Stability of Pseudo-Funicular Elastic Grid Shells

International audienceThe 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

Möbius Geometry and Cyclidic Nets: A Framework for Complex Shape Generation

International audienceFree-form architecture challenges architects, engineers and builders. The geometrical rationalization of complex structures requires sophisticated tools. To this day, two frameworks are commonly used: NURBS modeling and mesh-based approaches. The authors propose an alternative modeling framework called generalized cyclidic nets that automatically yields optimal geometrical properties for the façade and the structure. 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 new shapes can be generated from generalized cyclidic nets. Finally, it is demonstrated that this framework gives a simple method to generate curved-creases on free-forms. These findings open new perspectives for structural design of complex shells

Affordable inline structuration measurements of printable mortar with a pocket shear vane

The control of mortar rheology is of paramount importance in the design of systems and structures in 3D printing concrete by extrusion. This is particularly sensitive for two-component (2K) processes that use an accelerator to switch the printed mortar very quickly from a liquid behavior to a sufficiently solid behavior to be able to be printed. It is necessary to set up simple and effective tests within a precise methodological framework to qualify materials evolving so quickly in an industrial context. It is obvious that inline solutions, that is to say, post-printing solutions, will be more desirable than benchtop-type solutions reproducing the printing conditions as well as possible, but imperfectly. After some main key points about measuring the structuration of mortars, we propose an original inline test using a pocket shear vane tester. The protocols are precisely described and the simplicity and quality of the results are demonstrated.Comment: 27 pages, 18 figure

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

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

Generating high node congruence in freeform structures with Monge's Surfaces

International audienceThe repetition of elements in a free-form structure is an important topic for the cost rationalization process of complex projects. Although nodes are identified as a major cost factor is steel grid shells, little research has been done on node repetition. This paper proposes a family of shapes, called isogonal moulding surfaces, having high node congruence, flat panels and torsion-free nodes. It is shown that their generalization, called Monge's surfaces, can be approximated by surfaces of revolution, yielding high congruence of nodes, panels and members. These shapes are therefore interesting tools for geometrically-constrained design approach

Stability of elastic grid shells

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 83-86).The elastic grid shell is a solution that combines double curvature and ease of mounting. This structural system, based on the deformation of an initially at grid without shear stiffness was invented more than fifty years ago. The apparition of new materials such as GFRP increased the potential of such structures whose properties depend on the deformation, or equivalently pre-stress of an initial structure. Elastic grid shells seem particularly promising as shelters, lightweight roofs, or kinetic structures. Although fundamental to the behavior of the strucure, the influence of the pre-stress on the stability of elastic grid shells has yet to be studied. Understanding this phenomenon could allow engineers to design more efficiently elastic grid shells. This thesis studies the influence of pre-stress on the stability of elastic grid shells. The research conducts a parametric study that focuses both a pre-buckled arch and initially at circular elastic grid shells with dierent grid spacing and levels of pre-stress. Realistic values of the parameters are determined from existing projects. The buckling analysis as well as the form-finding of the different structures are performed using finite element analysis. The tools are validated with comparison of the shape and buckling capacity of a pre-buckled arch with existing experiments. The parametric studies lead to recommendations aiming to facilitate the design of elastic grid shells. Keywords Elastic grid shell, Low-Speed Dynamics, form-finding, linear buckling analysisby Romain Mesnil.M.Eng

Design and construction of a shell-nexorade hybrid timber structure

International audienceThis paper presents the design and fabrication of an innovative structure, spanning 6.5m with a structural thickness of 12cm. The structural system derives from nexorades, also called reciprocal frames by some authors, obtained by a novel form-finding method based upon translation of the edges. It also allows for the covering with planar facets if the geometry before transformation is covered with planar facets. This property is used for the pavilion, covered with planar timber panels used as bracing elements. The benefit of this structural system, called shell-nexorade hybrid is discussed through a comparative study between the braced and un-braced nexorade (the stiffness is multiplied by ten adding only 30% mass). Finally, the fabrication process, achieved through robotized milling of the beams, is shown, illustrating the potential of pluri-disciplinary approach for conceptual design

Structural explorations of fabrication-aware design spaces for non-standard architecture

