Topology optimization using a reaction-diffusion equation

Jae Seok Choi, Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki, Jeonghoon Yoo

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)


This paper presents a structural topology optimization method based on a reaction-diffusion equation. In our approach, the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction-diffusion equation. The distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction-diffusion equation, so free generation of new holes is allowed without the use of the topological gradient method. Our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model. The evolution of the density field is based on the implicit finite element method. As numerical examples, compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method's effectiveness and utility.

Original languageEnglish
Pages (from-to)2407-2420
Number of pages14
JournalComputer Methods in Applied Mechanics and Engineering
Issue number29-32
Publication statusPublished - 2011 Jul 1

Bibliographical note

Funding Information:
The authors are deeply grateful for the support received from JSPS Scientific Research (C) , No. 19560142 , and JSPS Fellows.

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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