We introduce a variant of the timber grid shell, the timber Voronoi shell, whose surface is reticulated by Voronoi tessellation and whose edges are made of discrete dimensional timber. This work explores form-finding methods of the Voronoi shell as a compressive funicular shell. Two closed-form solutions to shape initialization are proposed. We develop methods for minimizing the deviation from coplanarity between timber members and adjacent surface normal in order to facilitate manufacturing. A well-defined fabrication process is important for making the physical structure consistent with the structural model. A 6-axis robot with a motor spindle is employed to prefabricate the timber so the in situ manual assembly becomes easier. A parametric model describes the joint details. We formulate the robotic toolpath as a closed-form function of the resultant mesh from form finding. Thus, a general-purpose programming language can directly implement the mesh optimization and manufacturing processes without CAD or CAM software. The physical implementations, including an exhibition pavilion, validated the approach.
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The prefabrication and assembly of the structures were organized by Prof. Biao Li’s Institute of Architectural Algorithms and Applications, Southeast University, Nanjing. The team members of the Upsilon project include H. Hua, J.C. Wang, B. Li, P. Tang, Y.Y. Chen, C.Y. Cai, J.N. Xu, J.Z. Chen, S.Y. Li, H.J. Li, N.L. Liu, H. Li, J.R. Zeng, H.C. Guo, X. Wang, Y.L. Chen, H.D. Wu, L.X. Wei, and J.S. Zhang.
We thank the reviewers and the editor for their constructive remarks towards improving the manuscript. We also thank Prof. Lei He from School of Civil Engineering at Southeast University for his advice on numerical optimization.
This work was financially supported by the National Natural Science Foundation of China  and the Ministry of Housing and Urban-Rural Development of China [UDC2017020212].
Conflict of interest
The authors declare that they have no conflict of interest.
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Replication of results
The Java codes at https://github.com/whitegreen/Voronoi-Timber-Shell can fully reproduce the results.
Responsible Editor: Mehmet Polat Saka
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Hua, H., Hovestadt, L. & Tang, P. Optimization and prefabrication of timber Voronoi shells. Struct Multidisc Optim (2020). https://doi.org/10.1007/s00158-019-02445-x
- Grid shell
- Form finding
- Structural optimization