Abstract
We present a 3-D to 2-D dimension reduction procedure as applied to the periodicity cell problem (PCP) of the homogenization theory for plates reinforced with a unidirectional system of fibers. The original 3-D PCP is reduced to several 2-D problems. The reduction procedures are not trivial, in one case we encounter the incompatibility condition, which makes impossible to transform the 3-D elasticity problem to the 2-D elasticity problem (only the transformation to 2-D thermoelasticity problem is possible). Numerical analysis of 2-D periodicity cell problems demonstrates new phenomena: the boundary layers on the top and bottom surfaces of the plate and, as a result, the wrinkling of the top and bottom surfaces of the plate. Note that these phenomena never occur in uniform plates or plates made of uniform layers.
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Kolpakov, A.G., Rakin, S.I. (2022). Bending/Tension of Plate Reinforced by a System of Parallel Fiber. In: Giorgio, I., Placidi, L., Barchiesi, E., Abali, B.E., Altenbach, H. (eds) Theoretical Analyses, Computations, and Experiments of Multiscale Materials. Advanced Structured Materials, vol 175. Springer, Cham. https://doi.org/10.1007/978-3-031-04548-6_20
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