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Networks and Heterogeneous Media

2009, Volume 4, Issue 3: 577-604. doi: 10.3934/nhm.2009.4.577
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Asymptotic analysis in elasticity problems on thin periodic structures

  • 1.
    Moscow State Institute of Radioengineering, Electronics and Automatics (Technical University)
  • Received: 01 May 2009 Revised: 01 May 2009

  • Primary: 58F15, 58F17; Secondary: 53C35.

  • Thin periodic structures depend on two interrelated small geometric parameters ε and h(ε) which control the thickness of constituents and the cell of periodicity. We study homogenisation of elasticity theory problems on these structures by method of asymptotic expansions. A particular attention is paid to the case of critical thickness when limε→0h(ε)ε−1 is a positive constant. Planar grids are taken as a model example.

    Citation: S. E. Pastukhova. Asymptotic analysis in elasticity problems on thin periodic structures[J]. Networks and Heterogeneous Media, 2009, 4(3): 577-604. doi: 10.3934/nhm.2009.4.577

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  • Thin periodic structures depend on two interrelated small geometric parameters ε and h(ε) which control the thickness of constituents and the cell of periodicity. We study homogenisation of elasticity theory problems on these structures by method of asymptotic expansions. A particular attention is paid to the case of critical thickness when limε→0h(ε)ε−1 is a positive constant. Planar grids are taken as a model example.


  • This article has been cited by:

    1. Kirill Cherednichenko, Shane Cooper, HOMOGENIZATION OF THE SYSTEM OF HIGH‐CONTRAST MAXWELL EQUATIONS, 2015, 61, 0025-5793, 475, 10.1112/S0025579314000424
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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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