Influence of length scale parameter on size-dependent nonlinear bending of MCST microplates made from FG saturated porous material

Using a variational method, the nonlinear governing equations of the equilibrium of functionally graded (FG) saturated porous microplates have been derived on the basis of von Kármán hypotheses, first-order shear deformation plate, and modified couple stress theories. The microplate pore distribution is considered functionally graded across thickness. The nonlinear boundary conditions and the coupled nonlinear partial differential equations are discretized via generalized differential quadrature method and assembled throughout the domain grid points, in a manner that can be regenerated for any number of the microplate length and width grid points by means of a computer, in order to guarantee the numerical stability. The assembled nonlinear equations, as well as corresponding linear equations, have been numerically solved via a Newton-Raphson iteration method for bending analysis of the microplate. The results are given a structure to appropriately show how the bending deflection of the microplate changes under the influences of both length scale parameter and either porosity, pore distributions, the Skempton coefficient, geometric parameters, or type of boundary conditions. A few coincidences of the result with the relevant literature, especially a mathematically-analogous FG microplate, have been verified as necessary conditions for the validity of the result.