Large deflection analysis of functionally graded saturated porous rectangular plates on nonlinear elastic foundation via GDQM

In the current study, large deflection analysis of a functionally graded saturated porous (FGSP) rectangular plate subjected to transverse loading which is located on a nonlinear three-parameter elastic foundation is provided. The constitutive law for the porous materials is written based on Biot's model which considers the effect of fluids within the pores. The mechanical properties of the plate are changed through its thickness according to different functions which are called porosity distributions. The shear deformation effects are taken into account, accordingly, the first-order shear deformation theory (FSDT) is used to describe the displacement components of the plate. Employing the Minimum total potential energy principle and calculus of variation, the governing equations, and associated boundary conditions are extracted. A generalized differential quadrature method (GDQM) is used to solve them for various boundary conditions. The results for the simpler state are validated with the previously published works and then the effects of different parameters on the deflection of the plate are investigated. It is seen increasing the porosity and Skempton coefficient, enhances and reduces the deflection of the structure, respectively. The results of this study may help to design and manufacture more reliable engineering structures that are exposed to loads.