield 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 article 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 also demonstrates that this framework gives a simple method to generate corrugated shells.

International audience; 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.

International audience; The 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.

By reinforcing the links between mechanics of materials, structural engineering and applied mathematics at a sufficiently high level, new paths may be explored and building innovations proposed, making complex structures more affordable constructions. Three main keys are explained and illustrated with examples. The first key is a deep knowledge of materials, a second one is based on a rigorous mathematical management of shapes and geometry and a last one is related to new digital and technological prospects as robots and 3d printing. In the paper, several illustrations from Navier laboratory are shown such as composite gridshell (Créteil cathédrale), complex shapes designed to be natively “fabrication-aware” (nodes and facets considerations). ThenBuild’Inthe Ecole des Ponts ParisTech technological platform devoted to digital fabrication (3d printing, robotic constructions…) is presented and an illustration is made on a wood structure prototype, realized in 2017. About 100 m2, the structure involves the management of a complex geometry, respecting the material specificities (economical and mechanical), and using a construction process permitting to make it affordable.

International audience; The paper presents some results on the influence of the pre-stress induced by the erection method of elastic grid shells on their buckling capacity. It starts with the numerical methods and their validation with the study of a prebuckled arch. Then, a form-finding scheme using low-speed dynamics is used to generate automatically a family of elastic grid shells, and their buckling capacity is compared to the one of grid shells with the exact same geometry, but without any pre-stress. The paper demonstrates finally that the pre-stress decreases by a few percent the buckling capacity of elastic grid shells.