A non-local asymptotic theory for thin elastic plates

The three-dimensional dynamic non-local elasticity equations for a thin plate are subject to asymptotic analysis assuming the plate thickness to be much greater than a typical microscale size. The integral constitutive relations, incorporating the variation of an exponential non-local kernel across...

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Bibliographic Details
Published inProceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 473; no. 2203; p. 20170249
Main Authors Chebakov, R., Kaplunov, J., Rogerson, G. A.
Format Journal Article
LanguageEnglish
Published London The Royal Society Publishing 01.07.2017
EditionRoyal Society (Great Britain)
Subjects
Asymptotic
Boundary Layer
Boundary layers
Constitutive relationships
Dynamics
Elastic plates
Elasticity
Mathematical analysis
Non-Local
Plate
Stiffness
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ISSN1364-5021
1471-2946
DOI10.1098/rspa.2017.0249

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Summary:The three-dimensional dynamic non-local elasticity equations for a thin plate are subject to asymptotic analysis assuming the plate thickness to be much greater than a typical microscale size. The integral constitutive relations, incorporating the variation of an exponential non-local kernel across the thickness, are adopted. Long-wave low-frequency approximations are derived for both bending and extensional motions. Boundary layers specific for non-local behaviour are revealed near the plate faces. It is established that the effect of the boundary layers leads to the first-order corrections to the bending and extensional stiffness in the classical two-dimensional plate equations.
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ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2017.0249