Giga-voxel computational morphogenesis for structural design

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In the design of industrial products ranging from hearing aids to automobiles and aeroplanes, material is distributed so as to maximize the performance and minimize the cost. Historically, human intuition and insight have driven the evolution of mechanical design, recently assisted by computer-aided design approaches. The computer-aided approach known as topology optimization enables unrestricted design freedom and shows great promise with regard to weight savings, but its applicability has so far been limited to the design of single components or simple structures, owing to the resolution limits of current optimization methods1,2. Here we report a computational morphogenesis tool, implemented on a supercomputer, that produces designs with giga-voxel resolution—more than two orders of magnitude higher than previously reported. Such resolution provides insights into the optimal distribution of material within a structure that were hitherto unachievable owing to the challenges of scaling up existing modelling and optimization frameworks. As an example, we apply the tool to the design of the internal structure of a full-scale aeroplane wing. The optimized full-wing design has unprecedented structural detail at length scales ranging from tens of metres to millimetres and, intriguingly, shows remarkable similarity to naturally occurring bone structures in, for example, bird beaks. We estimate that our optimized design corresponds to a reduction in mass of 2–5 per cent compared to currently used aeroplane wing designs, which translates into a reduction in fuel consumption of about 40–200 tonnes per year per aeroplane. Our morphogenesis process is generally applicable, not only to mechanical design, but also to flow systems3, antennas4, nano-optics5 and micro-systems6,7.

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This work was funded by the Villum Foundation through the NextTop project and a PRACE (Partnership for Advanced Computing in Europe) grant TopWING giving access to the Curie supercomputer (GENCI@CEA, France). Access to, and efficient support from, the technical staff at Curie is highly appreciated. We also acknowledge access to and support from the Visualization Cluster at Copenhagen University through T. Haugbølle and Å. Norlund, and discussions with A. Horsewell and J. J. Thomsen from the Technical University of Denmark.

Author information


  1. Department of Mechanical Engineering, Technical University of Denmark, Nils Koppels Allé, Building 404, 2800 Kongens Lyngby, Denmark

    • Niels Aage
    • , Erik Andreassen
    • , Boyan S. Lazarov
    •  & Ole Sigmund
  2. Centre for Acoustic-Mechanical Micro Systems, Technical University of Denmark, 2800 Kongens Lyngby, Denmark

    • Niels Aage


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N.A. contributed to the original idea, method development, implementation, supercomputing, visualization, renderings and manuscript preparation. E.A. contributed to the original idea, method development, implementation, visualization and manuscript preparation. B.S.L. contributed to mesh mapping and manuscript editing. O.S. contributed to the original idea, method development, analytical studies and manuscript preparation.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Niels Aage.

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Extended data

Supplementary information

PDF files

  1. 1.

    Supplementary Figure 1

    The full wing structure seen from the side, a high resolution and zoomable image of the optimized wing structure from Figure 1.

  2. 2.

    Supplementary Figure 2

    The optimized wing structure seen from the wing tip, a high resolution and zoomable image of the optimized wing structure from Figure 1.


  1. 1.

    Optimization history for the jet engine bracket

    Animation of the computational morphogenesis process exemplified on the GrabCAD jet engine design challenge from Extended Data Figure 1.


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