Les dernières décennies ont vu l’émergence de formes architecturales non standard. Les concepteurs se retrouvent généralement démunis face à la complexité géométrique de ces objets, dont la fabrication rime souvent avec complication. De plus, les outils utilisés dissocient forme et fonctionnement structurel,ce qui complexifie le processus de décision pour ingénieurs et architectes. Ce mémoire prend un point de vue fondé sur la notion d’invariance par transformation géométrique et étudie plusieurs strategies de génération de formes naturellement constructibles pour remédier à ces manques. Trois contraintes constructives ont été identifiées et correspondent à trois contributions indépendantes de cette thèse.La répétition des noeuds d’assemblage est étudiée via les transformations par maillages parallèles. Ces dernières sont utilisées pour créer une généralisation des surfaces de révolution. On retrouve par là un paramétrage particulier des surfaces moulures de Monge avec une grande répétition d’éléments, et notamment de noeuds d’assemblage.Les réseaux de cyclides sont ensuite utilisés pour dessiner des formes parametrées par leurs lignes de courbures. Cela permet la couverture par panneaux plans ainsi que l’offset des éléments structurels sans excentricité. L’apport de cette thèse est l’implémentation de plusieurs améliorations, notamment l’introduction de plis à double courbure, un algorithme permettant de généraliser les réseaux de cyclides à des topologies quelconques, et la génération de surfaces généralisant les surfaces canal à partir de deux courbes rail et une courbe profil.Finalement, une méthode innovante inspirée de la géométrie descriptive permettant la génération de formes courbes couvertes par des quadrilatères plans est proposée. La méthode, baptisée méthode marionnette, réduit ce problème à un système linéaire, ce qui permet une manipulation de ces forms constructibles en temps réel. Une étude comparative montre que cette technique peut être utilisée pour paramétrer des problèmes d’optimisation de forme de coques sans perte de performance par rapport aux paramétrages utilisés de façon classique. L’intégration des contraintes de fabrication dans le processus d’optimisation structurelle ouvre de nouvelles possibilités d’applications, comme des résilles gauches et des coques plissées. La pertinence de ces nouvelles solutions est démontrée par de multiples études de casThe 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-studie

Explorations structurelles de domaines de formes constructibles pour l’architecture non-standard

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-studiesLes dernières décennies ont vu l’émergence de formes architecturales non standard. Les concepteurs se retrouvent généralement démunis face à la complexité géométrique de ces objets, dont la fabrication rime souvent avec complication. De plus, les outils utilisés dissocient forme et fonctionnement structurel,ce qui complexifie le processus de décision pour ingénieurs et architectes. Ce mémoire prend un point de vue fondé sur la notion d’invariance par transformation géométrique et étudie plusieurs strategies de génération de formes naturellement constructibles pour remédier à ces manques. Trois contraintes constructives ont été identifiées et correspondent à trois contributions indépendantes de cette thèse.La répétition des noeuds d’assemblage est étudiée via les transformations par maillages parallèles. Ces dernières sont utilisées pour créer une généralisation des surfaces de révolution. On retrouve par là un paramétrage particulier des surfaces moulures de Monge avec une grande répétition d’éléments, et notamment de noeuds d’assemblage.Les réseaux de cyclides sont ensuite utilisés pour dessiner des formes parametrées par leurs lignes de courbures. Cela permet la couverture par panneaux plans ainsi que l’offset des éléments structurels sans excentricité. L’apport de cette thèse est l’implémentation de plusieurs améliorations, notamment l’introduction de plis à double courbure, un algorithme permettant de généraliser les réseaux de cyclides à des topologies quelconques, et la génération de surfaces généralisant les surfaces canal à partir de deux courbes rail et une courbe profil.Finalement, une méthode innovante inspirée de la géométrie descriptive permettant la génération de formes courbes couvertes par des quadrilatères plans est proposée. La méthode, baptisée méthode marionnette, réduit ce problème à un système linéaire, ce qui permet une manipulation de ces forms constructibles en temps réel. Une étude comparative montre que cette technique peut être utilisée pour paramétrer des problèmes d’optimisation de forme de coques sans perte de performance par rapport aux paramétrages utilisés de façon classique. L’intégration des contraintes de fabrication dans le processus d’optimisation structurelle ouvre de nouvelles possibilités d’applications, comme des résilles gauches et des coques plissées. La pertinence de ces nouvelles solutions est démontrée par de multiples études de ca

A Re-Parameterization Approach for the Construction of domes with planar facets

International audienceThe 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