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      From Shape to Shell: A Design Tool to Materialise FreeForm Shapes Using Gridshell Structures

      Lionel du Peloux, Olivier Baverel, Jean-François Caron and Frederic Tayeb

      Abstract This paper introduces and explains the design process of a gridshell in composite materials built in Paris in 2011 for the festival Soliday. A brief introduction presents the structural concept and the erection methodology employed. It explains why composite materials are relevant for such applications. Following this practical case, the whole process from 3D shape to real-shell is then detailed. Firstly, the shape is rationalized and optimized to smooth local curvature concentrations. Secondly, a specific computing tool is used to mesh the surface according to the compass method. This tool allows designers to look for optimal mesh orientations regarding the elements curvature. Finally, a full structural analysis is performed to find the relaxed shape of the grid and check its stability, strength and stiffness under loads. The authors conclude on the overall relevance of such structures.

      Olivier Baverel

      UR Navier, Ecole des Ponts ParisTech, Champs-sur-Marne, France

      ENSAG, Grenoble, France

      Jean-François Caron, Frederic Tayeb

      UR Navier, Ecole des Ponts ParisTech, Champs-sur-Marne, France

      Lionel du Peloux

      UR Navier, Ecole des Ponts ParisTech, Champs-sur-Marne, France

      T/E/S/S, Paris, France

      1 Introduction

      The emergence of gridshell structures – intensively studied by the German architect Frei Otto – is a major step in the development of complex shapes in AEC (Architecture, Engineering and Construction). Since the 1970s this structural concept has led to emblematic realizations (Mannheim [Happold and Lidell 1975], Downland [Harris et al 2003], Savill, Hanovre [Ban 2006]). They have shown that beyond their architectural potential, gridshells are well suitable for complex shape materialization because of their intrinsic geometric rationality.

      However, the very few number of gridshells constructed up to now attests that they are quite tricky to design compared to standard buildings. Architects and engineers would face both demanding conceptual knowledge in 3D geometry, form-finding techniques, non-linear behaviour, large-scale deformations, permanent bending stresses, etc. and real lack of tools dedicated to their design.

      This paper presents a computing tool based on Rhinoceros & Grasshopper that aims at meshing NURBS surfaces with the compass method. This tool also includes a one-way interface for GSA (a structural analysis software from Oasys) to perform the structural analysis of the resulting grid. Thereby, this tool introduces shape-driven design of gridshells. Following a case study – the construction of the first composite gridshell to host people – a methodology to design these shape-driven structures is proposed. Finally, future prospects to their development are discussed.

      1.1 Gridshell: Concept, Erection Process, Materials

      Concept

      A gridshell is a structure, which behaves like a shell but is made of a grid. Thus, the material is not spread continuously as shells, but it is organized in a discrete grid pattern. Like shells, gridshells derive their stiffness from their double curvature shape. These structures can cross large spans with very few materials. They offer a rich and voluble lexicon to express blob-shapes.

      Erection Process

      Usually, the grid morphology is not trivial and leads to design numerous costly and complex joints. To overcome this issue, an original and innovative erection process was developed that takes advantage of the flexibility inherent to slender elements.

      A regular planar grid made of long continuous linear members is built on the ground (Fig. 1). The elements are pinned together so the grid has no in-plane shear stiffness. Thus, the grid can accommodate large-scale deformations during erection (Fig. 2). Then the grid is bent elastically to its final shape (Fig. 3). Finally, the grid is frozen in the desired shape with a third layer of bracing members (Fig. 4). The grid becomes a shell and the structure’s stiffness is multiplied by about 15.

      Fig. 1 Regular grid on the ground

      Fig. 2 Grid erection

      Fig. 3 Erected grid

      Fig. 4 Grid triangulation

      Material Flexibility for Structural Rigidity

      Composite materials like glass fibre reinforced polymer (GFRP) could favourably replace wood in this case where both resistance and bending ability of the material is sought. Thus, the structure’s stiffness derives from its geometric curvature and not from the material’s intrinsic rigidity. Moreover, using synthetic materials free us from the painful problematic of wood joining and wood durability (Douthe, Caron and Baverel 2010).

      High Tech & Low Cost

      Though gridshells require high-tech design techniques, they seem to be a low-cost way to materialise non-standard morphologies (200€/m2), because of their geometric rationality. The project complexity is shifted upstream.

      1.2 From-Finding Versus Grid-Finding

      One can identify two different ways of designing gridshells: those with a given outline and those with a given shape. The first approach considers the final shape a consequence of a form-finding process, driven by the supports of a grid which is thought to be an input data. The second approach consists of deriving a grid from a given shape. When erected on its supports, the grid should give back the intended morphology.

      Form-Finding

      A physical or numerical grid-model is handled until a structural shape is found, in compliance with the architectural intents. This way, Frei Otto designed the Multihalle of Mannheim using hanging funicular nets and photogrammetry (Otto and Hennicke 1974), see Figs. 5-6. Nowadays, this form-finding stage would probably be done by computer, relying on numerical methods such as dynamic relaxation or force density.

      Fig. 5 Hanging net

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