非均匀长圆柱超导体的热应力分析  

Analysis of thermal stress in inhomogeneous long cylindrical superconductor

作　　者：赵玉峰[1] 刘泓杉 ZHAO Yu-feng;LIU Hong-shan(School of Science,Lanzhou Univ. of Tech.,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《兰州理工大学学报》2018年第6期167-172,共6页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11662009;11862013);甘肃省自然科学基金(17JR5RA129)

摘　　要：用解析法研究了非均匀长圆柱超导体在冷却过程中,随着时间及位置变化的温度场以及热应力应变的分布.其中,假定杨氏模量呈现出与坐标和温度相关的指数形式变化.利用贝塞尔方程解析求解了热传导方程,得到了温度场的分布.结果表明:计算结果与实验结果相符,温度场在很短的时间内达到稳定,并最终趋于液氮温度,而剧烈变化的温度会导致较大的热应力.结果表明,径向应力先增大后减小,直至趋于热平衡状态;环向应力则表现为靠近中心处应力为拉应力,反之靠近边界处为压应力.The analytic method is employed to investigate the temporal and positional distribution of temperature field and thermal stress-strain in inhomogeneous long cylindrical superconductor during its cooling process,where Young’s modulus is supposed to change in the form of exponential function of coordinate and temperature.The heat conduction equation is analytically solved by using Bessel equation and the temperature field distribution is obtained thereby.The result shows that the results of both calculation and experiment will be consistent with each other and the temperature field will reach steady within a short time and finally tend to liquid nitrogen temperature,so that a larger thermal stress will be resulted in due to violent change of temperature.The radial stress will increase at first and then decrease until tend to the thermal equilibrium state and the circumferential stress will be tensile stress at the central area,but become compressive stress near the boundary.

关 键 词：热应力 贝塞尔方程 非均匀超导体 YBCO块材 解析解 

分 类 号：O343.6[理学—固体力学]