Size-Dependent Hygro-Thermal Buckling of Porous FGM Sandwich Microplates and Microbeams Using a Novel Four-Variable Shear Deformation Theory

Based on a new shear deformation theory and the modified couple stress theory, in this paper, the hygro-thermal buckling of porous FGM sandwich microplates and microbeams is investigated. Unlike the classical elasticity theory, the present model involves a material length scale parameter, and, thereby, can capture the small size effect. The four-variable shear deformation theory with a new shape function is utilized to derive the governing stability equations for the microplates and microbeams from the principle of virtual work. The present microstructures are composed of three layers and subjected to hygro-thermal conditions. The core is assumed to be fully homogeneous and isotropic material. While, the face layers are made from porous functionally graded materials that vary only in the thickness direction. The governing equations are solved analytically to obtain the thermal buckling of FGM sandwich microplates and microbeams under humidity effects. The temperature rise and moisture concentration are graded uniformly, linearly or nonlinearly through the thickness. Comparison studies are made between the present results and those available in the literature to check the validity of the obtained formulations and results. Moreover, the effects played by the length scale parameter, power-law exponent, moisture concentration, core thickness and other parameters on the thermal buckling of microplates and microbeams are all investigated.