Bending analysis of FGSP nanoplate resting on elastic foundation by using nonlocal quasi-3D theory

•A quasi-3D higher-order shear deformation theory, which fulfills transverse shear stress-free on the upper and lower surfaces of the nanoplate in combination with Eringen's nonlocal elasticity theory and Biot's poroelasticity theory is used.•The material properties of FGSP materials are assumed to change gradually along the thickness direction following three patterns of porosity distribution: uniform, symmetric, and asymmetric. The pores are saturated by the fluid.•The closed-form solutions are obtained by using Navier's technique for simply supported rectangular nanoplate.•The effects of the porosity distribution patterns, porosity coefficient, Skempton coefficient, geometrical parameters, elastic foundation, and nonlocal parameters on the bending behaviour have been explored. In this paper, the bending response of a functionally graded saturated porous (FGSP) nanoplate resting on the Pasternak elastic foundation is analyzed within the framework of quasi-3D higher-order shear deformation theory (quasi-3D HSDT) for the first time. The material properties are presumed to change gradually along the thickness direction following three patterns of porosity distribution: uniform, non-uniform symmetric, and asymmetric. The theory of poroelasticity developed by Biot is utilized in modeling the stress-strain relationships for the saturated condition. Moreover, the nanoscale effects of the structures are considered by Eringen's nonlocal elasticity theory. The governing equations are derived by using the principle of minimum potential energy according to quasi-3D HSDT, which ensures transverse shear stress-free on the upper and lower surfaces of the nanoplate. Based on the obtained closed-form solution, the impacts of the porosity distribution patterns, porosity coefficient, Skempton coefficient, geometrical parameters, elastic foundation, and nonlocal parameters on the bending behavior have been explored. According to the findings, when the pores are saturated by the fluid, the plate stiffness increases. Additionally, increasing the values of the nonlocal parameter for FGSP nanoplates leads to an increase in deflection and stresses. Finally, the present study quantitatively reveals the size-dependent effects of a saturated porous medium.