A numerical method for magneto-hygro-thermal postbuckling analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions

Many researchers work on the mechanical analysis of perfect graphene sheets while these structures have some defects actually. In this paper, postbuckling of the defective quadrilateral single layered graphene sheets (SLGS) is presented for the first time. Three types of defects including single vacancy (SV), double vacancy (DV) and Stone–Wales (SW) in conjunction with the influence of vacancy defect reconstruction are considered. Nonlocal higher order strain gradient theory with three parameters for size effects is used. The quadrilateral graphene sheet is subjected to temperature, moisture and in-plane magnetic loads. The elastic foundation is modelled by Pasternak medium. The equations of motion are obtained imposing higher order shear deformation theory and Hamilton’s principle. The transformed weighing (TW) and differential quadrature (DQ) method are applied for postbuckling load–deflection relation of the structure. Due to the hygrothermal load, different movable boundary conditions are used. The influences of various parameters such as defect types, defect degree, defect reconstruction, hygrothermal load, magnetic field, nonlocal parameters, 7 different quadrilateral SLGS, boundary conditions and elastic medium on the postbuckling behaviour of the quadrilateral graphene sheet are shown. The numerical results are validated with other published works in the literature. Results show that with increasing the defect degree, the buckling load decreases.