A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory

Abstract

Recently, graphene sheets have shown significant potential for environmental engineering applications such as wastewater treatment. In the present work, the posbuckling response of orthotropic single-layered graphene sheet (SLGS) is investigated in a closedform analytical manner using the nonlocal theory of Eringen. Two opposite edges of the plate are subjected to normal stresses. The nonlocality and geometric nonlinearity are taken into consideration, which arises from the nanosized effects and mid-plane stretching, respectively. Nonlinear governing differential equations (nonlocal compatibility and equilibrium equations) are derived and presented for the aforementioned study. Galerkin method is used to solve the governing equations for simply supported boundary conditions. It is shown that the nonlocal effect plays a significant role in the nonlinear stability behavior of orthotropic nanoplates. Unlike first and second postbuckling modes, nonlocal effects decrease with the increase of lateral deflection at higher postbuckling modes. It is also observed that the nonlocality and nonlinearity is more pronounced for higher postbuckling modes.

Smart electrical and magnetic stability analysis of exponentially graded shear deformable three-layered nanoplate based on nonlocal piezo-magneto-elasticity theory

“…(III) For a magneto-electro-elastic nanoplate, the buckling load and vibration frequency decrease linearly with electric potential, spring and shear coefficients of the Pasternak foundation, and increases with magnetic potential. Asemi et al [9] presented nonlocal theory to study the free vibration of orthotropic SLGS resting on a Pasternak foundation under shear in-plane load based on classical plate theory (CLPT) and used the combined Galerkindifferential quadrature method to solve the obtained equation. They concluded that increasing nonlocal parameter reduces the non-dimensional frequency of the SLGS.…”

“…Asemi et al. [9] presented nonlocal theory to study the free vibration of orthotropic SLGS resting on a Pasternak foundation under shear in-plane load based on classical plate theory (CLPT) and used the combined Galerkin-differential quadrature method to solve the obtained equation. They concluded that increasing nonlocal parameter reduces the non-dimensional frequency of the SLGS.…”

The computation of bending eigenfrequencies of single-walled carbon nanotubes based on the nonlocal theory

“…The vibrations of tensioned nanobeams using the nonlocal beam theory are investigated by Bagdatli (2015). The nonlinear frequencies for fixed-fixed and simply-simply supported Euler-Bernoulli nanobeams are presented.…”

Vibration Analysis of Bilayered Graphene Sheets for Building Materials in Thermal Environments Based on the Element-Free Method

“…Asemi et al [30] presented an axisymmetric buckling analysis of circular SLGS using Eringen's theory. Additionally, Asemi et al [31] used nonlocal theory of Eringen to simulate postbuckling response of orthotropic SLGS.…”