一种特殊梯度分布的功能梯度圆柱壳的二维分析

Two Dimensional Analysis of a Functionally Graded Cylindrical Shell with Specific Material Gradient

功能梯度材料是一种新型材料,其结构分析已成为当今力学研究的热点。本文对一种特殊梯度分布的功能梯度材料圆柱壳进行了二维精确分析。从弹性力学平面应变问题的基本方程出发,引入应力函数,导出功能梯度材料圆柱壳受静载作用下的控制微分方程。假设材料的杨氏模量沿半径方向呈幂函数分布,泊松比为常数,利用分离变量法,导出了简支边界情况下功能梯度圆柱壳的精确解。通过算例分析了不同梯度变化时,功能梯度圆柱壳内的应力和位移变化规律。计算结果表明不同梯度分布的圆柱壳结构中的应力、位移沿厚度方向的变化规律是不同的,有时甚至差别很大。因此对于材料性质梯度变化的功能梯度材料圆柱壳,必须针对其自身特点,建立相应的理论分析模型。

It has becoming a new research hotspot of structural analysis for functionally graded material recently. Two dimensional analysis of a functionally graded cylindrical shell with specific material gradien was presented. In terms of stress function, the governing differential equation was obtained for the simple supported functionally graded cylindrical shell from the basic equations of plane elasticity. Assuming that Young＇s modulus of the material was distributed through a power function in the radius direction, an exact solution of the governing differential equation was obtained by variable separation method. Through numerical examples, the variations of displacement and stress components with different graded material distributions were analyzed. And the differem graded parameters have significant effects on the structural behavior. It is necessary to establish the corresponding analytical model for functionally graded materials.