带功能梯度过渡区域的各向异性转动圆环的弹性分析

彭旭龙; 谢小朋; 黄海平; 魏文超; 唐雪松

doi:10.21656/1000-0887.440003

带功能梯度过渡区域的各向异性转动圆环的弹性分析

doi: 10.21656/1000-0887.440003

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

基金项目:

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

详细信息

通讯作者:
彭旭龙(1983—)，女，副教授，博士，硕士生导师(通讯作者. E-mail: peng_xulong@csust.edu.cn)

中图分类号: O343.6;O343.8
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出版历程
- 收稿日期: 2023-01-04
- 修回日期: 2023-01-27
- 刊出日期: 2023-09-01

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

1.
Department of Mechanics, School of Civil Engineering, Changsha University of Science & Technology, Changsha 410114, P.R.China
2.
CRRC Zhuzhou Locomotive Co. Ltd., Zhuzhou, Hunan 412000, P.R.China

摘要

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.
- 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
Abstract: 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 transition 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 accuracy of the integral equation method were verified through comparison of the numerical solutions with the exact ones for a special power function gradient variation form. The more general Voigt function model was adopted 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 sandwich ring structures. The numerical results make a theoretical guidance for the safety design of anisotropic functionally graded sandwich ring structures.
- functionally graded material /
- sandwich circular ring /
- anisotropy /
- arbitrary gradient variation /
- integral equation method

HTML全文

图 1 功能梯度夹层圆环模型

Figure 1. Diagram of a functionally graded sandwich ring

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图 2 幂函数时数值解和解析解的比较(q_n=ρ^Ⅲω²b², u_n=ρ^Ⅲω²b²/E_r^Ⅲ)

Figure 2. Comparisons of the exact and numerical results with the power law function (q_n=ρ^Ⅲω²b², u_n=ρ^Ⅲω²b²/E_r^Ⅲ)

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图 3 各向异性度λ对应力场和位移场的影响

Figure 3. The influences of anisotropic degree λ on the stress field and the displacement field

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图 4 梯度参数β对应力与位移场的影响

Figure 4. The influences of gradient parameter β on the stress field and displacement fields

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图 5 功能过渡区域厚度参数t对应力场和位移场的影响

Figure 5. The influences of thickness parameter t in the functional transition region on the stress field and the displacement field

下载: 全尺寸图片幻灯片

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