Since 2000

Systems consisting of beams mutually supporting each other have been known for centuries, they are referred as reciprocal systems. Numerous illustrations of such structural systems can be found in the book of O. Popovic Larsen. The term ‘nexorade’ describes the spatial generalisation of the flat beam arrangements proposed by the previous authors. This generalisation relies on the fact that it is the eccentricity between the elements at connection points that dictates the final form.

Description of the research

Systems consisting of beams mutually supporting each other have been known for centuries and numerous illustrations of such structural systems. For example, during the medieval ages, the French architect Villard de Honnecourt provided a solution based on a mutually supporting frame for the problem of covering a space with beams shorter than the span. Leonardo Da Vinci was also interested in this concept and made sketches for beam arrangements similar to Villard de Honnecourt.

The definition of the parameter of a nexorade where defined in (Baverel 2000). This type of structure which is rather simple to assemble technologically has a complex form-finding  procedure. (Baverel 2004 ) tried to generate the form-finding with the genetic algorithms. (Douthe 2009) managed to generated the structure with the help of a fictuous mechanical behaviour solved by dynamic relaxation. This method is now implemented in rhino grasshopper. An analytical investigation was done by (Baverel 2007) and (Senechal 2011). A review of the different types of interlaced structures was made by (Baverel 2011).

 

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  • Architectural Geometry
  • Nexorade

 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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 Form Finding and Design of a Timber Shell-Nexorade Hybrid – R. Mesnil et al. (2018)

Authors

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

Abstract

The aim of this paper is to discuss the form-finding of an innovative structural system through the design and construction of a full-scale timber pavilion. Nexorades, or multi-reciprocal grids, are structures where members support each other along their spans. This structural principle allows simple assembly and connection details, but leads in counterpart to poor structural performance. Introducing planar plates as bracing components solves this issue, but result in a complex and intricate geometry of the envelope and supporting structure. This paper discusses the different challenges for the designers of shell-nexorade hybrids and algorithmic framework to efficiently handle them in a project workflow.

Date

September 2018

Conference

Advances in Architectural Geometry 2018

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 Fabrication-Aware Design of timber shell-nexorade hybrids – T. Gobin et al. (2018)

Authors

T. Gobin, R. Mesnil, C. Douthe, P. Margerit, N. Ducoulombier, L. Demont, H. Delmi and J.-F. Caron

Abstract

The aim of this paper is to discuss the dialectic form-finding of a complex timber structure based on an innovative structural system: shell-nexorade hybrids. Nexorades, also known as reciprocal frames are elegant structures that suffer from a relatively poor structural behavior due to in-plane shear and bending of the members. Introducing plates as bracing elements significantly improves their performance, but increases the manufacturing complexity and sets high tolerance constraints. We present the fabrication and assembly of a 50m² timber pavilion with 6-axis robotized milling. The use of a mobile robot and fixed machining stations is explored to allow for maximal flexibility of iterations between design and fabrication.

Date

September 2018

Conference

RobArch 2018

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 Design and construction of a shell-nexorade hybrid timber structure – C. Douthe et al. (2018)

Authors

Cyril Douthe, Romain Mesnil, Olivier Baverel, Tristan Gobin, Xavier Tellier, Nicolas Ducoulombier and Nicolas Montagne

Abstract

The aim of this paper is to present the design and fabrication of an innovative timber structure, built on the campus of l’Ecole des Ponts ParisTech. The structural principle of the pavilion, spanning 6.5 meters with a structural thickness of 14cm, is derived from nexorades, also called reciprocal frames by some authors. Nexorades are constituted of load-bearing elements which support each other along their span and not extremities. The paper applies a novel form-finding method based upon translation of the edges [1]. The method yields a linear subspace for shape explorations, which can easily be computed. The form-finding technique also allows for the covering of nexorades with planar facets if the geometry before transformation is covered with planar facets [2].

