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.

摘要

在这项工作中，开发了一种数值 3D 有限元方法来研究饱和 FG 多孔环形椭圆扇形板的固有频率和静态响应。利用 3D 弹性理论对问题进行建模。沿厚度方向假定了三种不同的孔隙率模式，例如孔隙率非线性对称分布（PNSD）、孔隙率非线性非对称分布（PNND）和孔隙率均匀分布（PUD）。多孔弹性的比奥理论代替简单的胡克定律被用来描述应力和应变之间的关系。为了推导控制方程，应用了根据 Rayleigh-Ritz 能量公式的有限元方法。一项彻底的调查研究了板的静态行为和固有频率对不同参数的敏感性，