Size-dependent nonlinear bending and postbuckling of functionally graded Mindlin rectangular microplates considering the physical neutral plane position

In this paper, the nonlinear bending and postbuckling characteristics of Mindlin rectangular microplates made of functionally graded (FG) materials are studied based on the modified couple stress theory (MCST). This theory facilitates considering size dependency through introducing material length scale parameters. The FG microplates, whose volume fraction is expressed by a power law function, are considered to be made of a mixture of metals and ceramics. By considering the physical neutral plane position, the stretching–bending coupling is eliminated in both nonlinear governing equations and boundary conditions of FG microplates. With the aid of MCST and the principle of virtual work, the governing equations and corresponding boundary conditions are derived. Then, the obtained governing equations and boundary conditions are discretized through the generalized differential quadrature (GDQ) method. Finally, the resulting nonlinear parameterized equations are solved by the pseudo-arclength continuation technique. The effects of material gradient index, length scale parameter, length-to-thickness ratio, and boundary conditions on the nonlinear bending and postbuckling responses of FG microplates are investigated.