功能梯度厚壁中空圆柱体弹性动力学平面应变响应的解析解

Elastodynamic Solution for Plane-Strain Response of Functionally Graded Thick Hollow Cylinders by Analytical Method

研究了边界表面受均布动压力作用的功能梯度(FGM)厚壁中空圆柱体,给出了其平面应变响应下的弹性动力学解.假设材料性能(除Poisson比外)随厚度按幂律函数变化.为了得到一个精确解,将动力径向位移分为准静力部分和动力部分,导出了每个部分的一个解析解.先由Euler方程得到准静力学部分的解,再由分离变量法和正交展开法得到动力学部分的解.在不同动荷载作用下,对不同的FGM中空圆柱体,画出径向位移和应力图,并对本方法的优点进行了讨论.该解析解适用于中空圆柱体各种组合的FGM,厚度可以是任意的,初始条件也可以是任意的,壁面上均匀分布着任意形式的动压力.

An elastodynamic solution for the plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at the boundary surfaces,was presented.The material properties,except Poisson＇s ratio,were assumed to vary through the thickness following a power law function.To achieve an exact solution,the dynamic radial displacement was divided into two quasi-static and dynamic parts.For each part,an analytical solution was derived.Firstly,the quasi-static solution was obtained by means of Euler＇s equation,and then the dynamic solution was derived by utilizing the separation of variables method and the orthogonal expansion technique.Radial displacement and stress distributions were plotted for various FGM hollow cylinders under different dynamic loads and the advantages of the presented method were discussed.The presented analytical solution was suitable for analyzing various arrangements of FGM hollow cylinders with arbitrary thickness and arbitrary initial conditions,subjected to arbitrary form of dynamic pressures distributed uniformly at the boundary surfaces.Finally,radial displacement and stress distributions were plotted for various FGM hollow cylinders under different dynamic loads and the advantages of the presented method were considered.