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Giga-voxel computational morphogenesis for structural design


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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Figure 1: Optimized wing structure.
Figure 2: Morphogenesis evolution, 3D printing and comparison to the hornbill bird beak.

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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.

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Authors and Affiliations



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.

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Correspondence to Niels Aage.

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The authors declare no competing financial interests.

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Extended data figures and tables

Extended Data Figure 1 Schematic of the morphogenesis process.

The figure illustrates the design of a jet engine bracket by morphogenesis. a, The design domain and the four load scenarios (coloured arrows). b, Snapshots from the design evolution. c, Rendering of the final titanium bracket design.

Extended Data Figure 2 Wing design model problem.

Rendering of the full wing model is shown. All load cases use symmetry conditions at the root (orange) with only the top-most layer of elements being fully fixed (red). The bottom right insets show the pressure coefficients Cp of the two aerodynamic load cases (adapted from figure 10 in ref. 11) and the top left inset indicates the position and direction of the simulated engine loads for the third load case (purple arrows). The section highlighted in blue marks the cut-out region used in Fig. 2a, b.

Extended Data Figure 3 Influence of multiple load cases.

ad, Top view of the NASA Common Research Model (blue), along with the optimized wing-box structures for varying loading cases (grey). The NASA Common Research Model shows a standard wing-box design with spars (dark blue) and ribs (red). The optimized designs are for a single load at 0° incidence (a), a single load at 4° incidence (b), two loads at 0° and 4° incidence (c), and three loads, including engine load and two aerodynamic loads at 0° and 4° incidence (d). The load cases are shown in Extended Data Fig. 2.

Extended Data Figure 4 Curved spars.

Stiffness improvement (per cent) is shown as function of the dimensions of the curved spar (h/H = 0 indicates a straight spar and h/H = 1/2 indicates a half-circular spar; some approximate shapes are sketched, indicated by arrows). Red, blue and green lines correspond to torsion boxes with aspect ratios of 4, 6 and 8, respectively. Solid lines indicate increased torsion stiffness and dashed lines decreased bending stiffness. The inset shows the parameterization of the cross-section of the wing box.

Extended Data Figure 5 Non-traditional ribs.

Simplified wing-box models were used to estimate the stiffness gain from non-traditional wing rib geometries. Both images show the optimized wing box for two aerodynamic load cases (compare with Extended Data Fig. 3c) in grey. The optimized design is overlaid in blue (left), showing a wing box with conventional straight ribs, or red (right), showing a wing box with unconventional ribs. Thicknesses of ribs are tailored to ensure equal mass.

Extended Data Table 1 Performance of non-traditional and traditional rib structures

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Supplementary information

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. (PDF 9783 kb)

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. (PDF 10294 kb)

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. (MOV 536 kb)

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Aage, N., Andreassen, E., Lazarov, B. et al. Giga-voxel computational morphogenesis for structural design. Nature 550, 84–86 (2017).

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