Size-Dependent Mechanical Analysis of Imperfect FG Mindlin Microplate with Porosities Resting on Elastic Foundation Through the Modified Couple Stress Theory

This work presents the analytical analysis of bending, buckling and free vibration responses of an imperfect functionally graded (FG) microplate resting on an elastic foundation. The Mindlin plate theory (MPT) and the modified couple stress theory (MCST) are used in this study to model the microplate and Hamilton’s principle is utilized to establish the equations of motion. The material properties of the FG microplate are estimated based on a classical rule of mixture in which the material properties are assumed to vary continuously in the thickness direction. Two porosity distribution models including even and uneven porosity distributions are considered to account for the influence of porosities. Analytical solutions for the bending, buckling and free vibration problems of imperfect FG simply-supported (S–S) microplates are carried out. The results for the perfect FG microplate are verified with other published results. The influences of some key parameters on the linear and nonlinear behaviors of the microplate are investigated and discussed in detail.