[1]薛国新,王树立,肖立川.MAPLE 用于轴对称热传导问题边界奇异积分计算[J].常州大学学报(自然科学版),2006,(03):40-42.
　XUE Guo- xin,WANG Shu- li,XIAO Li- chuan.Using MAPLE on the Calculation of Singular Boundary Integrations in Thermal Conduction Problems of Symmetrical Structures[J].Journal of Changzhou University(Natural Science Edition),2006,(03):40-42.
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MAPLE 用于轴对称热传导问题边界奇异积分计算()
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常州大学学报(自然科学版)[ISSN:2095-0411/CN:32-1822/N]

卷:
期数:
2006年03期
页码:
40-42
栏目:
出版日期:
2006-09-25

文章信息/Info

Title:
Using MAPLE on the Calculation of Singular Boundary Integrations in Thermal Conduction Problems of Symmetrical Structures
作者:
薛国新1;  王树立2 ;  肖立川2
1.江苏工业学院计算机科学与工程系, 江苏 常州 213164; 2.江苏工业学院机械工程系
Author(s):
XUE Guo- xin 1;  WANG Shu- li 2;  XIAO Li- chuan 2
1. Department of Computer Science and Technology, Jiangsu Poly technic University, Changzhou 213164, China; 2. Department of Mechanical Engineering, Jiang su Polytechnic University
关键词:
MAPLE;  热传导;  边界元法;  奇异积分
Keywords:
MAPLE;  thermal conduct ion;  boundary element method;  singular integ rat ion
分类号:
T E 973.?101
文献标志码:
A
摘要:
轴对称热传导问题是能源动力工程中基本问题之一。对这类问题应用边界元法必然会遇到奇异积分, 其有效而准确的计 算是关键。传统的处理方法是通过近似方法或积分变换方法将被积函数表示为简单形式的初等函数, 处理手段既不统一, 又不 那么简洁。为此提出使用MAPLE 软件处理轴对称热传导问题边界元奇异积分, 它将被积函数表示为多项式和椭圆函数乘积形 式, 能使MAPLE 直接算得对应积分的具体数值结果。这一方法程序处理统一, 简单明了, 便于推广应用。
Abstract:
Thermal conduction of a symmet ricalst ructure is a basic problem in power engineering. When a boundary element method is adopted for this kind of problem, singular integrations would be encountered. How to calculate them validly and accurately is a key point. T radit ionally, the function to be integrated w as expressed in a simpler form through math transformation or accumulation methods to ensure that it could be integ rated out . These traditional methods are not unified, and are not brief, either. To this end, it presented a MAPLE based method for the calculation of the singular integrations. It expresses the function to be integrated as the product of a polynomial and an elliptic function. In this w ay the singular integration could be calculated out by MAPLE. The new method is brief and unif ied in form, and it is easy to be programmed. It is worth being popularized.

参考文献/References:

[1] Sladek V, Sladek J , Tanaka M. Opt imal Transf ormations of the Int egration Variables in Com put at ion of Singular Int egrals in BEM [J] . Int J Number Methods Eng, 2000, 47: 1 263- 1 283??
[2] Kouit at Njiw a R, St ebut JV. Boundary Element Numerical Modeling as a Surface Engineering T ool: Applicat ion to Very T hin Coatings [J] . Surf ace and Coat ings Technology, 1999, 116 - 119: 573- 579??
[3] Davey K, H in duja S. Analyt ical Integration of Linear T hree- D-i mensional Triangular Element s in BEM [J] . Appl Math Model, 1989, 13: 450- 461??
[4] 陈晓霞?? 超强数学工具精点Maple 指令参考手册[M] ?? 第1 版?? 北京: 国防工业出版社, 2002??
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备注/Memo

备注/Memo:
基金项目: 中国石油化工股份有限公司资助项目( J302001, X504007) 作者简介: 薛国新( 1962- ) , 男, 江苏武进人, 研究员, ??计算机仿真?? 编委, 主要研究方向为计算机应用等。
更新日期/Last Update: 2006-09-25