Dynamic stress analysis of functionally gradient material subject to SH waves  

SH波作用下功能梯度材料的动应力响应分析

作　　者：Qi Lu Zhenqing Wang Yun Zhu Zailin Yang Yong Yang 卢淇;王振清;朱云;杨在林;杨勇

机构地区：[1]College of Aerospace and Civil Engineering,Harbin Engineering University,Harbin 150001,China [2]Key Laboratory of Advanced Material of Ship and Mechanics,Ministry of Industry and Information Technology,Harbin Engineering University,Harbin 150001,China

出　　处：《Acta Mechanica Sinica》2024年第10期24-40,共17页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12072085);the Natural Science Foundation of Heilongjiang Province of China(Grant No.ZD2021A001);the program for Innovative Research Team in China Earthquake Administration.

摘　　要：In this paper, the wave propagation in functionally graded materials (FGM) is studied by the elastic wave theory based on thewave problems in homogeneous media. The auxiliary function and modulus function are introduced to construct the displacementfield and density function. The displacement field, modulus function, and density function are connected to proposea design theory of special FGM. An analytical method for elastic wave propagation in inhomogeneous media with varyingmodulus and density is derived to provide theoretical references for material design and dynamic stress analysis under elasticwaves. Taking the problem of dynamic stress concentration caused by shallow buried elliptical cavity in half space designedunder SH waves as an example, the calculation results are obtained and analyzed. The results show that the dynamic stressconcentration is sensitive to the change of the inhomogeneity of the medium.本文基于弹性波动理论,在均匀介质波动问题的研究基础上,研究功能梯度材料中的弹性波传播问题.结合材料设计理论,两次引入辅助函数与模量变化函数构造弹性波位移场函数和密度变化函数,将位移场、模量变化函数以及密度变化函数相互建立联系,提出了一种特殊功能梯度材料设计理论,并借此得出一种研究模量和密度连续变化的非均匀介质中弹性波传播问题的解析方法.通过该方法,可以设计满足特定需求的材料并研究材料介质中的弹性波传播问题,将FGM的模型化设计和物理机理研究紧密联系起来,为材料设计和弹性波作用下的动应力集中问题分析提供研究思路和理论参考.以SH作用下,该理论方法设计的半空间介质中浅埋椭圆空腔引起的动应力集中问题为例,计算并得出算例进行分析.结果表明,椭圆空腔引起的动应力集中(DSCF)现象对介质的非均匀性变化较为敏感.

关 键 词：Functional gradient materials Elastic wave MODULUS DENSITY Dynamic stress concentration 

分 类 号：O341[理学—固体力学]