Skip to main content
Log in

Robust structural topology optimization under random field loading uncertainty

  • BRIEF NOTE
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

A new approach to solving the robust topology optimization problem considering random field loading uncertainty was developed. The Karhunen-Loeve expansion was employed to characterize the random field as a reduced set of random variables. Efficient method of sensitivity analysis was developed and integrated into the density based topology optimization approach. The numerical example demonstrated the efficiency of the proposed approach and the effect of loading uncertainty on the robust design results.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Alvarez F, Carrasco M (2005) Minimization of the expected compliance as an alternative approach to multiload truss optimization. Struct Multidisc Optim 29(6):470–476

    Article  MATH  MathSciNet  Google Scholar 

  • Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202

    Article  Google Scholar 

  • Carrasco M, Ivorra B, Ramos A M (2012) A variance-expected compliance model for structural optimization. J Optim Theory Appl 152 (1):136–151

    Article  MATH  MathSciNet  Google Scholar 

  • Chen S, Chen W, Lee S (2010) Level set based robust shape and topology optimization under random field uncertainties. Struct Multidisc Optim 41(4):507–524

    Article  MATH  MathSciNet  Google Scholar 

  • Dunning P D, Kim H A, Mullineux G (2011) Introducing loading uncertainty in topology optimization. AIAA J 49(4):760–768

    Article  Google Scholar 

  • Ghanem R G, Doostan A (2006) On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data. J Comput Phys 217(1):63–81

    Article  MATH  MathSciNet  Google Scholar 

  • Ghanem R G, Spanos P D (2003) Stochastic finite elements: a spectral approach. Courier Dover Publications

  • Guest J K, Igusa T (2008) Structural optimization under uncertain loads and nodal locations. Comput Methods Appl Mech Engrg 198 (1):116–124

    Article  MATH  MathSciNet  Google Scholar 

  • Kim H, Guyer R A (2013) Robust topology optimisation with generalised probability distribution of loading. Tech. rep., Los Alamos National Laboratory (LANL)

  • Lee S H, Chen W (2009) A comparative study of uncertainty propagation methods for black-box-type problems. Struct Multidisc Optim 37(3):239–253

    Article  MathSciNet  Google Scholar 

  • Lee S H, Chen W, Kwak B M (2009) Robust design with arbitrary distributions using gauss-type quadrature formula. Struct Multidisc Optim 39(3):227–243

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Svanberg K (1987) The method of moving asymptotesa new method for structural optimization. J Numer Meth Engng 24(2):359– 373

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Xiu D (2010) Numerical methods for stochastic computations: a spectral method approach. Princeton University Press

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

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Krister Svanberg for providing the matlab code of MMA optimizer. This paper is supported by the project of Defense Industrial Technology Development Program(Grant No.C0320110002 ) and the Innovation Foundation of BUAA for PhD Graduates.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Junpeng Zhao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, J., Wang, C. Robust structural topology optimization under random field loading uncertainty. Struct Multidisc Optim 50, 517–522 (2014). https://doi.org/10.1007/s00158-014-1119-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-014-1119-6

Keywords

Navigation