Structural and Multidisciplinary Optimization

, Volume 56, Issue 6, pp 1319–1339 | Cite as

Topology optimization of phononic crystals with uncertainties

  • Longxiang Xie
  • Baizhan Xia
  • Guoliang Huang
  • Jirong Lei
  • Jian LiuEmail author


Topology optimization of phononic crystals (PnCs) is generally based on deterministic models without considering effects of inherent uncertainties existed in PnCs. However, uncertainties presented in PnCs may significantly affect band gap characteristics. To address this, an interval Chebyshev surrogate model-based heuristic algorithm is proposed for topology optimization of PnCs with uncertainties. Firstly, the interval model is introduced to handle the uncertainties, and then the interval Chebyshev surrogate model (ICSM), in which the improved fast plane wave expansion method (IFPWEM) is used to calculate the integral points to construct the ICSM, is introduced for band structure analysis with uncertainties efficiently. After that, the sample data, which is randomly generated by the Monte Carlo method (MCM), is applied to the ICSM for predicting the interval bounds of the band structures. Finally, topology optimization of PnCs is conducted to generate the widest band gaps with uncertainties included by utilizing the genetic algorithm (GA) and the ICSM. Numerical results show the effectiveness and efficiency of the proposed method which has promising prospects in a range of engineering applications.


Topology optimization Uncertainties Phononic crystals Interval Chebyshev surrogate model Band gap 



The paper is supported by National Natural Science Foundation of China (No.11402083, 11572121), Independent Research Project of State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body in Hunan University (No.51375002), and Heavy-duty Tractor Intelligent Manufacturing Technology Research and System Development (No.2016YFD0701105).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Longxiang Xie
    • 1
  • Baizhan Xia
    • 1
  • Guoliang Huang
    • 2
  • Jirong Lei
    • 1
  • Jian Liu
    • 1
    Email author
  1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaChina
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of MissouriColumbiaUSA

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