Adaptive topology optimization with independent error control for separated displacement and density fields

Yiqiang Wang, Zhan Kang, Qizhi He

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


This paper proposes a new adaptive method for topology optimization of structures, by using independent error control for the separated displacement and material density fields. Since the arrangement of the density points is unnecessarily associated with the analysis mesh in the topology optimization based on analysis-separated density interpolation, the refinements of each field can be separately implemented. Here, the analysis mesh is refined to improve the computational accuracy of the displacement field and the associated strain field within certain local regions (e.g. the regions around concentrated loading points and displacement restrictions), while the density field is refined in the regions between fully solid and void phases to improve the geometrical description quality of design boundaries. With such a strategy, the refinements of the analysis mesh and the density field are naturally separated and not bond together anymore. Actually, each refinement process is independently performed only when and where necessary. Numerical examples show that the proposed method can achieve high-quality and high-accuracy optimal solutions comparable to those obtained with fixed globally fine analysis meshes and fine distributed density points, but with much less computational cost.

Original languageEnglish (US)
Pages (from-to)50-61
Number of pages12
JournalComputers and Structures
StatePublished - Apr 15 2014
Externally publishedYes

Bibliographical note

Funding Information:
The supports of Key Project of Chinese National Programs for Fundamental Research and Development ( 2010CB832703 ) and Natural Science Foundation of China ( 11072047 , 91130025 ) are gratefully acknowledged.


  • Adaptive refinement
  • GTR indicator
  • Independent Point-wise Density Interpolation
  • Independent error control
  • Nodal design variable
  • Topology optimization


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