Micromechanical Models for Analyzing Bending of Porous/Perfect FG Plates in a Hygro-Thermomechanical Environment by a Quasi-3D Theory

An analytical formulation based on a quasi-3D shear deformation theory is proposed to examine the bending response of functionally porous/perfect plates supported on a Kerr/Pasternak/Winkler elastic foundation in hygro-thermo-mechanical conditions. Two kinds of plates, perfect and porous, were studied. For the perfect plates, Mori–Tanaka, LRVE, Voigt, and Reuss models were employed to calculate their mechanical properties changing across the thickness. For the porous plates, different porosity patterns were considered to estimate their mechanical properties. After establishing the governing equations, the Navier solution for simply supported plates was used to calculate their displacements and stresses. The results obtained were compared with data published in the literature, and a good agreement was revealed. Some numerical results were used to investigate the effects of the porosity function, porosity percentage, micromechanical models, and the elastic foundation on the displacements and stresses of a simply supported porous/perfect plate under hygro-thermo-mechanical loadings. The results obtained reveal that these variables have a great influence on the response of the plate in hygro-thermo-mechanical environments.