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Elasticity of a perforated plate with very different elasticity coefficients. (English) Zbl 0895.73002
Cioranescu, Doina (ed.) et al., Homogenization and applications to material sciences. Proceedings of the international conference, Nice, France, June 6–10, 1995. Tokyo: Gakkotosho. GAKUTO Int. Ser., Math. Sci. Appl. 9, 225-239 (1995).
Summary: We consider the equations of linearized elasticity for a plate periodically perforated by many square holes. Its geometry is characterized by three small parameters. The thickness of the plate, the period of the square holes and the ratio between the width of a bar and the period. We study the behavior of the displacement when these three small parameters tend to zero. We assume that the elasticity coefficients are of very different orders, and we consider two particular cases which correspond to membrane equations or to thin plate equations when the thickness of the plate tends to zero.
For the entire collection see [Zbl 0873.00028].
74B05 Classical linear elasticity
74E05 Inhomogeneity in solid mechanics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure