Dimension reduction in the plate with a system of periodic unidirectional inclusions

We present a three-dimension (3-D) to two-dimension (2-D) reduction procedure for the plates with the unidirectional system of inhomogeneities (fibers, cylindrical channels, etc.). The original 3-D problem is reduced to several (different) 2-D problems. The reduction procedures are not trivial, in o...

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Bibliographic Details
Published in:Mechanics of advanced materials and structures 2022-12, Vol.29 (28), p.7559-7568
Main Authors: Kolpakov, A. G., Rakin, S. I.
Format: Article
Language:English
Subjects:
boundary layer
Boundary layers
Dimension reduction
homogenization
Inclusions
Incompatibility
Laminates
plate
Plates
Reduction
Thermoelasticity
Two dimensional analysis
wrinkling
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Summary:We present a three-dimension (3-D) to two-dimension (2-D) reduction procedure for the plates with the unidirectional system of inhomogeneities (fibers, cylindrical channels, etc.). The original 3-D problem is reduced to several (different) 2-D problems. The reduction procedures are not trivial, in one case we meet the incompatibility condition, which makes impossible elasticity-to-elasticity problem reduction (only elasticity-to-thermoelasticity transformation is possible, generally). Our analysis of 2-D periodicity cell problems demonstrates a new phenomenon-the existence of the boundary layers on the top and bottom surfaces of the plate. One result of the found boundary layers is the wrinkling of the top and bottom surfaces of the plate. The found phenomena influence the strength of the plate and the plate-to-surrounding media interaction. Note that these phenomena never occur in uniform plates or laminated plates made of uniform layers.
ISSN:1537-6494
1537-6532
DOI:10.1080/15376494.2021.2001880