Static response and free-vibration analysis of a functionally graded annular elliptical sector plate made of saturated porous material based on 3D finite element method

Abstract

In this work, a numerical 3D finite element method is developed to investigate the natural frequencies and static responses of saturated FG porous annular elliptical sector plate. 3D elasticity theory is utilized to model the problem. Three various porosity patterns are assumed along the thickness direction such as porosity nonlinear symmetric distribution (PNSD), porosity nonlinear nonsymmetric distribution (PNND), and porosity uniform distribution (PUD). Biot theory of poroelasticity instead of the simple Hooke’s law is applied to describe the relation between stress and strain. To derive the governing equations, finite element approach according to Rayleigh-Ritz energy formulation is applied. A thorough investigation studies the sensitivity of the static behavior and natural frequencies of the plate to different parameters, including the Skempton and porosity coefficients, geometric parameters, and various patterns of porosity.