Robust topology optimization of phononic crystals with random field uncertainty

Xiaopeng Zhang, Jingjie He, Akihiro Takezawa*, Zhan Kang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Citations (Scopus)


The uncertain spatial variation of material properties can remarkably affect the band gap characteristics of phononic crystals (PnCs). It is necessary to consider this issue when designing and manufacturing PnC materials/structures. This paper investigates a robust topology optimization method for designing the microstructures of PnCs by considering random-field material properties. Herein, the spatial distribution of the material properties is first represented by a random field and then discretized into uncorrelated stochastic variables with the expansion optimal linear estimation method; stochastic band gap analysis is then conducted with polynomial chaos expansion. Furthermore, a robust topology optimization formulation of PnCs is proposed on the basis of the relative elemental density, where a weighted objective function handles the compromise of the mean value and standard deviation of the PnC band gap. The band gap response is analyzed, employing the finite element method for each sample of polynomial chaos expansion. In this context, the sensitivities of the stochastic band gap behaviors to the design variables are also derived. Numerical examples demonstrate that the proposed method can generate meaningful optimal topologies of PnCs with a relatively large width and less sensitive band gap. Additionally, the effects of the weight factors in the objective function and the variation coefficient of material properties are discussed.

Original languageEnglish
Pages (from-to)1154-1173
Number of pages20
JournalInternational Journal for Numerical Methods in Engineering
Issue number9
Publication statusPublished - 2018 Aug 31
Externally publishedYes


  • phononic crystals
  • random material property
  • robust design
  • stochastic response
  • topology optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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