[1]许杨健,白雪,刘硕.复杂边界条件下二维功能梯度结构温度场解析解[J].燕山大学学报,2018,42(6):525-531.
 XU Yangjian,BAI Xue,LIU Shuo.Analytical solution of temperature field of two dimensional functionally graded structure under complex boundary conditions[J].Journal of YanShan University,2018,42(6):525-531.
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复杂边界条件下二维功能梯度结构温度场解析解
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《燕山大学学报》[ISSN:1007-791X/CN:13-1219/N]

卷:
42
期数:
2018年第6期
页码:
525-531
栏目:
材料科学与工程
出版日期:
2018-11-30

文章信息/Info

Title:
Analytical solution of temperature field of two dimensional functionally graded structure under complex boundary conditions
文章编号:
1007-791X(2018)06-0525-07
作者:
许杨健1*白雪1刘硕2
1. 河北工程大学 土木工程学院,河北 邯郸 056038;2. 哈尔滨工业大学 特种环境复合材料技术国防科技重点实验室,黑龙江 哈尔滨 150001
Author(s):
XU Yangjian1 BAI Xue1 LIU Shuo2
1.College of Civil Engineering, Hebei University of Engineering, Handan, Hebei 056038,China; 2. Key Laboratory of Special Environment Composite Technology, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
关键词:
分离变量法热流密度第三类边界条件功能梯度材料解析法
Keywords:
separation of variables heat flux density third boundary conditions FGM analytic method
分类号:
TB333
文献标志码:
A
摘要:
假设功能梯度材料的热导率以指数函数的形式沿水平、竖直方向分布,在已知二维稳态热传导方程的基础上,采用分离变量法推导出该结构在第一、二、三类边界条件共同作用下的稳态温度场解析解。将该解析解与有限元解对比计算,所得到的节点温度基本一致,误差均小于1%。选取数值算例进行计算,得到了该结构的二维稳态温度场并分析了材料的热导率、上边界介质温度以及下边界热流密度对温度场的影响。
Abstract:
On the basis of the known two-dimensional steady heat conduction equation, it is assumed that the thermal conductivity of functionally graded materials is distributed in horizontal and vertical directions in an exponential function, the analytical solution of the steady temperature field under the first, second, third boundary conditions is derived by the method of separation of variables. Comparing the analytical solution with the finite element method, the temperature of the obtained node is basically the same, and the error is less than 1%. Through the numerical calculations, the plane steady temperature field distributions in the structure were obtained, and the effects of thermal conductivity, upper boundary medium temperature and lower boundary heat flux of the structure on the temperature fields were studied.

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[1]马继光,白象忠,张旭光,等.导电悬臂梁磁弹性弯曲的辛解答[J].燕山大学学报,2009,(2):146.
 MA Ji-guang,BAI Xiang-zhong,ZHANG Xu-guang,et al.Symplectic solution of a conductive cantilever beam bending in the electromagnetic field[J].Journal of YanShan University,2009,(6):146.

备注/Memo

备注/Memo:
收稿日期:2017-07-12        责任编辑:王建青
基金项目:河北省自然科学基金资助项目 (E2011402033)
作者简介:*许杨健 (1956-),男,四川富顺人,教授,主要研究方向为固体力学计算、有限元应用和梯度功能材料,Email:xuyangjian@sohu.com
更新日期/Last Update: 2019-01-10