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Asymptotic analysis in elasticity problems on thin periodic structures

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  • Thin periodic structures depend on two interrelated small geometric parameters $\varepsilon$ and $h(\varepsilon)$ 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 $\lim_{\varepsilon\to 0} h(\varepsilon)\varepsilon^{-1}$ is a positive constant. Planar grids are taken as a model example.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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