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

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      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.

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      Helical microtubules of graphitic carbon

       Sumio Iijima (1991)
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        Nanoelectromechanical systems.

        Nanoelectromechanical systems are evolving, with new scientific studies and technical applications emerging. Mechanical devices are shrinking in thickness and width to reduce mass, increase resonant frequency, and lower the force constants of these systems. Advances in the field include improvements in fabrication processes and new methods for actuating and detecting motion at the nanoscale. Lithographic approaches are capable of creating freestanding objects in silicon and other materials, with thickness and lateral dimensions down to about 20 nanometers. Similar processes can make channels or pores of comparable dimensions, approaching the molecular scale. This allows access to a new experimental regime and suggests new applications in sensing and molecular interactions.
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          On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves

           A. Eringen (1983)
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            Author and article information

            Affiliations
            [1 ] Islamic Azad University Iran
            [2 ] Islamic Azad University Iran
            [3 ] Islamic Azad University Iran
            Contributors
            Role: ND
            Role: ND
            Role: ND
            Journal
            lajss
            Latin American Journal of Solids and Structures
            Lat. Am. j. solids struct.
            Associação Brasileira de Ciências Mecânicas (Rio de Janeiro )
            1679-7825
            2014
            : 11
            : 9
            : 1515-1540
            S1679-78252014000900004
            10.1590/S1679-78252014000900004

            http://creativecommons.org/licenses/by/4.0/

            Product
            Product Information: SciELO Brazil
            Categories
            ENGINEERING, CIVIL
            ENGINEERING, MECHANICAL
            MECHANICS
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            Keywords:

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