American Institute of Mathematical Sciences

September  2009, 4(3): 577-604. doi: 10.3934/nhm.2009.4.577

Asymptotic analysis in elasticity problems on thin periodic structures

 1 Moscow State Institute of Radioengineering, Electronics and Automatics (Technical University), Russian Federation

Received  May 2009 Revised  May 2009 Published  July 2009

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