Since 2014

Free-form architecture challenges designers and makers. Non-standard geometries bring many issues for the rationalisation of facades and structural layout.  This research investigates two fabrication constraints relevant for glazed structures: the covering of doubly-curved shapes with planar facets, and the proper offset of support structure.

Free-form surfaces with planar facets

The covering of free-form shapes with planar panels has been an active topic of research since the 1980’s. Jörg Schlaich and Hans Schober introduced surfaces of translations in 1989. This method allows the covering of complex shapes with planar quadrangles. Triangular panels are always planar but are more complex to construct than quadrilateral meshes. In average, six beams meet along one node in triangular meshes. This number decreases to four for quadrilateral meshes, and three for hexagonal meshes.

Rather than trying to post-process arbitrary shapes, we propose simple methods to generate complex shapes covered with planar quadrilaterals. These methods often use two curves that mould curved shapes. They can be easily used and bring intuition back into free-form design.Monge’s surfaces and moulding surfaces can be covered with planar panels and can be covered with high node repetition (Mesnil et al. 2015 & 2015).

Inspiration was taken from the work of Gaspard Monge, known as the inventor of descriptive geometry, to propose an innovative technique for shape modelling. This method, called ‘Marionette technique’ by the authors, guarantees real-time modelling of shapes covered by planar facets (Mesnil et al. 2016).

Gridshells with multiple layers and torsion free nodes

Meshes are theoretical objects with zero thickness, which is not the case for civil engineering structures. This results in specific geometrical challenges. The research on this topic focuses on meshes with offsets. An offset of a mesh is a second mesh that is parallel to the first one, and which lies at a constant distance. The existence of this offset yields two benefits :

  • The mesh can be built with multiple layers;
  • At each node, all beams intersect on a unique axis. This considerably eases the fabrication of the nodes.

Special attention is given to circular and conical meshes. Circular meshes are meshes for which each face is inscribed in a circle. This quality implies automatically the existence of an offset at constant node distance. The research focuses on the development of design tools to generate free-form circular meshes. Conical meshes are closely related to circular meshes. They have offsets at constant face distance.

A first method has been implemented to generate discrete Monge and moulding surfaces as conical meshes (Mesnil et al. 2015). A second method has been developed to generate circular meshes based on cyclidic nets (Mesnil et al. 2015).

  • All
  • Architectural Geometry
  • Gridshell
  • Nexorade
  • Steel Structures
  • Active Bending

 Gridshells without kink angle between beams and cladding panels – X. Tellier et al. (2018)

Author

Xavier Tellier, Cyril Douthe, Olivier Baverel, Laurent Hauswirth

Abstract

In double-curvature gridshells covered with rigid flat panels, panels cannot lay flat on the top surface of beams. In many cases, costly elements need to be inserted in-between to insure a proper beam-panel connection. Precedent research on the geometric rationalization of gridshells has mostly focused on minimizing cladding panel curvature, simplifying node and beam fabrication, and allowing for repeatability of elements. The connection between beams and panels has received very little attention. This paper explores the possible gridshell geometries under the constraint of having a full planar contact between beams and cladding panels. A strategy that consists of folding panels is studied in details. It turns out that a rich variety of panel shapes and folding patterns is possible. Two generation methods for such shapes are proposed: a method for quad meshes of revolution covered with folded panels, and a method for folded hexagonal panels based on the projection algorithm developed by Bouaziz et al. The resulting structures are of particular interest for opaque doubly curved facades covered with metal sheets or other foldable material. The good contact between beams and panels also offers the possibility to use the panels as bracing elements. Hence the proposed method proves to be efficient for construction purposes, but also for mechanical behavior.

Status

Published

Journal

Proceedings of the IASS 2018

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 Discrete CMC surfaces for doubly-curved building envelopes – X. Tellier et al. (2018)

Author

Xavier Tellier, Cyril Douthe, Olivier Baverel, Laurent Hauswirth

Abstract

Constant mean curvature surfaces (CMCs) have many interesting properties for use as a form for doubly curved structural envelopes. The discretization of these surfaces has been a focus of research amongst the discrete differential geometry community. Many of the proposed discretizations have remarkable properties for envelope rationalization purposes. However, little attention has been paid to generation methods intended for designers.
This paper proposes an extension to CMCs of the method developed by Bobenko, Hoffmann and Springborn (2006) to generate minimal S-isothermic nets. The method takes as input a CMC (smooth or finely triangulated), remeshes its Gauss map with quadrangular faces, and rebuilds a CMC mesh via a parallel transformation. The resulting mesh is S-CMC, a geometric structure discovered by Hoffmann (2010). This type of mesh have planar quads and offset properties, which are of particular interest in the fabrication of gridshells.

Status

Published

Journal

Advances in Architectural Geometry 2018

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 Fabrication-aware shape parametrisation for the structural optimisation of shell structures – R. Mesnil et al. (2018)

Author

R. Mesnil, C. Douthe, C. Richter, O. Baverel

Abstract

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 quadrilateral 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 NURBS, an ubiquitous modelling technique. The proposed method conciliates thus fabrication and structural performance.

