A nonlocal asymptotic theory for thin elastic plates

Kaplunov

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.

Citation

Kaplunov. (2017). A nonlocal asymptotic theory for thin elastic plates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rspa.2017.0249

• Acceptance Date: Jun 12, 2017
• Publication Date: Jul 12, 2017
• 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