Background: In the present article, thermal stability of single-layered graphene sheets
(SLGSs) resting on Winkler–Pasternak elastic medium is investigated.
Method: Eringen’s nonlocal elasticity equations are introduced in novel four-variable plate theory considering
the small-scale influences. The advantage of the presented theory is that, in addition to considering
the small scale effect, the displacement field is expressed with only four unknowns by utilizing
undetermined integral terms. Analytical solutions are determined for three types of temperature variations
as uniform, linear and nonlinear temperature rise within the thickness of the SLGS. The effects induced
by shear deformation, thickness ratio, size parameter, and elastic foundation coefficients are all