Skip to main content
SpringerLink
Log in

Topology optimization of 3D shell structures with porous infill

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

This paper presents a 3D topology optimization approach for designing shell structures with a porous or void interior. It is shown that the resulting structures are significantly more robust towards load perturbations than completely solid structures optimized under the same conditions. The study indicates that the potential benefit of using porous structures is higher for lower total volume fractions. Compared to earlier work dealing with 2D topology optimization, we found several new effects in 3D problems. Most notably, the opportunity for designing closed shells significantly improves the performance of porous structures due to the sandwich effect. Furthermore, the paper introduces improved filter boundary conditions to ensure a completely uniform coating thickness at the design domain boundary.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Clausen, A., Aage, N., Sigmund, O.: Topology optimization of coated structures and material interface problems. Comput. Methods Appl. Mech. Eng. 290, 524–541 (2015)

    Article  MathSciNet  Google Scholar 

  2. Schaedler, T.A., Jacobsen, A.J., Torrents, A., et al.: Ultralight metallic microlattices. Science 334(6058), 962–965 (2011)

  3. Møller, P., Nielsen, L.P: Advanced Surface Technology, vols. 1–2. Møller and Nielsen (2013). ISBN 9788792765239

  4. Clausen, A., Aage, N., Sigmund, O.: Exploiting additive manufacturing infill in topology optimization for improved buckling load. Engineering 2(2), 250–257 (2016)

    Article  Google Scholar 

  5. Vermaak, N., Michailidis, G., Parry, G., et al.: Material interface effects on the topology optimization of multi-phase structures using a level set method. Struct. Multidiscip. Optim., 1–22 (2014) (online)

  6. Donoso, A., Sigmund, O.: Topology optimization of piezo modal transducers with null-polarity phases. Struct. Multidiscip. Optim. 53(2), 193–203 (2016)

    Article  Google Scholar 

  7. Aage, N., Andreassen, E., Lazarov, B.S.: Topology optimization using PETSc: an easy-to-use, fully parallel, open source topology optimization framework. Struct. Multidiscip. Optim. 51(3), 565–572 (2015)

    Article  MathSciNet  Google Scholar 

  8. Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11(2), 127–140 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  9. Torquato, S., Gibiansky, L.V., Silva, M.J., et al.: Effective mechanical and transport properties of cellular solids. Int. J. Mech. Sci. 40(1), 71–82 (1998)

  10. Andreassen, E., Lazarov, B.S., Sigmund, O.: Design of manufacturable 3D extremal elastic microstructure. Mech. Mater. 69(1), 1–10 (2014)

    Article  Google Scholar 

  11. Clausen, A., Andreassen, E.: On filter boundary conditions in topology optimization. Struct. Multidiscip. Optim. (2017). doi:10.1007/s00158-017-1709-1

  12. Sigmund, O.: Morphology-based black and white filters for topology optimization. Struct. Multidiscip. Optim. 33(4–5), 401–424 (2007)

  13. Lazarov, B.S., Sigmund, O.: Filters in topology optimization based on Helmholtz-type differential equations. Int. J. Numer. Methods Eng. 86(6), 765–781 (2011)

  14. Guest, J.K., Prevost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int. J. Numer. Methods Eng. 61(2), 238–254 (2004)

  15. Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Struct. Multidiscip. Optim. 41(4), 495–505 (2010)

  16. Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Struct. Multidiscip. Optim. 43(6), 767–784 (2011)

    Article  MATH  Google Scholar 

  17. Zhou, M., Lazarov, B.S., Wang, F., et al.: Minimum length scale in topology optimization by geometric constraints. Comput. Methods Appl. Mech. Eng. 293, 266–282 (2015)

  18. Svanberg, K.: Method of moving asymptotes—a new method for structural optimization. Int. J. Numer. Methods Eng. 24(2), 359–373 (1987)

  19. Sigmund, O., Aage, N., Andreassen, E.: On the (non-)optimality of Michell structures. Struct. Multidiscip. Optim. 54(2), 361–373 (2016)

Download references

Acknowledgements

The authors acknowledge financial support from the Villum Foundation (the NextTop Project) and DTU Mechanical Engineering.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, 2800, Lyngby, Denmark

    Anders Clausen, Erik Andreassen & Ole Sigmund

Authors
  1. Anders Clausen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik Andreassen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ole Sigmund
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ole Sigmund.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Clausen, A., Andreassen, E. & Sigmund, O. Topology optimization of 3D shell structures with porous infill. Acta Mech. Sin. 33, 778–791 (2017). https://doi.org/10.1007/s10409-017-0679-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-017-0679-2

Keywords

Search

Navigation