The non-linear hygrothermal and mechanical buckling responses of FG sandwich plates resting on two-parameter elastic foundations are presented in this study. Non-linear Fourier temperature distribution is considered as a special case. A hyperbolic displacement model is proposed in the present investigation. The present model involves four unknown variables, and the shear stresses on the bottom and top of the plate surfaces are equal to zero. The effective material properties of the FG sandwich face sheets are presumed to be varied in the direction of the thickness using a simple power law distribution, while the core is supposed to be purely ceramic. The stability equations are deduced by the principle of virtual work, containing the effect of foundations interaction and hygrothermal effects based on the present model. The hygrothermal effects are considered as non-linear, linear and uniform distribution through the plate thickness. Comparison examples are presented to verify the accuracy of the present model. The effects played by the temperature rise, moisture concentration, parameters of elastic foundation, side-to-thickness ratio, aspect ratio of the plate, the inhomogeneity parameter on the critical buckling of FG sandwich plates are investigated.

Hygrothermal and mechanical buckling responses of functionally graded (FG) plates resting on Winkler–Pasternak’s foundations are presented in this paper using a refined quasi-3D model. The effects due to transverse normal strain and shear deformation are both included. The present model exactly satisfies stress boundary conditions on the upper and lower surfaces of the FG plate without using shear correction factors. It is assumed that the material properties vary according to a power law of the thickness coordinate variable. The hygrothermal buckling equilibrium equations are derived from the principle of virtual work for FG plates resting on Winkler–Pasternak’s foundations with simply-supported boundary conditions. Two types of thermal and hygrothermal loading, uniform thermal and hygrothermal rise, linear thermal and hygrothermal distribution through the thickness are considered. Numerical results are presented to verify the accuracy of the present study. The effects played by Winkler–Pasternak’s parameters, plate aspect ratio, side-to-thickness ratio, gradient index, and loading type on the critical buckling of the FG plates are all investigated.

This work is devoted to the bending analysis of functionally graded (FG) nano-scale plate by using the nonlocal mixed variational formula under simply supported edge conditions. According to Eringen’s nonlocal elasticity theory, the mixed formula is utilized in order to obtain the governing equations. The system of equations is derived by using the principle of virtual work. The governing equations include both the small and the mechanical effects. The impact of the small-scale parameter, aspect and thickness nano-scale plate ratios, and gradient index on the displacement and stresses are explored, numerically presented, and discussed in detail. Different comparisons are made to check the precision and validity of the bending outcomes obtained from the present analysis of FG nano-scale plates. Parametric examinations are then performed to inspect the impacts of the thickness of the plate on the by and large mechanical reaction of the practically evaluated plates. The displayed outcomes are valuable for the configuration procedures of keen structures and examination from materials.

For the first time, Levy-type solution model and the state-space concept are employed to investigate the hygrothermal bending response of a cross-ply laminated plate on a three-parameter Kerr foundation subjected to a 2D magnetic field. The displacement field is established based on Shimpi’s two-variable plate theory. Based on Maxwell’s equations, the magnetic body force (Lorentz force) is established. In the present analysis, two opposite edges of the plate are simply supported. While, the other two edges have arbitrary boundary conditions. For more generality and reality, the mechanical load, temperature and moisture that are applied to the upper surface of the plate are assumed to be uniformly, linearly, exponentially, and sinusoidally varied. The principle of virtual displacements is employed to derive the governing partial differential equations based on the present theory, including Lorentz magnetic force. Levy procedure is employed to obtain the nonhomogeneous ordinary differential equations. The matrix method is utilized to get the homogeneous solution. While, the particular solution is obtained by employing the method of undetermined coefficients. The effects of Kerr foundation, loading type, boundary conditions, side-to-thickness ratio, plate aspect ratio, magnetic parameter, temperature, and moisture on deflection and stresses of Levy plate are investigated. It is noted that the magnetic field and hygrothermal loads reduce the structure’s strength, which leads to an increment in the deflection and stresses.