Asymptotic analysis in elasticity problems on thin periodic structures

S. E. Pastukhova

doi:10.3934/nhm.2009.4.577

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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

S. E. Pastukhova^1,

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

Received: April 30, 2009

Revised: April 30, 2009

Published: August 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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