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Study of a perforated thin plate according to the relative sizes of its different parameters
Author(s) -
El Otmani S.,
SacÉpée J.M.,
Paulin J. Saint Jean
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670180706
Subject(s) - mathematics , perpendicular , geometry , plane (geometry) , mathematical analysis , section (typography) , poisson distribution , zero (linguistics) , work (physics) , physics , statistics , thermodynamics , linguistics , philosophy , advertising , business
Abstract We are interested in the study of a thin plate, periodicially perforated by cylindrical holes, the axes of which are perpendicular to the plane of the plate. A horizontal section of the plate specifies its geometry, and shows a periodicity in the order of ϵ. The thickness of the plate is equal to e . The ratio of material is small, and is characterized by the parameter δ, the thickness of the bars being equal to ϵδ. In this paper, we study the dependence of displacements on e , ϵ and δ, and to give equivalent limits when e , then ϵ, and finally δ, tend towards zero. An interesting result obtained in this work is the negative Poisson coefficient of the final equivalent material. Although this coefficient is theoretically between −½ and 1, most materials encountered in practice have a positive one.