Geometrically Nonlinear Study of Functionally Graded Saturated Porous Plates Based on Refined Shear Deformation Plate Theory and Biot’s Theory

Abstract

This research presents the geometrically nonlinear investigation of functionally graded saturated porous material (FGSPM) plate under undrained conditions. In conjunction with von Karman’s nonlinearity, the refined shear deformation plate theory (RSDPT) is implemented to model the FGSPM plate. The effective material characteristics of the saturated porous plate change constantly in the thickness direction. The pores of the saturated porous plate are examined in fluid-filled conditions. Thus, the constitutive equations are established using Biot’s linear poroelasticity theory. The governing equations are developed by combining a nonlinear finite element technique with Hamilton’s principle. Then, the direct iterative approach is utilized to extract the geometrically nonlinear numerical results. The emphasis is placed on exploring the effects of numerous parameters such as Skempton coefficient, volume fraction grading index, porosity volume index, porosity distributions, and boundary conditions during the extensive numerical analyses on the linear frequency, large amplitude frequencies, and nonlinear central deflections of the FGSPM plate. It is evident from the investigation that saturated fluid in the pores substantially impacts the nonlinear deflection and vibration behavior of the FGSPM plate.