带功能梯度过渡区域的各向异性转动圆环的弹性分析  

Elastic Analysis of Anisotropic Rotating Sandwich Circular Ring With a Functionally Graded Transition Region

作　　者：彭旭龙 谢小朋 黄海平 魏文超 唐雪松 PENG Xulong;XIE Xiaopeng;HUANG Haiping;WEI Wenchao;TANG Xuesong(Department of Mechanics,School of Civil Engineering,Changsha University of Science&Technology,Changsha 410114,P.R.China;CRRC Zhuzhou Locomotive Co.Ltd.,Zhuzhou,Hunan 412000,P.R.China)

机构地区：[1]长沙理工大学土木工程学院力学系,长沙410114 [2]中车株洲电力机车有限公司,湖南株洲412000

出　　处：《应用数学和力学》2023年第9期1145-1156,共12页Applied Mathematics and Mechanics

基　　金：湖南省自然科学基金项目(2022JJ30583);湖南省教育厅自然科学研究基金项目(21B0315)。

摘　　要：对绕刚性轴匀速转动的各向异性转动圆环进行了弹性分析.仿照自然界中贝壳的三层构造结构,假定圆环由相互黏结非常好的3个区域组成,内外区域由均匀各向异性材料组成,而过渡区域的材料性能沿径向任意梯度变化.结合边界条件和界面处的连续性条件,采用积分方程方法可得关于径向应力的第二类Fredholm积分方程,进而通过对其进行数值求解,得到了夹层圆环结构的应力场与位移场.对于工程实际中不同梯度变化情况,只需代入相应的材料性能变化形式即可求解.数值算例部分,通过与常用的特殊幂函数梯度变化形式得到的精确解进行对比,验证了积分方程方法的有效性和精确性.同时重点分析了过渡区域材料性能按Voigt函数变化时各向异性度、材料梯度参数、过渡区域厚度等对夹层圆环结构应力场和位移场的影响.该文采用的积分方程方法将为带功能梯度层的各向异性夹层圆环结构的优化设计提供强有力的分析方法.数值分析结果也将为夹层圆环结构的安全设计提供理论指导依据.The elastic analysis of anisotropic rotating sandwich ring with a functionally graded transition region was carried out.Like the shell sandwich structure in nature,the ring is composed of 3 well⁃bonded regions,of which the inner and outer regions are made of homogeneous anisotropic materials,and the intermediate transi⁃tion region is made of a material with arbitrary⁃gradient properties along the radial direction.Based on the boundary conditions and the continuity conditions at the interface,the 2nd Fredholm integral equation for the radial stress was obtained with the integral equation method,then the stress and displacement fields of the sandwich ring structure were obtained through numerical solution.The distributions of the stress and displacement fields in the sandwich ring structure were given.Different gradient changes encountered in engineering practice can be solved only through substitution of the corresponding function model.The effectiveness and ac⁃curacy of the integral equation method were verified through comparison of the numerical solutions with the ex⁃act ones for a special power function gradient variation form.The more general Voigt function model was adopt⁃ed for the intermediate transition region,and the influences of the anisotropy degree,the gradient parameter,and the thickness on the stress and displacement fields were analyzed.The proposed Fredholm integral equation method provides a powerful tool for the optimal design of anisotropic functionally graded materials and sand⁃wich ring structures.The numerical results make a theoretical guidance for the safety design of anisotropic functionally graded sandwich ring structures.

关 键 词：功能梯度材料 夹层圆环 各向异性 任意梯度变化 积分方程方法 

分 类 号：O343.6[理学—固体力学] O343.8[理学—力学]