Structural and Multidisciplinary Optimization

, Volume 46, Issue 3, pp 385–398 | Cite as

Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity

  • X. HuangEmail author
  • Y. M. Xie
  • B. Jia
  • Q. Li
  • S. W. Zhou
Research Paper


This paper presents a bidirectional evolutionary structural optimization (BESO) method for designing periodic microstructures of two-phase composites with extremal electromagnetic permeability and permittivity. The effective permeability and effective permittivity of the composite are obtained by applying the homogenization technique to the representative periodic base cell (PBC). Single or multiple objectives are defined to maximize or minimize the electromagnetic properties separately or simultaneously. The sensitivity analysis of the objective function is conducted using the adjoint method. Based on the established sensitivity number, BESO gradually evolves the topology of the PBC to an optimum. Numerical examples demonstrate that the electromagnetic properties of the resulting 2D and 3D microstructures are very close to the theoretical Hashin-Shtrikman (HS) bounds. The proposed BESO algorithm is computationally efficient as the solution usually converges in less than 50 iterations. The proposed BESO method can be implemented easily as a post-processor to standard commercial finite element analysis software packages, e.g. ANSYS which has been used in this study. The resulting topologies are clear black-and-white solutions (with no grey areas). Some interesting topological patterns such as Vigdergauz-type structure and Schwarz primitive structure have been found which will be useful for the design of electromagnetic materials.


Topology optimization Bidirectional evolutionary structural optimization (BESO) Homogenization Effective permeability Effective permittivity 



This research is supported by the Australian Research Council under its Discovery Projects funding scheme (project number DP1094403).


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • X. Huang
    • 1
    Email author
  • Y. M. Xie
    • 1
  • B. Jia
    • 2
  • Q. Li
    • 3
  • S. W. Zhou
    • 3
  1. 1.School of Civil, Environmental and Chemical EngineeringRMIT UniversityMelbourneAustralia
  2. 2.Centre for Micro-Photonics, Faculty of Engineering & Industrial ScienceSwinburne University of TechnologyHawthornAustralia
  3. 3.School of Aerospace, Mechanical and Mechatronic EngineeringThe University of SydneySydneyAustralia

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