二维各向异性功能梯度材料热传导的边界元分析

刘俊俏 1; 2; 苗福生 1; 3; 李星 4

doi:10.7652/xjtuxb201305014

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二维各向异性功能梯度材料热传导的边界元分析

更新时间：2025-07-09

- 二维各向异性功能梯度材料热传导的边界元分析
- Boundary Element Analysis of the Two-Dimensional Heat Conduction Equation for Anisotropic Functional Graded Materials
- 西安交通大学学报 2013年47卷第5期页码：77-81
- 作者机构：
  
  1. 宁夏大学土木与水利工程学院,银川,750021
  2. 运城学院应用数学系,山西,运城,044000
- 作者简介：
- 基金信息：
  
  : 2012-09-04。作者简介: 刘俊俏(1973—)男,博士生,运城学院副教授;李星(通信作者),男,教授,博士生导师。基金项目: 国家自然科学基金资助项目(10962008, 51061015);高等学校博士学科点专项科研基金资助项目(20116401110002)
- DOI：10.7652/xjtuxb201305014
  中图分类号： O241.8
- 网络首发：2013-05-10，
  
  纸质出版：2013
- 稿件说明：
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刘俊俏 1, 2, 苗福生 1, 等. 二维各向异性功能梯度材料热传导的边界元分析[J]. 西安交通大学学报, 2013,47(5):77-81.

Boundary Element Analysis of the Two-Dimensional Heat Conduction Equation for Anisotropic Functional Graded Materials[J]. 2013, 47(5): 77-81.
刘俊俏 1, 2, 苗福生 1, 等. 二维各向异性功能梯度材料热传导的边界元分析[J]. 西安交通大学学报, 2013,47(5):77-81. DOI： 10.7652/xjtuxb201305014.

Boundary Element Analysis of the Two-Dimensional Heat Conduction Equation for Anisotropic Functional Graded Materials[J]. 2013, 47(5): 77-81. DOI： 10.7652/xjtuxb201305014.

摘要

为分析各向异性功能梯度材料的热传导问题

热传导系数采用指数模型

利用二维傅里叶积分变换和脉冲函数

得到了各向异性功能梯度材料的热传导问题基本解; 利用基本解和边界条件

推导出了热传导问题的边界积分方程; 将边界积分方程离散得到了边界元公式

进一步给出了内点和边界点上的温度和热流计算公式。最后利用常边界单元方法给出了正方形模型算例

说明了各向异性功能梯度材料具有缓解热应力和耐高温的特点。文中所得基本解可以为采用边界元法研究高温下各向异性功能梯度材料的力学性能提供理论上的支持。

Abstract

Focusing on heat conduction in anisotropic functionally graded materials

the thermal conductivity is taken as an exponent

and the fundamental solution to the heat conduction equation is derived by means of the two-dimensional Fourier integral transformation and the generalized function. Following the solution and the boundary conditions

the boundary integral equation is established. The temperatures and the heat flux at the internal points and the nodes are given in terms of the discretized boundary integral equation. The numerical examples are given by using constant boundary elements and a square model. It explains that the anisotropic functionally graded materials are endowed with some specific physical qualities

such as withstanding high temperature

and resisting thermal and remnant stresses. The fundamental solution is expected to investigate the thermo-mechanical behavior of the anisotropic functionally graded materials with the boundary element method.

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