Status

Submitted

Journal

Engineering Structures

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 A re-parameterization approach for the construction of domes with planar facets – R. Mesnil (2018)

Author

R. Mesnil

Abstract

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.

Status

Submitted

Journal

Journal of the IASS

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 Morphogenesis of surfaces with planar lines of curvature and applications to architectural design – R. Mesnil et al. (2018)

Authors

R. Mesnil, C. Douthe, O. Baverel,  B. Léger

Abstract

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.

Status

Submitted

Journal

Automation in Construction

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 Form finding of reciprocal frames using the translations method – R. Mesnil et al. (2018)

Authors

R. Mesnil, C. Douthe, O. Baverel,  T. Gobin

Abstract

This article proposes a new computational method for the form-finding of nexorades, also called reciprocal frames by some authors. The method is based on the translations of the 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 is thus based on linear algebra, so that fitting problems can be formulated as 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 50m² timber pavilion.

Status

Submitted

Journal

Automation in Construction

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 Non-standard patterns for gridshell structures: Fabrication and Structural Optimization – R. Mesnil et al. (2017)

Authors

R. Mesnil, C. Douthe, O. Baverel

Abstract

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.

 Marionette meshes: modelling free-form architecture with planar facets – R. Mesnil et al. (2017)

Authors

Mesnil R., Douthe C., Baverel O. and Léger B.

Abstract

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 most engineering problems related to free-form architecture.

Status

Under review

Date

2017

Journal

International Journal of Space Structures

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 Isoradial meshes: covering elastic gridshells with planar facets – C. Douthe et al. (2017)

Authors

Douthe C.,Mesnil R., Orts H. and Baverel O.

Abstract

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 PQ-Mesh which confirm the practical feasibility of elastic gridshells covered with planar facets.

Date

2017

Journal

Automation in Construction

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 Structural Morphology And Performance of Plated Structures with Planar Quadrilateral Facets – R. Mesnil et al. (2017)

Authors

Mesnil R., Douthe C., Baverel O., Caron J.-F. and Léger B.

Abstract

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.

Date

March 2017

Journal

Journal of the IASS

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 Linear buckling of quadrangular and kagome gridshells: a comparative assessment – R. Mesnil et al. (2017)

Authors

Mesnil R., Douthe C., Baverel O. and Léger B.

Abstract

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.

Date

2017

Journal

Engineering Structures

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 New shapes for elastic gridshells covered by planar facets – C. Douthe et al. (2016)

Authors

Douthe C., Mesnil R., Orts H. and  Baverel O.

Abstract

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.

 

Date

Sept. 2016

Conference

Annual Symposium of the IASS 2016

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 Marionette Mesh: from descriptive geometry to fabrication-aware design – R. Mesnil et al. (2016)

Authors

Mesnil R., Douthe C., Baverel O. and Léger B.

Abstract

The objective of this paper is to introduce an intuitive method for the modelling of free-form architecture with planar facets. The method, called Marionette by the authors, takes inspiration from descriptive geometry and allows to design complex shapes with one projection and the control of elevation curves. The proposed framework only deals with linear equations and therefore achieves exact planarity, for quadrilateral, Kagome and dual Kagome meshes in real-time. Remarks on how this framework relates to continuous shape parameterisation and on possible applications to engineering problems are made.

 Structural exploration of a fabrication-aware design space with Marionette Meshes – R. Mesnil et al. (2016)

Authors

Mesnil R., Richter C., Douthe C., Baverel O. and Léger B.

Abstract

This paper presents a new methodology for generating doubly-curved shapes covered with planar facets. The proposed method, called marionette method relies mainly on descriptive geometry, and it is shown that specifying appropriate projections, e.g. plane view and elevations, defines uniquely a free-form shape. This methodology is highly intuitive and can be used in real-time, mainly because only linear systems of equations are solved. The design-space offered by the marionette method is extremely large, and easily parameterized. Some applications show the potential of this technique for the parameterization of a fabrication-aware design space for structural optimization

Date

Sept. 2016

Conference

Symposium of the IASS 2016

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 Isogonal moulding surfaces: a family of shapes for high node congruence in free-form structures – R. Mesnil et al. (2015)

Authors

Mesnil R., Douthe C., Baverel O., Léger B., Caron J.-F.

Abstract

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 O ffset 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.

Date

accepted July 2015

Journal

Automation in Construction

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 Möbius Geometry and Cyclidic Nets: A Framework for Complex Shape Generation – R. Mesnil et al. (2015)

Authors

Mesnil R., Douthe C., Baverel O., Léger B.

Abstract

Free-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.

Date

Aug. 2015

Conference

IASS 2015

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 Generating high node congruence in freeform structures with Monge’s Surfaces – R. Mesnil et al. (2015)

Authors

Mesnil R., Santerre Y., Douthe C., Baverel O., Léger B.

Abstract

The 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.

Date

Aug. 2015

Conference

IASS 2015

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Coming soon

Architectural geometry is an active topic of research for architects, engineers and mathematicians. Some books or articles can be recommended on the topic of polyhedral surfaces.

Coming soon