Nonlinear Bending and Vibration Analysis of Imperfect Functionally Graded Microplate with Porosities Resting on Elastic Foundation Via the Modified Couple Stress Theory

This paper represents the nonlinear bending and free vibration analysis of a simply supported imperfect functionally graded (FG) microplate resting on an elastic foundation based on the modified couple stress theory and the Kirchhoff plate theory (KPT) together with the von-Kármán’s geometrical nonlinearity. The FG microplates with even and uneven distributions of porosities are considered. Analytical solutions for the nonlinear bending and free vibration are obtained. Comparing the obtained results with the published one in the literature shows the accuracy of the current solutions. Numerical examples are further presented to investigate the effects of the material length scale parameter to thickness ratio, the length to thickness ratio, the power-law index and the elastic foundation on the nonlinear bending and free vibration responses of the FG microplate.