High-Order Boundary Element Analysis of Temperature Fields in Thin-Walled Structures

HU Zong-jun; NIU Zhong-rong; CHENG Chang-zheng; ZHOU Huan-lin

doi:10.3879/j.issn.1000-0887.2015.02.004

Volume 36 Issue 2

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Article Navigation > Applied Mathematics and Mechanics > 2015 > 36(2): 149-158

HU Zong-jun, NIU Zhong-rong, CHENG Chang-zheng, ZHOU Huan-lin. High-Order Boundary Element Analysis of Temperature Fields in Thin-Walled Structures[J]. Applied Mathematics and Mechanics, 2015, 36(2): 149-158. doi: 10.3879/j.issn.1000-0887.2015.02.004

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High-Order Boundary Element Analysis of Temperature Fields in Thin-Walled Structures

doi: 10.3879/j.issn.1000-0887.2015.02.004

School of Civil Engineering, Hefei University of Technology, Hefei 230009, P.R.China

Funds: The National Natural Science Foundation of China(11272111;11372094)

Received Date: 2014-09-24
Rev Recd Date: 2014-11-10
Publish Date: 2015-02-15

Abstract

Abstract

The geometric features of 3-node elements in the 2D BEM were analyzed, and the relative distance (namely the approach degree) from a source point to a high-order element was defined. Based on the geometric features, the approximate kernel functions were constructed with the same II-type singularity as the nearly singular kernel functions. For the nearly singular integrals, the dominant singular parts were separated from the original kernel functions through subtraction. After subtraction of the approximate kernel functions, the original kernel functions were rid of near singularity and turned into the sum of two integrals, of which one was a regular integral to be evaluated accurately with the conventional Gaussian quadrature, the other was a singular integral to be calculated with a series of analytical formulae derived herein. Then a new semi-analytical algorithm was established to compute the nearly singular integrals for the high-order elements effectively. In verification, the new method was applied to calculate several temperature field examples of thin-body structures for 2D potential boundary element analysis. The results indicate that the presented high-order-element semi-analytic algorithm takes full advantage of the BEM and has highly improved calculation accuracy and efficiency.
- thin-walled structure,
- BEM,
- high-order element,
- nearly singular integral,
- semi-analytic method

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References(19)

