Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates

In this study, bending, free vibration, and buckling response of functionally graded porous micro-plates are investigated using the classical and first-order shear deformation plate theories. The Navier solution technique is utilized to obtain analytical solutions to simply supported rectangular plates. A power-law distribution is used to model the variation of two material constituents through the plate thickness. Three different porosity distributions are considered and assumed to take forms of cosine functions. The microstructure-dependent size effects are captured using the modified couple stress theory. Numerical results of bending, free vibration, and buckling are presented to determined the effects of constituent material variation, microstructure-dependent size effects, and porosity distributions on the mechanical response of functionally graded porous micro-plates.