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Advances in Nano Research
  Volume 4, Number 4, December 2016 , pages 309-326

Buckling of a single-layered graphene sheet embedded in visco-Pasternak
Ashraf M. Zenkour

    The buckling response of a single-layered graphene sheet (SLGS) embedded in visco-Pasternak\'s medium is presented. The nonlocal first-order shear deformation elasticity theory is used for this purpose. The visco-Pasternak\'s medium is considered by adding the damping effect to the usual foundation model which characterized by the linear Winkler\'s modulus and Pasternak\'s (shear) foundation modulus. The SLGS be subjected to distributive compressive in-plane edge forces per unit length. The governing equilibrium equations are obtained and solved for getting the critical buckling loads of simply-supported SLGSs. The effects of many parameters like nonlocal parameter, aspect ratio, Winkler-Pasternak\'s foundation, damping coefficient, and mode numbers on the buckling analysis of the SLGSs are investigated in detail. The present results are compared with the corresponding available in the literature. Additional results are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak\'s parameters for future comparisons.
Key Words
    nonuniform buckling; nonlocal shear deformation model; visco-Pasternak\'s medium
Ashraf M. Zenkour: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabial Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt

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