MATHEMATICAL MODELING OF THE STRESS-STRAIN STATE OF A THIN ISOTROPIC NANOPLATE
O.V. Germider, V.N. Popov
Lomonosov Northern (Arctic) Federal University, Arkhangelsk, Russia
Keywords: isotropic nanoplate, stress-strain state, Chebyshev polynomial of the first kind, collocation method
Abstract
The nonlocal theory of microstructural deformation of thin plates is applied to derive an equilibrium equation for a thin isotropic nanoplate along with the corresponding boundary conditions. An approach to constructing a solution to this equation for a rectangular nanoplate with simply supported edges is proposed, employing Chebyshev polynomials of the first kind and the collocation method. The deflection of the nanoplate midplane and the bending moments are analyzed as functions of a nonlocal nanoscale parameter.
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