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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.

Aero-engine casings commonly use composite cylindrical shell structures with excellent properties such as corrosion resistance and fatigue resistance. Still, their vibration behavior is relatively complex and may cause fatigue vibration damage, so it is essential to analyze the vibration characteristics of composite cylindrical shells. The purpose of this paper is to analyze the vibration characteristics of multilayer composite cylindrical shells subjected to external pressures and having different interlayer thickness ratios and provide some theoretical basis for the fatigue damage prediction of cylindrical shell casing to ensure the safety and stability of the engine during flight.

Firstly, the vibration differential equation with external pressure is established based on Soedel theory considering nonlinear effects, while four symmetric boundary conditions are chosen to constrain the cylindrical shell. Then the Rayleigh–Ritz method, which is more efficient and accurate in calculating large structural systems, is applied to solve the problem, and the theoretical model of three-layer cylindrical shell under external pressure is established. The accuracy of the model is verified by comparing the data with the specialized literature. Subsequently, the effects of different external pressures and different thickness-to-diameter ratios, different length-to-diameter ratios and different interlayer thickness percentages on the natural frequency of multilayer composite cylindrical shells were investigated by control variable analysis.

The conclusions obtained show that the external pressure increases the natural frequency of the cylindrical shell and that the frequency characteristics of the cylindrical shell vary for different boundary conditions. The effect of length-to-diameter ratio, thickness-to-diameter ratio and the percentage of the thickness of the intermediate layer on the natural frequency of the cylindrical shell are significantly increased under external pressure. Because the presence of external pressure increases the frequency of the cylindrical shell by about 70%, it has almost no effect on the frequency at the minimum number of circumferential waves, and the effect on the frequency at the maximum number of circumferential waves is reduced to about 50%. The frequencies in the SL-SL boundary condition are all in perfect agreement with the S-S boundary condition under the influence of different influencing factors.

In this paper, the effect of external pressure and the natural properties of the cylindrical shell under external pressure on the cylindrical shell’s frequency is considered, emphasizing the effect of different layer thickness ratios on the frequency. This paper aims to summarize the changing law between the natural frequency of the cylindrical shell itself and different design parameters during the flight pressure process. Reliable theoretical predictions are provided for analyzing the vibrational behavior of shells subjected to external pressures in aerospace, as well as a database for the practical production of cylindrical shells.

Understanding the mechanical and thermal behavior of materials is the goal of the branch of study known as fractional thermoelasticity, which blends fractional calculus with thermoelasticity. It accounts for the fact that heat transfer and deformation are non-local processes that depend on long-term memory. The sphere is free of external stresses and rotates around one of its radial axes at a constant rate. The coupled system equations are solved using the Laplace transform. The outcomes showed that the viscoelastic deformation and thermal stresses increased with the value of the fractional order coefficients.

The results obtained are considered good because they indicate that the approach or model under examination shows robust performance and produces accurate or reliable results that are consistent with the corresponding literature.

This study introduces a proposed viscoelastic photoelastic heat transfer model based on the Moore-Gibson-Thompson framework, accompanied by the incorporation of a new fractional derivative operator. In deriving this model, the recently proposed Caputo proportional fractional derivative was considered. This work also sheds light on how thermoelastic materials transfer light energy and how plasmas interact with viscoelasticity. The derived model was used to consider the behavior of a solid semiconductor sphere immersed in a magnetic field and subjected to a sudden change in temperature.

This study introduces a proposed viscoelastic photoelastic heat transfer model based on the Moore-Gibson-Thompson framework, accompanied by the incorporation of a new fractional derivative operator. In deriving this model, the recently proposed Caputo proportional fractional derivative was considered. This work also sheds light on how thermoelastic materials transfer light energy and how plasmas interact with viscoelasticity. The derived model was used to consider the behavior of a solid semiconductor sphere immersed in a magnetic field and subjected to a sudden change in temperature.