Date

July 2018

Conference

IASS 2018

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 A Review of Woven Structures with Focus on Reciprocal Systems – Nexorades – O. Baverel and O. Popovich Larsen (2011)

Author

O. Baverel and O. Popovic Larsen

Abstract

The main aim of this paper is to present the different types of load-bearing woven systems that stand by friction or with the use of a locking device. A review of the different types of systems has been done and an attempt of classification has been proposed. The paper focuses on the different types of elements that can be used to create reciprocal systems or nexorades. Configurations with elongated, ring, tile and block elements are shown. The different parameters that define such structures are also presented. Although the description of the parameters is quite easy for simple construction, a broader approach is still needed to be done for more complex configurations.

 Analytical Investigations on Elementary Nexorades – B. Sénéchal et al. (2011)

Authors

B. Sénéchal , C., Douthe, O. Baverel

Abstract

Nexorades or reciprocal frames can be seen as a practical way to reduce the complexity of connections in spatial structures by connecting reciprocally the members by pairs. This reduction of the technological complexity of the connections is however replaced by a geometrical complexity due to numerous compatibility constraints. The purpose of this article is to make explicit these constraints for elementary structures and to solve analytically the resulting system of equations. Applications to regular polyhedrons are presented and a practical realization (a 3 m high dodeca-icosahedron) is shown. In the brief conclusion, perspectives for complementary analytical developments for spatial structures are drawn forth.

 Design of reciprocal frames with the dynamic relaxation method – C. Douthe and O. Baverel (2009)

Authors

C., Douthe, O. Baverel

Abstract

The objective of this paper is to propose a simple method using dynamic relaxation algorithm to find the form and perform a structural analysis of reciprocal frame systems, also called nexorades. After a brief historical note, details of the parameters that govern the design of nexorades are introduced together with details of the assembly. These parameters induce strong geometrical constrains on this kind of structures so that a form-finding step is required. It is suggested here to introduce a fictitious mechanical behaviour to solve this problem. The dynamic relaxation algorithm is used with a model that takes into account the eccentricity between the elements. Its implementation is explained and its versatility is illustrated through several examples covering various fields of applications going from form-finding problems to non-linear structural analysis of structures. In a last example the structural behaviour of nexorades is compared with more conventional triangulated structures.

Date

2009

Journal

Computers and structures

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 Nexorade based on regular polyhedra – O. Baverel and H. Nooshin (2007)

Author

O. Baverel and H. Nooshin

Abstract

Starting from simple notions of paper folding, a review of current challenges regarding folds and structures is presented. A special focus is dedicated to folded tessellations which are raising interest from the scientific community. Finally, the different mechanical modeling of folded structures are investigated. This reveals efficient applications of folding concepts in the design of structures.

Date

2007

Journal

Nexus Network Journal Architecture and Mathematics

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 Nexorade: a structure for ‘free form’ architecture – O. Baverel et al. (2006)

Author

O. Baverel,  C. Douthe, and J.F. Caron

Abstract

The objective of this paper is to discuss the geometrical properties of different grids used for the creation of nexorades.

Date

2000

Conference

Adaptables 2006, TU/e,
International Conference On Adaptable Building Structures
Eindhoven The Netherlands

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 Configuration processing of Nexorade using genetic algorithm – O. Baverel and H. Nooshin (2004)

Author

O. Baverel and H. Nooshin

Abstract

The objective of this paper is to discuss the generation of configurations of nexorades using genetic algorithm. The process of genetic algorithm allows one to create a nexorade from an initial simple configuration. An important application of nexorades is for shelters of various sizes and shapes for temporary or permanent purposes.

Date

2004

Journal

Journal of the IASS

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 Nexorades – O. Baverel et al. (2000)

Author

O. Baverel,  H. Nooshin, Y. Kuroiwa and G.A.R. Parke

Abstract

The objective of this paper is to discuss the characteristics of a family of space structures that are referred to as 'nexorades'. Typically, a nexorade is constructed from scaffolding tubes, connected together with swivel couplers. An important application of nexorades is for shelters of various sizes and shapes for temporary or permanent purposes. In such a shelter, the structural skeleton is provided by a nexorade and the cover is provided by a membrane material.

Date

2000

Journal

International Journal of Space Structures

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