Skip to main content
SpringerLink
Log in

A new adaptive penalization scheme for topology optimization

  • Computer Aided Engineering
  • Published:
Production Engineering Aims and scope Submit manuscript

Abstract

In the product development process topology optimization can successfully be applied in the early product design stages. In this work a new penalization scheme for the SIMP-method (Solid Isotropic Material with Penalization) is presented. One advantage of the presented method is a linear density-stiffness relationship, which has advantages for self-weight or eigenfrequency problems. The optimization problem is solved through derived optimality criteria (OC), which is also introduced in this paper. The derived OC uses no sensitivities of the optimization function but is equivalent to the classical OC in the case of no penalization. In the case with penalization we present an objective function for the penalty factor. By maximizing the objective function in each iteration, we get an adaptive penalty factor. Numerical experiments show, that the adaptive penalty factor leads to better optimization results then a fixed penalty factor. The presented topology optimization method is implemented in the commercial FEM package ANSYS under the name TopoAD. One useful extension of TopoAD is the concept of “meta elements”, which is also presented in this paper.

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.

Institutional subscriptions

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. Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202

    Article  Google Scholar 

  2. Bruyneel M, Duysinx P (2005) Note on topology optimization of continuum structures including self-weight. Struct Multidiscip Optim 29(4):245–256

    Article  Google Scholar 

  3. Pedersen NL (2000) Maximization of eigenvalues using topology optimization. Struct Multidiscip Optim 20(2):2–11

    Article  Google Scholar 

  4. Petersson J, Sigmund O (1998) Slope constrained topology optimization. Int J Num Methods Eng 41:1417–1434

    Article  MATH  MathSciNet  Google Scholar 

  5. Stolpe M, Svanberg K (2001) On the trajectories of penalization methods for topology optimization. Struct Multidiscip Optim 21:128–139

    Article  Google Scholar 

  6. Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidiscip Optim 22:116–124

    Article  Google Scholar 

  7. Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654 Springer

    Article  Google Scholar 

  8. Rozvany GIN, Querin OM, Gaspar Z, Pomezanski V (2003) Weight-increasing effect of topology simplification. Struct Multidiscip Optim 25:459–465

    Article  Google Scholar 

  9. Bendsøe MP (2003) Topology optimization, theory, methods and applications. Springer, Berlin, Heidelberg

    Google Scholar 

  10. Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21(2):120–127

    Article  Google Scholar 

  11. ANSYS, Inc. (2009) Documentation for ANSYS, v12

  12. Park K, Chang S, Youn S (2003) Topology optimization of the primary mirror of a multi-spectral camera. Struct Multidiscip Optim 25(1):46–53

    Article  Google Scholar 

  13. Sekler P, Dietmair A, Dadalau A et al (2007) Energieeffiziente Maschinen durch Massenreduktion, wt-online

  14. Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16:68–75

    Article  Google Scholar 

  15. Schmidt M, Pohle D, Rechtenwald T (2007) Selective laser sintering of PEEK. CIRP Ann Manuf Technol 56(1):205–208

    Article  Google Scholar 

  16. Daebritza S, Faustenb B, Hermanns B et al (2004) Introduction of a flexible polymeric heart valve prosthesis with special design for aortic position. Eur J Cardiothorac Surg 25:946–952

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the Institute of Control of Manufacturing Units Stuttgart (ISW) and by the excellence cluster SimTech Stuttgart. This support is highly appreciated.

Author information

Authors and Affiliations

  1. Institute for Control Engineering of Machine Tools and Manufacturing Units (ISW), Stuttgart, Germany

    A. Dadalau, A. Hafla & A. Verl

Authors
  1. A. Dadalau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Hafla
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Verl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Dadalau.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dadalau, A., Hafla, A. & Verl, A. A new adaptive penalization scheme for topology optimization. Prod. Eng. Res. Devel. 3, 427 (2009). https://doi.org/10.1007/s11740-009-0187-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11740-009-0187-8

Keywords

Search

Navigation