Numerical Implementation of Variational Asymptotic Homogenization Method for Periodic Plate Structures

Abstract

The variational asymptotic homogenization (VAM) theory is extended to access freely to commercial finite element (FE) software to deal with periodic plate structures. In this work, the finite element format for periodic plate structures based on the variational asymptotic homogenization is developed, ensuring the commercial finite element software can be utilized to obtain the effective plate stiffness. A standard numerical framework and an integration algorithm are proposed for unifying the dimensional reduction analysis and the homogenization analysis in a formalized manner. As for model validation, the periodic plates composed of unit cells with three-dimension (3D) heterogeneous geometry are simulated by various elements and modeling techniques using the commercial FE software rather than programming in-house code. Compared to the results provided in the existing literature, the proposed approach shows excellent performance in terms of computational efficiency and time without compromising the VAM accuracy. It is preferable to enhance the application of the variational asymptotic homogenization theory for the more sophisticated heterogeneous plate structures.

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Acknowledgements

The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (No. 11272146).

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Correspondence to Xiwu Xu.

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Qiao, K., Xu, X. & Guo, S. Numerical Implementation of Variational Asymptotic Homogenization Method for Periodic Plate Structures. Int. J. Aeronaut. Space Sci. 22, 64–78 (2021). https://doi.org/10.1007/s42405-020-00285-4

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Keywords

  • Variational asymptotic homogenization theory
  • Periodic plate structures
  • Effective plate stiffness
  • Numerical implementation