Elastic instability analysis of functionally graded nanoplates under nonlinear coupling loads on a shear elastic foundation via non-local theory

Nanostructures are generally used in environments where they can be subjected to different types of loading; understanding and determining their reaction to a hygro-thermo-mechanical environment is crucial for their design. This analysis's main objective is to evaluate the buckling sensitivity of sandwich nanoplates of FGMs subjected to a hygrothermomechanical loading while resting on a two-parameter elastic medium. To accomplish this investigation, a quasi-3D highshear deformation theory involving five variables containing integral terms, including the nonlocal elasticity theory of Eringen, is used. The assumed sandwich nanoplate is placed on an elastic medium, submitted to multiple boundary conditions, and subjected to a hygro-thermo-mechanical stress. The sandwich nameplate's material properties are intended to be continuously graded across its whole thickness. An elastic foundation with two parameters is used to model the elastic environment. The equilibrium equations are constructed using the concept of virtual displacements, and the solution is displayed for several boundary conditions. The obtained outcomes are approved and validated by comparison with those found by other scholars discussing the same topic in the literature. The impact and influence of various parameters on the stability of FGM sandwich nanoplates in a hygro-thermomechanical situation are investigated through the intermediary of parametric analysis.