Abstract

This paper proposes a new general framework of higher-order shear deformation theory (HSDT) and solves the structural responses of the functionally graded (FG) plates using novel exponential shape functions for the Ritz method. Based on the fundamental equations of the elasticity theory, the displacement field is expanded in a unified form which can recover to many different shear deformation plate theories such as zeroth-order shear deformation plate theory, third-order shear deformation plate theory, various HSDTs and refined four-unknown HSDTs. The characteristic equations of motion are derived from Lagrange’s equations. Ritz-type solutions are developed for bending, free vibration and thermal buckling analysis of the FG plates with various boundary conditions. Three types of temperature variation through the thickness are considered. Numerical results are compared with those from previous studies to verify the accuracy and validity of the present theory. In addition, a parametric study is also performed to investigate the effects of the material parameters, side-to-thickness ratio, temperature rise and boundary conditions on the structural responses of the FG plates.

摘要

本文提出了一种新的高阶剪切变形理论（HSDT）的通用框架，并使用新颖的指数形状函数对Ritz方法求解了功能梯度（FG）板的结构响应。根据弹性理论的基本方程式，位移场以统一的形式扩展，可以恢复到许多不同的剪切变形板理论，例如零阶剪切变形板理论，三阶剪切变形板理论，各种HSDT和精制了四个未知的HSDT。运动的特征方程式是从拉格朗日方程式导出的。开发了Ritz型解决方案，用于在各种边界条件下对FG板进行弯曲，自由振动和热屈曲分析。考虑了三种厚度范围内的温度变化。将数值结果与以前的研究结果进行比较，以验证本理论的准确性和有效性。另外，还进行了参数研究，以研究材料参数，边厚比，温度升高和边界条件对FG板结构响应的影响。