Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Giga-voxel computational morphogenesis for structural design

Abstract

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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

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

References

  1. Bendsøe, M. P. & Kikuchi, N. Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  2. Bendsøe, M. P. & Sigmund, O. Topology Optimization — Theory, Methods and Applications (Springer, 2004)

  3. Alexandersen, J., Sigmund, O. & Aage, N. Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection. Int. J. Heat Mass Transfer 100, 876–891 (2016)

    Article  Google Scholar 

  4. Nomura, T., Sato, K., Taguchi, K., Kashiwa, T. & Nishiwaki, S. Structural topology optimization for the design of broadband dielectric resonator antennas using the finite difference time domain technique. Int. J. Numer. Methods Eng. 71, 1261–1296 (2007)

    Article  Google Scholar 

  5. Jensen, J. S. & Sigmund, O. Topology optimization for nano-photonics. Laser Photonics Rev. 5, 308–321 (2011)

    Article  CAS  ADS  Google Scholar 

  6. Sardan, O. et al. Rapid prototyping of nanotube-based devices using topology-optimized microgrippers. Nanotechnology 19, 495503 (2008)

    Article  CAS  Google Scholar 

  7. Dühring, M., Mortensen, N. A. & Sigmund, O. Plasmonic versus dielectric enhancement in thin-film solar cells. Appl. Phys. Lett. 100, 211914 (2012)

    Article  ADS  Google Scholar 

  8. Cavazzuti, M. et al. High performance automotive chassis design: a topology optimization based approach. Struct. Multidiscipl. Optim. 44, 45–56 (2011)

    Article  Google Scholar 

  9. Zhu, J., Zhang, W. & Xia, L. Topology optimization in aircraft and aerospace structures design. Arch. Comput. Methods Eng. 23, 1–28 (2015)

    CAS  ADS  MathSciNet  Google Scholar 

  10. Vassberg, J. C., DeHaan, M. A., Rivers, S. M. & Wahls, R. A. Development of a common research model for applied CFD validation studies. In 26th AIAA Applied Aerodynamics Conference 6919 (AIAA, 2008)

  11. Bell, J. H. Pressure-sensitive paint measurements on the NASA Common Research Model in the NASA 11-ft transonic wind tunnel. In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 1128 (AIAA, 2011)

  12. Kennedy, G. & Martins, J. A comparison of metallic and composite aircraft wings using aerostructural design optimization. In 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 5475, https://arc.aiaa.org/doi/abs/10.2514/6.2012-5475 (AIAA, 2012)

  13. Rao, J., Kiran, S., Kamesh, J., Padmanabhan, M. & Chandra, S. Topology optimization of aircraft wing. J. Aerosp. Sci. Technol. 61, 402–414 (2009)

    Google Scholar 

  14. Chin, T. & Kennedy, G. Large-scale compliance-minimization and buckling topology optimization of the undeformed Common Research Model wing. In 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 0939 (AIAA, 2016)

  15. Stanford, B. & Dunning, P. Optimal topology of aircraft rib and spar structures under aeroelastic loads. J. Aircr. 52, 1298–1311 (2015)

    Article  Google Scholar 

  16. Wolff, J. The Law of Bone Remodeling (Springer, 1986) [transl.]

  17. Hesthaven, J., Rozza, G. & Stamm, B. Certified Reduced Basis Methods for Parametrized Partial Differential Equations (Springer, 2015)

  18. Groen, J. P. & Sigmund, O. Homogenization-based topology optimization for high-resolution manufacturable microstructures. Int. J. Num. Methods Eng. https://doi.org/10.1002/nme.5575 (2017)

  19. Alexandersen, J. & Lazarov, B. Topology optimisation of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner. Comput. Methods Appl. Mech. Eng. 290, 156–182 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  20. Bourdin, B. Filters in topology optimization. Int. J. Numer. Methods Eng. 50, 2143–2158 (2001)

    Article  MathSciNet  Google Scholar 

  21. Bruns, T. E. & Tortorelli, D. A. Topology optimization of non-linear elastic structures and compliant mechanisms. Comput. Methods Appl. Mech. Eng. 190, 3443–3459 (2001)

    Article  ADS  Google Scholar 

  22. Tortorelli, D. A. & Michaleris, P. Design sensitivity analysis: overview and review. Inverse Probl. Eng. 1, 71–105 (1994)

    Article  Google Scholar 

  23. Sigmund, O. A 99 line topology optimization code written in Matlab. Struct. Multidiscipl. Optim. 21, 120–127 (2001)

    Article  Google Scholar 

  24. Evgrafov, A., Rupp, C. J., Maute, K. & Dunn, M. L. Large-scale parallel topology optimization using a dual-primal substructuring solver. Struct. Multidiscipl. Optim. 36, 329–345 (2008)

    Article  MathSciNet  Google Scholar 

  25. Aage, N., Andreassen, E. & Lazarov, B. S. Topology optimization using PETSc: an easy-to-use, fully parallel, open source topology optimization framework. Struct. Multidiscipl. Optim. 51, 565–572 (2015)

    Article  MathSciNet  Google Scholar 

  26. Amir, O., Aage, N. & Lazarov, B. S. On multigrid-CG for efficient topology optimization. Struct. Multidiscipl. Optim. 49, 815–829 (2014)

    Article  MathSciNet  Google Scholar 

  27. Balay, S. et al. PETSc Users Manual. Technical Report No. ANL-95/11, Revision 3.6, (Argonne National Laboratory, 2015)

  28. Saad, Y. Iterative Methods for Sparse Linear Systems Ch. 9.4.1 (SIAM, 2003)

  29. Kenway, G. K. W., Kennedy, G. J. & Martins, J. R. R. A. Scalable parallel approach for high-fidelity steady-state aeroelastic analysis and adjoint derivative computations. AIAA J. 52, 935–951 (2014)

    Article  ADS  Google Scholar 

  30. Helms, H. & Lambrecht, U. The potential contribution of light-weighting to reduce transport energy consumption. Int. J. Life Cycle Assess. 12, 58–64 (2007)

    CAS  Google Scholar 

Download references

Acknowledgements

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

Authors and Affiliations

Authors

Contributions

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.

Corresponding author

Correspondence to Niels Aage.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Related audio

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)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Aage, N., Andreassen, E., Lazarov, B. et al. Giga-voxel computational morphogenesis for structural design. Nature 550, 84–86 (2017). https://doi.org/10.1038/nature23911

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature23911

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing