Continuous approximation of material distribution for topology optimization

K. Matsui, K. Terada

Research output: Contribution to journalArticlepeer-review

168 Citations (Scopus)


In this paper, we propose a checkerboard-free topology optimization method without introducing any additional constraint parameter. This aim is accomplished by the introduction of finite element approximation for continuous material distribution in a fixed design domain. That is, the continuous distribution of microstructures, or equivalently design variables, is realized in the whole design domain in the context of the homogenization design method (HDM), by the discretization with finite element interpolations. By virtue of this continuous FE approximation of design variables, discontinuous distribution like checkerboard patterns disappear without any filtering schemes. We call this proposed method the method of continuous approximation of material distribution (CAMD) to emphasize the continuity imposed on the 'material field'. Two representative numerical examples are presented to demonstrate the capability and the efficiency of the proposed approach against some classes of numerical instabilities.

Original languageEnglish
Pages (from-to)1925-1944
Number of pages20
JournalInternational Journal for Numerical Methods in Engineering
Issue number14
Publication statusPublished - 2004 Apr 14


  • Homogenization design method
  • Homogenization theory
  • Structural design
  • Topology optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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