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 closed-form 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.
Highlights
Since the discovery of carbon nanotubes (CNTs) by Iijima (1991), many scientific researches have been carried out in the field of mechanical, electrical, physical and chemical properties of nanostructures
N = 1 n = 2 300 n = 3 n = 4 n = 5. This manuscript presents closed-form solutions for the postbuckling behavior of single-layered graphene sheet subjected to axial compression based on the nonlocal continuum mechanics
Higher postbuckling mode is more significant at smaller lateral deflection
Summary
Since the discovery of carbon nanotubes (CNTs) by Iijima (1991), many scientific researches have been carried out in the field of mechanical, electrical, physical and chemical properties of nanostructures. Mohammadi et al / A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory force microscope, electrical batteries and nanocomposites (Craighead 2000; Li et al 2007; Murmu and Adhikari 2010). Nanostructures such as armchair carbon nanotubes and nanoplates have shown significant potential applications in the field of environmental technologies (Saremi et al 2008). Both atomistic simulation results and experimental observations on phonon dispersion have shown the accuracy of this observation (Eringen 1983; Chen et al 2004)
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