Multiphase topology optimization with a single variable using the phase-field design method

Hong Kyoung Seong, Cheol Woong Kim, Jeonghoon Yoo, Jaewook Lee

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


In this study, a multimaterial topology optimization method using a single variable is proposed by combining the solid isotropic material with penalization method and the reaction-diffusion equation. Unlike ordinary multimaterial optimization, which requires several variables depending on the number of material types, this method intends to represent various materials as one variable. The proposed method combines two special functions in the sensitivity analysis of the objective function to converge the design variable into prespecified density values defined for each of the multimaterials. The composition constraint based on a normal distribution function is also introduced to estimate the distribution of each target density value in a single variable. It enables density exchange between multiple materials by increasing or decreasing the amount of a specific material. The proposed method is applied to structural and electromagnetic problems to verify its effectiveness, and its usefulness is also confirmed from the viewpoint of cost and computation time.

Original languageEnglish
Pages (from-to)334-360
Number of pages27
JournalInternational Journal for Numerical Methods in Engineering
Issue number5
Publication statusPublished - 2019 Aug 3

Bibliographical note

Funding Information:
This work was supported in part by the National Research Foundation of Korea funded by the Korean government (NRF-2016R1A2B4008501) and in part by the Korea Institute of Energy Technology Evaluation and Planning through the Human Resources Program in Energy Technology funded by the Ministry of Trade, Industry and Energy, Republic of Korea (20184030201940).

Publisher Copyright:
© 2019 John Wiley & Sons, Ltd.

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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