References

[1]	Bouzakis K D, Vidakis N. Prediction of the fatigue behavior of physically vapor deposited coatings in the ball-on-rod rolling contact fatigue test, using an elastic-plastic finite elements method simulation[J]. Wear,1997,206(1/2): 197-203.
[2]	Dobrzański L A, liwa A, Kwa〖KG-4〗s〖DD(-3/4〗′〖DD)〗ny W. Employment of the finite element method for determining stresses in coatings obtained on high-speed steel with the PVD process[J]. Journal of Materials Processing Technology,2005,164/165: 1192-1196.
[3]	周焕林, 牛忠荣, 王秀喜. 薄体位势问题边界元法中的解析积分算法[J]. 力学季刊, 2003,24(3): 319-326.(ZHOU Huan-lin, NIU Zhong-rong, WANG Xiu-xi. An analytical integral algorithm in BEM for potential problems with thin bodies[J]. Chinese Quarterly of Mechanics,2003,24(3): 319-326.(in Chinese))
[4]	张耀明, 谷岩, 袁飞, 李功胜. 涂层结构中温度场的边界元解[J]. 固体力学学报, 2011,32(2): 133-141.(ZHANG Yao-ming, GU Yan, YUAN Fei, LI Gong-sheng. Boundary element analysis of the temperature field in coating structures[J]. Acta Mechanica Solida Sinica,2011,32(2): 133-141.(in Chinese))
[5]	谷岩, 张耀明, 李功胜. 精确几何单元下弹性薄体结构问题的边界元法分析[J]. 计算物理, 2011,28(3): 397-403.(GU Yan, ZHANG Yao-ming, LI Gong-sheng. Boundary element analysis of thin-walled structures in elasticity problems with exact geometrical representation[J]. Chinese Journal of Computational Physics,2011,28(3): 397-403.(in Chinese))
[6]	李平, 张耀明. 热弹性问题直接边界元法中的边界层效应[J]. 山东理工大学学报(自然科学版), 2011,25(3): 1-5.(LI Ping, ZHANG Yao-ming. The boundary layer effect in the BEM of thermo elasticity problems with direct formulation[J]. Journal of Shandong University of Technology(Natural Science Edition), 2011,25(3): 1-5.(in Chinese))
[7]	牛忠荣, 张晨利, 王秀喜. 边界元法分析狭长体结构[J]. 计算力学学报, 2003,20(4): 391-396.(NIU Zhong-rong, ZHANG Chen-li, WANG Xiu-xi. Boundary element analysis of the thin-walled structures[J]. Chinese Journal of Computational Mechanics,2003,20(4): 391-396.(in Chinese))
[8]	张耀明, 刘召颜, 谷岩, 李功胜. 二维弹性问题边界元法中边界层效应问题的变换法[J]. 计算力学学报, 2010,27(5): 775-780.(ZHANG Yao-ming, LIU Zhao-yan, GU Yan, LI Gong-sheng. A transformation algorithm applied to boundary layer effect in BEM for elastic plane problems[J]. Chinese Journal of Computational Mechanics,2010,27(5): 775-780.(in Chinese))
[9]	周焕林, 牛忠荣, 王秀喜. 位势问题边界元法中几乎奇异积分的正则化[J]. 应用数学和力学, 2003,24(10): 1069-1074.(ZHOU Huan-lin, NIU Zhong-rong, WANG Xiu-xi. Regularization of nearly singular integrals in the boundary element method of potential problems[J]. Applied Mathematics and Mechanics,2003,24(10): 1069-1074.(in Chinese))
[10]	GAO Xiao-wei, Davies T G. Adaptive integration in elasto-plastic boundary element analysis[J]. Journal of the Chinese Institute of Engineers,2000,23(3): 349-356.
[11]	王静, 高效伟. 基于单元子分法的结构多尺度边界单元法[J]. 计算力学学报, 2010,27(2): 258-263.(WANG Jing, GAO Xiao-wei. Structural multi-scale boundary element method based on element subdivision technique[J]. Chinese Journal of Computational Mechanics,2010,27(2): 258-263.(in Chinese))
[12]	Ma H, Kamiya N. Domain supplemental approach to avoid boundary layer effect of BEM in elasticity[J]. Engineering Analysis With Boundary Elements,1999,23(3): 281-284.
[13]	Qin X Y, Zhang J M, Xie G Z, Zhou F L, Li G Y. A general algorithm for the numerical evaluation of nearly singular integrals on 3D boundary element[J]. Journal of Computational and Applied Mathematics,2011,235(14): 4174-4186.
[14]	Johnston P R, Johnston B M, Elliott D. Using the iterated sinh transformation to evaluate two dimensional nearly singular boundary element integrals[J]. Engineering Analysis With Boundary Elements,2013,37(4): 708-718.
[15]	Gu Y, Chen W, Zhang C Z. The sinh transformation for evaluating nearly singular boundary element integrals over high-order geometry elements[J]. Engineering Analysis With Boundary Elements,2013,37(2): 301-308.
[16]	牛忠荣, 王左辉, 胡宗军, 周焕林. 二维边界元法中几乎奇异积分的解析法[J]. 工程力学, 2004,21(6): 113-117.(NIU Zhong-rong, WANG Zuo-hui, HU Zong-jun, ZHOU Huan-lin. Analytical algorithm for nearly singular integrals in two-dimensional boundary element analysis[J]. Engineering Mechanics,2004,21(6): 113-117.(in Chinese))
[17]	NIU Zhong-rong, CHENG Chang-zheng, ZHOU Huan-lin, HU Zong-jun. Analytic formulations for calculating nearly singular integrals in two-dimensional BEM[J]. Engineering Analysis With Boundary Elements,2007,31(12): 949-964.
[18]	王有成. 工程中的边界元方法[M]. 北京: 中国水利电力出版社, 1996: 52-57.(WANG You-cheng. The Boundary Element Method in Engineering [M]. Beijing: China Water & Power Press, 1996: 52-57.(in Chinese))
[19]	Gao X W, Zhang C, Sladek G, Sladekc V. Fracture analysis of functionally graded materials by BEM[J]. Composites Science and Technology,2008,68(5): 1209-1215.