Isoradial meshes: Covering elastic gridshells with planar facets

Douthe, Cyril; Mesnil, Romain; Orts, Hugo; Baverel, Olivier

doi:10.1016/j.autcon.2017.08.015

Cited by 24 publications

(15 citation statements)

References 22 publications

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“…Nexorades have not benefited from recent advances in architectural geometry, where the fabrication of envelopes with planar or developable panels has been studied extensively [30]. Covering nexorades with planar panels could thus open new possibilities for their use, like for other structural systems [31].…”

Section: Previous Workmentioning

confidence: 99%

Form finding of nexorades using the translations method

Mesnil

Douthe

Baverel

et al. 2018

Automation in Construction

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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.

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Section: Previous Workmentioning

confidence: 99%

Form finding of nexorades using the translations method

Mesnil

Douthe

Baverel

et al. 2018

Automation in Construction

Self Cite

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“…The particles then moved within the design domain according to residual forces and damping, and once they were finally well positioned after the molecular dynamics simulation process, wellformed triangles were created using Delaunay triangulation. More recently, Douthe et al (2017) proposed a method to generate gridshells with quadrilateral cells using two intersection curves as guide lines. A circular mesh was generated, and the duality between a circular mesh with a unique radius and a Chebyshev net was used to obtain a quadrilateral grid that considered the planarity of each cell.…”

Section: Curve Fluiditymentioning

confidence: 99%

Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

Jun

Shepherd

et al. 2019

J. Comput. Civ. Eng.

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Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifest the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on "guide line" and "surface flattening" methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete NURBS (Non-Uniform Rational B-Spline) surface is firstly divided into a number of patches, and a discrete free-form surface formed by mapping dividing points onto the surface. The free-form surface was then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the 2D surface, with grids formed by applying a guide-line method. Subsequently, the intersections of the guide-lines and the complex boundary are obtained, and the guide-lines divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the 3D surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes bypresenting realistic examples to demonstrate the practical effectiveness of the proposed method.

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“…It is represented in Figure 1 and described by equation (6).The name 'duality' has many interpretations, and it is not used in the mathematical sense. The idea of creating a conjugate parameterization that is 'dual' to another parameterization can be found [3], where the parameterization by the lines of curvatures is dual to a Tchebycheff nets, which allows for the covering of elastic gridshells by planar facets.…”

Section: Construction Of a Dual Planar Parameterizationmentioning

confidence: 99%

A Re-Parameterization Approach for the Construction of Domes with Planar Facets

Mesnil¹

2018

Journal of the International Association for Shell and Spatial

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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.

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Isoradial meshes: Covering elastic gridshells with planar facets

Cited by 24 publications

References 22 publications

Form finding of nexorades using the translations method

Form finding of nexorades using the translations method

Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

A Re-Parameterization Approach for the Construction of Domes with Planar Facets

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