Abstract

In this article, the nonlocal strain gradient theory (NSGT) has been utilized to reveal the dynamic investigation of bi-directional (2D) functionally graded (FG) porous nanoplates resting on Winkler and Pasternak elastic foundations. The governing formulations are derived via Hamilton’s principle, first-order shear deformation theory (FSDT), von-Karman geometrical nonlinearity and the principal of mixtures. It is presumed that the materials graded in two directions and two different distributions of porosities including even and uneven patterns through the thickness of the FG nano-scale plate. The nonlinear equations are solved via the kinetic dynamic relaxation (KDR) numerical procedure and the Newmark integration as well as finite-difference discretization approach. In order to validate the present numeric outcomes, some comparison studies have been conducted with available papers. The parametric study of this paper reveals the roles of different effective factors such as porosity coefficients, nonlocal and strain gradient parameters, diverse boundary conditions, gradient indexes and elastic foundations on the dimensionless deflection. It can be inferred that nonlocal parameter and specially strain gradient coefficient affect the variations of deflection. Eventually, it can be comprehended that elastic foundation in even porosity distribution affects the deflection more remarkably than uneven porosity.

摘要

在本文中，非局部应变梯度理论 (NSGT) 已被用于揭示基于 Winkler 和 Pasternak 弹性基础的双向 (2D) 功能梯度 (FG) 多孔纳米板的动态研究。控制公式是通过哈密顿原理、一阶剪切变形理论 (FSDT)、冯-卡门几何非线性和混合原理推导出来的。据推测，材料在两个方向和两种不同的孔隙分布中分级，包括穿过 FG 纳米级板厚度的均匀和不均匀图案。通过动力学动态松弛 (KDR) 数值程序和 Newmark 积分以及有限差分离散化方法求解非线性方程。为了验证目前的数字结果，对现有论文进行了一些比较研究。本文的参数化研究揭示了孔隙率系数、非局部和应变梯度参数、不同边界条件、梯度指数和弹性地基等不同影响因素对无量纲挠度的影响。可以推断，非局部参数和特别是应变梯度系数会影响挠度的变化。最终可以理解，孔隙分布均匀的弹性地基比孔隙分布不均匀对挠度的影响更为显着。无量纲挠度的梯度指数和弹性基础。可以推断，非局部参数和特别是应变梯度系数会影响挠度的变化。最终可以理解，孔隙分布均匀的弹性地基比孔隙分布不均匀对挠度的影响更为显着。无量纲挠度的梯度指数和弹性基础。可以推断，非局部参数和特别是应变梯度系数会影响挠度的变化。最终可以理解，孔隙分布均匀的弹性地基比孔隙分布不均匀对挠度的影响更为显着。