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This paper aims to present a new one-variable first-order shear deformation theory (OVFSDT) using nonlocal elasticity concepts for buckling of graphene sheets.

The FSDT had errors in its assumptions owing to the assumption of constant shear stress distribution along the thickness of the plate, even though by using the shear correction factor (SCF), it has been slightly corrected, the errors have been remained owing to the fact that the exact value of SCF has not already been accurately identified. By using two-variable first-order shear deformation theories, these errors decreased further by removing the SCF. To consider nanoscale effects on the plate, Eringen’s nonlocal elasticity theory was adopted. The critical buckling loads were computed by Navier’s approach. The obtained numerical results were then compared with previous studies’ results using molecular dynamics simulations and other plate theories for validation which also showed the accuracy and simplicity of the proposed theory.

In comparing the biaxial buckling results of the proposed theory with the two-variable shear deformation theories and exact results, it revealed that the two-variable plate theories were not appropriate for the investigation of asymmetrical analyses.

A formulation for FSDT was innovated by reconsidering its errors to improve the FSDT for investigation of mechanical behavior of nanoplates.

Thermal buckling of double-layered piezoelectric nanoplates has been analyzed by applying an external electric voltage on the nanoplates. The paper aims to discuss this issue.

Double-layered nanoplates are connected to each other by considering linear van der Waals forces. Nanoplates are placed on a polymer matrix. A comprehensive thermal stress function is used for investigating thermal buckling. A linear electric function is used for taking external electric voltages into account. For considering the small-scale effect, the modified couple stress theory has been applied. An analytical solution has been used by taking various boundary conditions.

EEV has a considerable impacted on the results of various half-waves in all boundary conditions. By increasing EEV, the reduction of critical buckling temperature in higher half-waves is remarkably slower than lower half-waves. By considering long lengths, the effect of EEV on the critical temperature will be markedly decreased.

This paper uses electro-thermal stability analysis. Double-layered piezoelectric nanoplates are analyzed. A comprehensive thermal stress function is applied for taking into account critical temperature.

The purpose of this paper is to predict the mechanical behavior of a piezoelectric nanoplate under shear stability by taking electric voltage into account in thermal environment.

Simplified first-order shear deformation theory has been used as a displacement field. Modified couple stress theory has been applied for considering small-size effects. An analytical solution has been taken into account for various boundary conditions.

The length scale impact on the results of any boundary conditions increases with an increase in l parameter. The effect of external electric voltage on the critical shear load is more than room temperature effects. With increasing aspect ratio the critical shear load decreases and external electric voltage becomes more impressive. By considering piezoelectric nanoplates, it is proved that the temperature rise cannot become a sensitive factor on the buckling behavior. The length scale parameter has more effect for more flexible boundary conditions than others. By considering nanosize, the consideration has led to much bigger critical load vs macro plate.

In the current paper for the first time the simplified first-order shear deformation theory is used for obtaining governing equations by using nonlinear strains for shear buckling of a piezoelectric nanoplate. The couple stress theory for the first time is applied on the nonlinear first-order shear deformation theory. For the first time, the thermal environment effects are considered on shear stability of a piezoelectric nanoplate.