In this work, the buckling behaviour of a single-layer graphene sheet (SLGS) embedded in visco-Pasternak medium is studied using a non-local integral model with four unknowns. This model has an integral displacement field that includes the effect of transverse shear deformation without using shear correction factors. The visco-Pasternak medium is introduced by considering the damping effect of the classical foundation model modelled by the linear Winkler coefficient and the Pasternak foundation coefficient (shear). The SLGS considered is subjected to in-plane compressive loads per unit length. The influences of numerous parameters such as the non-local parameter, the geometric ratio, the visco-Pasternak coefficients, the damping parameter, and the mode numbers on the buckling response of SLGS are studied and discussed.Keywords: non-uniform buckling; integral model with four unknowns; non-local elasticity theory; visco-Pasternak support.
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