The effect of vacant defect on bending analysis of graphene sheets based on the Mindlin nonlocal elasticity theory

In the paper, effects of eccentric vacant defect on bending analysis of circular graphene sheets have been studied based on nonlocal elasticity theory considering the Mindlin theory of the plates. The governing equations have been derived for circular graphene sheet including eccentric vacant defect. Because of existence of an eccentric vacant defect on the plate, the anti-symmetric problem has been obtained. So, the constitutive equations are partial differential equations system. Considering this fact that there is not any analytical solution available for solving the nonlinear constitutive equations based on the first order shear deformation theory, a new semi-analytical polynomial method is applied which has been presented by the authors recently. By applying the mentioned method, the governing equations have been solved. Regarding this fact that no study has been done heretofore in case of the effects of eccentric vacant defect on bending analysis of graphene sheets, the obtained results of local analysis have been compared with the results of Abaqus software. At the following, the effects of nonlocal parameters, size and location of vacant defect on the results have been surveyed.