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Structural and Multidisciplinary Optimization

, Volume 59, Issue 3, pp 759–766 | Cite as

A computational study of symmetry and well-posedness of structural topology optimization

  • Daniel A. WhiteEmail author
  • Alexey Voronin
Research Paper
  • 306 Downloads

Abstract

We are concerned with the computational topological optimization of elastic structures, in particular minimization of compliance subject to a constraint on the mass. Through computational experiments, it is discovered that even very simple optimization problems can exhibit complex behavior such as critical points and bifurcation. In the vicinity of critical points, structural topology optimization problems are not well-posed since infinitesimally small perturbations lead to distinct topologies.

Keywords

Structures Topology Optimization Bifurcation Well-posed 

Notes

References

  1. Baier H (1994) Ill posed problems in structural optimization and their practical consequences. Struct Optim 7:184–190CrossRefGoogle Scholar
  2. Bendsoe MP, Sigmund O (2003) Topology Optimization Theory, Methods, and Applications. Springer, BerlinzbMATHGoogle Scholar
  3. Blanchard P, Devaney RL, Hall GR (2006) Differential Equations. Thomson Brooks/Cole, USAGoogle Scholar
  4. Cheng G, Lui X (2011) Discussion on symmetry of optimum topology design. Struct Multidisc Optim 44:713–717CrossRefzbMATHGoogle Scholar
  5. Guo X, Ni C, Cheng G, Du Z (2012) Some symmetry results for optimal solutions in structural optimization. Struct Multidisc Optim 46:631–645MathSciNetCrossRefzbMATHGoogle Scholar
  6. Kosakam I, Swan CC (1999) A symmetry reduction method for continuum structural topology optimization. Comp Struct 70:47–61MathSciNetCrossRefzbMATHGoogle Scholar
  7. Lazarov B, Sigmund O (2011) Filters in topology optimization based on Helmholtz-type differential equations. Int J Numer Meth Eng 86:765–781MathSciNetCrossRefzbMATHGoogle Scholar
  8. Richardson JN, Adriaenssens S, Bouillard P, Coelho RF (2013) Symmetry and asymmetry of solutions in discrete variable structural optimization. Struct Multidisc Optim 47:631–643MathSciNetCrossRefzbMATHGoogle Scholar
  9. Rozvany G (1998) Exact analytical solutions for some popular benchmark problems in topology optimization. Struct Optim 15:42–48CrossRefzbMATHGoogle Scholar
  10. Rozvany GIN (2011) On symmetry and non-uniqueness in exact topology optimization. Struct Multidisc Optim 43:297–317MathSciNetCrossRefzbMATHGoogle Scholar
  11. Sigmund O (2001) A 99 line topology optimization code written in matlab. Struct Multidis Optimiz 21:120–127CrossRefGoogle Scholar
  12. Stolpe M (2010) On some fundamental properties of structural topology optimization problems. Struct Multidisp Optim 41:661–670CrossRefzbMATHGoogle Scholar
  13. Wächter A, Biegler LT (2006) On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math Program 106(1):5–57CrossRefzbMATHGoogle Scholar

Copyright information

© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018

Authors and Affiliations

  1. 1.Lawrence Livermore National LaboratoryLivermoreUSA

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