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二维边界元法高阶元几乎奇异积分半解析算法

牛忠荣 胡宗军 葛仁余 程长征

牛忠荣, 胡宗军, 葛仁余, 程长征. 二维边界元法高阶元几乎奇异积分半解析算法[J]. 力学学报, 2013, 45(6): 897-907. doi: 10.6052/0459-1879-13-215
引用本文: 牛忠荣, 胡宗军, 葛仁余, 程长征. 二维边界元法高阶元几乎奇异积分半解析算法[J]. 力学学报, 2013, 45(6): 897-907. doi: 10.6052/0459-1879-13-215
Niu Zhongrong, Hu Zongjun, Ge Renyu, Cheng Changzheng. A NEW SEMI-ANALYTIC ALGORITHM OF NEARLY SINGULAR INTEGRALS IN HIGH ORDER BOUNDARY ELEMENT ANALYSIS OF 2D ELASTICITY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(6): 897-907. doi: 10.6052/0459-1879-13-215
Citation: Niu Zhongrong, Hu Zongjun, Ge Renyu, Cheng Changzheng. A NEW SEMI-ANALYTIC ALGORITHM OF NEARLY SINGULAR INTEGRALS IN HIGH ORDER BOUNDARY ELEMENT ANALYSIS OF 2D ELASTICITY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(6): 897-907. doi: 10.6052/0459-1879-13-215

二维边界元法高阶元几乎奇异积分半解析算法

doi: 10.6052/0459-1879-13-215
基金项目: 国家自然科学基金资助项目(11272111, 11102056).
详细信息
    通讯作者:

    牛忠荣,教授,主要研究方向:计算力学。E-mail:niu-zr@hfut.edu.cn

  • 中图分类号: O343.1

A NEW SEMI-ANALYTIC ALGORITHM OF NEARLY SINGULAR INTEGRALS IN HIGH ORDER BOUNDARY ELEMENT ANALYSIS OF 2D ELASTICITY

Funds: The project was supported by the National Natural Science Foundation of China (11272111,11102056).
  • 摘要: 针对边界元法中高阶单元中几乎奇异积分计算难题,解剖了二维边界元法高阶单元的几何特征,定义源点相对高阶单元的接近度。将高阶单元上奇异积分核函数用近似奇异函数逼近,从而分离出积分核中主导的奇异函数部分,其奇异积分核分解为规则核函 数和奇异核函数两项积分之和。规则核函数用常规高斯数值积分,再对奇异核函数积分导出解析公式,从而建立了一种新的半解析法,用于高阶边界单元上几乎强奇异和超奇异积分计算。给出3个算例,采用边界元法高阶单元的半解析法计算了弹性力学薄体结构和近边界点位移/应力,并与线性边界元正则化算法结果作了比较,结果表明提出的二次元的半解析算法更加有效。特别是分析薄体结构,采用正则化算法的线性边界元分析比有限元有显著优势,而用提出的二次边界元半解析算法分析比其线性元的有效接近度又减小了4个量级。

     

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出版历程
  • 收稿日期:  2013-07-03
  • 修回日期:  2013-08-01
  • 刊出日期:  2013-11-18

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