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应用边界积分法求圆形夹杂问题的解析解

郭树起

郭树起. 应用边界积分法求圆形夹杂问题的解析解[J]. 力学学报, 2020, 52(1): 73-81. doi: 10.6052/0459-1879-19-283
引用本文: 郭树起. 应用边界积分法求圆形夹杂问题的解析解[J]. 力学学报, 2020, 52(1): 73-81. doi: 10.6052/0459-1879-19-283
Guo Shuqi. EXACT SOLUTION OF CIRCULAR INCLUSION PROBLEMS BY A BOUNDARY INTEGRAL METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 73-81. doi: 10.6052/0459-1879-19-283
Citation: Guo Shuqi. EXACT SOLUTION OF CIRCULAR INCLUSION PROBLEMS BY A BOUNDARY INTEGRAL METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 73-81. doi: 10.6052/0459-1879-19-283

应用边界积分法求圆形夹杂问题的解析解

doi: 10.6052/0459-1879-19-283
基金项目: 1) 国家自然科学基金资助项目(11272219)
详细信息
    通讯作者:

    郭树起

  • 中图分类号: O302

EXACT SOLUTION OF CIRCULAR INCLUSION PROBLEMS BY A BOUNDARY INTEGRAL METHOD

  • 摘要: 边界元方法作为一种数值方法, 在各种科学工程问题中得到了广泛的应用.本文参考了边界元法的求解思路, 从Somigliana等式出发, 利用格林函数性质,得到了一种边界积分法, 使之可以用来寻求弹性问题的解析解.此边界积分法也可以从Betti互易定理得到. 应用此新方法, 求解了圆形夹杂问题.首先设定夹杂与基体之间完美连接, 将界面处的位移与应力按照傅里叶级数展开,根据问题的对称性与三角函数的正交性来简化假设, 减少待定系数的个数.其次选择合适的试函数(试函数满足位移单值条件以及无体力的线弹性力学问题的控制方程),应用边界积分法, 求得界面处的位移与应力的值. 然后再求解域内位移与应力.得到了问题的精确解析解, 当夹杂弹性模量为零或趋向于无穷大时,退化为圆孔或刚性夹杂问题的解析解. 求解过程表明,若问题的求解区域包含无穷远处时, 所取的试函数应满足无穷远处的边界条件.若求解区域包含坐标原点, 试函数在原点处位移与应力应是有限的.结果表明了此方法的有效性.

     

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出版历程
  • 收稿日期:  2019-10-14
  • 刊出日期:  2020-02-10

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