Shear buckling of rectangular nanoplates embedded in elastic medium based on nonlocal elasticity theory

In the present work, nonlocal elasticity theory has been implemented to study the shear buckling of singlelayered graphene sheets (SLGS). The nonlocal elasticity theory accounts for the small size effects when dealing with nanostructures. The influence of the surrounding elastic medium on the critical buckling load of the SLGS is investigated. Both Winkler-type and Pasternaktype models are employed to simulate the interaction of the graphene sheets with a surrounding elastic medium. Using the principle of virtual work the governing equations are derived for the rectangular nanoplates. The nonlocal small scale coefficients get introduced into the nonlocal theory through the constitutive relations. Differential quadrature method is employed and numerical solutions for the critical buckling load are obtained. Numerical results show that the critical buckling load of SLGS is strongly dependent on the small scale coefficient. Further, the scale coefficient has a decreasing effect on the buckling load and at higher scale coefficient values the influence of Winkler modulus decreases but shear modulus still has an increasing effect on the buckling load.

کلیدواژه ها:

shear buckling ، nonlocal elasticity model ، differential quadrature method (DQM) ، graphene