具有功能梯度过渡区的各向异性旋转夹层环的弹性分析

Q4 Mathematics
PENG Xulong, XIE Xiaopeng, HUANG Haiping, WEI Wenchao, TANG Xuesong
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引用次数: 0

摘要

对具有功能梯度过渡区的各向异性旋转夹芯环进行了弹性分析。环形结构类似于自然界的壳夹层结构,由3个键合良好的区域组成,其中内外区域由均质各向异性材料构成,中间过渡区域由沿径向方向具有任意梯度性质的材料构成。基于边界条件和界面连续条件,采用积分方程法得到径向应力的第2 Fredholm积分方程,然后通过数值求解得到夹层环结构的应力场和位移场。给出了夹芯环结构的应力场和位移场分布。工程实践中遇到的不同梯度变化,只能通过替换相应的函数模型来解决。通过对一类特殊幂函数梯度变分形式的数值解与精确解的比较,验证了积分方程法的有效性和准确性。中间过渡区采用较为通用的Voigt函数模型,分析各向异性程度、梯度参数、厚度对应力场和位移场的影响。Fredholm积分方程法为各向异性功能梯度材料和夹层环结构的优化设计提供了有力的工具。数值结果对各向异性功能梯度夹层环结构的安全设计具有理论指导意义。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Elastic Analysis of Anisotropic Rotating Sandwich Circular Ring With a Functionally Graded Transition Region
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.
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来源期刊
应用数学和力学
应用数学和力学 Mathematics-Applied Mathematics
CiteScore
1.20
自引率
0.00%
发文量
6042
期刊介绍: Applied Mathematics and Mechanics was founded in 1980 by CHIEN Wei-zang, a celebrated Chinese scientist in mechanics and mathematics. The current editor in chief is Professor LU Tianjian from Nanjing University of Aeronautics and Astronautics. The Journal was a quarterly in the beginning, a bimonthly the next year, and then a monthly ever since 1985. It carries original research papers on mechanics, mathematical methods in mechanics and interdisciplinary mechanics based on artificial intelligence mathematics. It also strengthens attention to mechanical issues in interdisciplinary fields such as mechanics and information networks, system control, life sciences, ecological sciences, new energy, and new materials, making due contributions to promoting the development of new productive forces.
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