In this reported work, surface effects and non-local two variable refined plate theories are combined on the shear/biaxial buckling and vibration of rectangular nanoplates. A silver sheet is selected as the case study to investigate the numerical results. Surface effects are considered by Gurtin-Murdoch's theory. The differential quadrature method is used to solve the governing equations. Differential quadrature solutions are verified by Navier's method. The influences of the non-local parameter on the surface effects of shear/biaxial buckling and vibration are investigated for various boundary conditions. Results show that by increasing the non-local parameter, the effects of surface on the buckling and vibration increase. This result is in contrast with the works of other researchers in the field. Moreover, the non-local effects on the shear buckling and vibration are more important than that of biaxial, whereas the surface effects on the biaxial buckling and vibration are more notable than that of shear.

In this article, buckling analysis of doubleorthotropic nanoplates (DONP) embedded in elastic media under biaxial, uniaxial and shear loading is numerically studied. The analysis is based on non-local theory. Both two-variable refined plate theory (TVRPT) and first-order shear deformation plate theory (FSDT) are used to derive the governing equations. Generalized differential quadrature method (GDQM) is utilized to solve the governing equations. In buckling analysis, both in-phase and out-ofphase modes are studied. A graphene sheet is selected as the case study to investigate the numerical results. GDQM results are validated by comparing with the Navier's solutions. After validating the formulation and method of solution, the effect of non-local parameter, geometrical parameters and boundary conditions on the critical buckling load of the double-orthotropic nanoplate are investigated and discussed in detail. It is shown that the effects of non-local parameter for shear buckling are more noticeable than that of biaxial buckling. Moreover, for higher values of non-local parameter, the shear buckling is not dependent on the van der Waals and Winkler moduli.Keywords Two-variable refined plate theory Á Non-local theory Á Buckling analysis Á Generalized differential quadrature method Á Double-orthotropic nanoplate Abbreviations DONP Double-orthotropic nanoplate DQM Differential quadrature method GDQM Generalized differential quadrature method TVRPT Two-variable refined plate theory FSDT First-order shear deformation theory HSDT Higher-order shear deformation theories CPT Classical plate theory NDCBL Non-dimensional critical buckling load

In this article, the influence of temperature change on the vibration, buckling, and bending of orthotropic graphene sheets embedded in elastic media including surface energy and small-scale effects is investigated. To take into account the small-scale and surface energy effects, the nonlocal constitutive relations of Eringen and surface elasticity theory of Gurtin and Murdoch are used, respectively. Using Hamilton's principle, the governing equations for bulk and surface of orthotropic nanoplate are derived using two-variable refined plate theory. Finite difference method is used to solve governing equations. The obtained results are verified with Navier's method and validated results reported in the literature. The results demonstrated that for both isotropic and orthotropic material properties, by increasing the temperature changes, the degree of surface effects on the buckling and vibration of nanoplates could enhance at higher temperatures, while it would diminish at lower temperatures. In addition, the effects of surface and temperature changes on the buckling and vibration for isotropic material property are more noticeable than those of orthotropic. On the contrary, these results are totally reverse for bending problem.

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