Thermal buckling of double-layered graphene sheets embedded in an elastic medium with various boundary conditions using a nonlocal new first-order shear deformation theory

In this paper, thermal buckling of double-layered graphene sheets (GSs) with various boundary conditions is analyzed. The new first-order shear deformation theory (NFSDT) is reformulated using nonlocal differential constitutive relations of Eringen. Unlike the conventional first-order shear deformation (FSDT), NFSDT contains only two unknowns. It is assumed that two GSs are bonded by an internal elastic medium and surrounded by external elastic foundations. The equations of equilibrium of the nonlocal model have been derived by using the virtual displacement method. Analytical solutions for the thermal buckling of double-layered GSs under various boundary conditions are presented. The analytical expression is given for the three types of temperature distribution as uniform, linear, and nonlinear temperatures rise through the thickness of the plate. Two comparison studies are carried out to demonstrate the high accuracy of the presented nonlocal NFSDT. The influences of nonlocal parameter, plate aspect ratio, elastic foundation parameters, boundary conditions on critical buckling temperature, and critical temperature ratio are investigated.