Structural and Multidisciplinary Optimization

, Volume 48, Issue 3, pp 487–499 | Cite as

Optimal design of two-dimensional band-gap materials for uni-directional wave propagation

  • Yu Huang
  • Shutian Liu
  • Jian Zhao
Research Paper


New configurations and new properties of materials used in engineering components can be developed by introducing band-gap materials for which a two-dimensional design domain is optimized for uni-directional wave propagation. In this paper, uni-directional band-gap materials with periodic two-dimensional appearances are designed for in-plane waves. By using the Finite Element Method to solve the dynamic behavior of the representative unit cell, the dispersion relation of wave propagation is built up based on Floquet-Bloch theory. With the goal of maximizing the width of band gaps for a certain direction, the distribution of two material phases in a two-dimensional unit cell is determined by a gradient-based topology optimization method. The numerical results show that the proposed periodic hierarchical laminates and the corresponding periodic layered material with homogenized anisotropic layers exhibit wider band gaps than multilayered materials optimized by a one-dimensional design domain. Meanwhile, the influence of the anisotropic property of combined layers and homogenized layers on the band-gap characteristics is analyzed.


Material design Band-gap Regularization Homogenization Hierarchical laminate Anisotropic 



This research is supported by the National Basic Research Program (973Program) of China (Grant No. 2011CB610304), the National Natural Science Foundation of China (Grant No. 11172052) and the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090041110023). The financial supports are greatly acknowledged.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering MechanicsDalian University of TechnologyDalianChina

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