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A nonlocal asymptotic theory for thin elastic plates

Kaplunov

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Abstract

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.

Acceptance Date Jun 12, 2017
Publication Date Jul 12, 2017
Publicly Available Date Mar 29, 2024
Journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print ISSN 1364-5021
Publisher The Royal Society
DOI https://doi.org/10.1098/rspa.2017.0249
Keywords nonlocal; elasticity; plate; asymptotic; boundary layer; dynamics
Publisher URL http://dx.doi.org/10.1098/rspa.2017.0249

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