Advertisement

Structural and Multidisciplinary Optimization

, Volume 39, Issue 2, pp 217–225 | Cite as

A simple heuristic for gray-scale suppression in optimality criterion-based topology optimization

  • Albert A. GroenwoldEmail author
  • L. F. P. Etman
BRIEF NOTE

Abstract

We propose a very simple heuristic to suppress gray-scale material in topology optimization in optimality criterion-like implementations. Gray-scale suppression (GSS) is recommended for use in conjunction with the SIMP material description, although gray-scale suppression in itself is adequate to effect predominantly black-and-white designs. Minimal changes are required to incorporate the gray-scale suppression technique in Sigmund’s popular 99-line Matlab code for topology optimization.

Keywords

Topology optimization SIMP Optimality criterion (OC) Gray-scale suppression 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beckers M (1996) Topology optimization using a dual method with discrete variables. Struct Optim 11:102–112CrossRefGoogle Scholar
  2. Bendsøe M (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202CrossRefGoogle Scholar
  3. Bendsøe M (1995) Optimization of structural topology, shape and material. Springer, BerlinGoogle Scholar
  4. Bendsøe M, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224CrossRefGoogle Scholar
  5. Bendsøe M, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, BerlinGoogle Scholar
  6. Bruns T (2005) A reevaluation of the SIMP method with filtering and an alternative formulation for solid-void topology optimization. Struct Multidisc Optim 30:428–436CrossRefMathSciNetGoogle Scholar
  7. Cheng KT, Olhoff N (1982) Regularized formulation for optimal design of axisymmetric plates. Int J Solids Struct 18:153–169zbMATHCrossRefGoogle Scholar
  8. Groenwold A, Etman L (2008) On the equivalence of optimality criterion methods and sequential approximate optimization in the classical topology layout problem. Int J Numer Methods Eng 73:297–316zbMATHCrossRefMathSciNetGoogle Scholar
  9. Olhoff N, Lurie K, Cherkaev A, Fedorov A (1981) Sliding regimes and anisotropy in optimal design of vibrating axisymmetric plates. Int J Solids Struct 17:931–948zbMATHCrossRefMathSciNetGoogle Scholar
  10. Rozvany G, Zhou M (1991) Applications of COC method in layout optimization. In: Eschenauer H, Mattheck C, Olhoff N (eds) Proc. engineering optimization in design processes. Springer, Berlin, pp 59–70Google Scholar
  11. Sigmund O (1994) Design of material structures using topology optimization. PhD thesis, Technical University of Denmark, Department of Solid MechanicsGoogle Scholar
  12. Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Machines 25:495–526Google Scholar
  13. Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidisc Optim 21:120–127CrossRefGoogle Scholar
  14. Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33:401–424CrossRefGoogle Scholar
  15. Svanberg K, Werme M (2005) A hierarchical neighborhood search method for topology optimization. Struct Multidisc Optim 29:325–340CrossRefMathSciNetGoogle Scholar
  16. Wang M, Zhou S, Ding H (2004) Nonlinear diffusions in topology optimization. Struct Multidisc Optim 28:262–276CrossRefMathSciNetGoogle Scholar
  17. Zhou M, Rozvany G (1991) The COC method. Part II. Topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 40:1–26Google Scholar
  18. Zhou M, Shyy Y, Thomas H (2001) Checkerboard and minimum member size control in topology optimization. Struct Multidisc Optim 21:152–158CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of StellenboschMatielandSouth Africa
  2. 2.Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations