Structural topology optimization for multiple load cases using a dynamic aggregation technique

Kai A. James, Jorn S. Hansen, Joaquim R.R.A. Martins

Research output: Contribution to journalArticlepeer-review


A series of techniques is presented for overcoming some of the numerical instabilities associated with SIMP materials. These techniques are combined to create a robust topology optimization algorithm designed to be able to accommodate a large suite of problems that more closely resemble those found in industry applications. A variant of the Kreisselmeier-Steinhauser (KS) function in which the aggregation parameter is dynamically increased over the course of the optimization is used to handle multi-load problems. Results from this method are compared with those obtained using the bound formulation. It is shown that the KS aggregation method produces results superior to those of the bound formulation, which can be highly susceptible to local minima. Adaptive mesh-refinement is presented as a means of addressing the mesh-dependency problem. It is shown that successive mesh-refinement cycles can generate smooth, well-defined structures, and when used in combination with nine-node elements, virtually eliminate checkerboarding and flexural hinges.

Original languageEnglish (US)
Pages (from-to)1103-1118
Number of pages16
JournalEngineering Optimization
Issue number12
StatePublished - Dec 2009
Externally publishedYes


  • Adaptive mesh refinement
  • Kreisselmeier-Steinhauser function
  • Multiple load cases
  • Topology optimization

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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