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弱不连续问题扩展有限元法的数值精度研究

江守燕 杜成斌

江守燕, 杜成斌. 弱不连续问题扩展有限元法的数值精度研究[J]. 力学学报, 2012, 44(6): 1005-1015. doi: 10.6052/0459-1879-12-102
引用本文: 江守燕, 杜成斌. 弱不连续问题扩展有限元法的数值精度研究[J]. 力学学报, 2012, 44(6): 1005-1015. doi: 10.6052/0459-1879-12-102
Jang Shouyan, Du Chengbin. STUDY ON NUMERICAL PRECISION OF EXTENDED FINITE ELEMEMT METHODS FOR MODELING WEAK DISCONTINUTIES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(6): 1005-1015. doi: 10.6052/0459-1879-12-102
Citation: Jang Shouyan, Du Chengbin. STUDY ON NUMERICAL PRECISION OF EXTENDED FINITE ELEMEMT METHODS FOR MODELING WEAK DISCONTINUTIES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(6): 1005-1015. doi: 10.6052/0459-1879-12-102

弱不连续问题扩展有限元法的数值精度研究

doi: 10.6052/0459-1879-12-102
基金项目: 国家自然科学基金(11132003,50779011)和江苏省研究生创新工程(CX10B_202Z)资助项目.
详细信息
    通讯作者:

    杜成斌

  • 中图分类号: TB115

STUDY ON NUMERICAL PRECISION OF EXTENDED FINITE ELEMEMT METHODS FOR MODELING WEAK DISCONTINUTIES

Funds: The project was supported by the National Natural Science Foundation of China (11132003, 50779011) and the Innovative Project for Graduate Students of Jiangsu Province (CX10B_202Z).
  • 摘要: 主要研究了扩展有限元法(extended finite element method, XFEM)在处理弱不连续问题时不同改进函数形式对XFEM数值求解精度的影响,阐述了各种改进函数影响XFEM求解精度的关键因素,指出校正的扩展有限元法(corrected-XFEM)能够提高数值求解精度的实质在于它拓展了改进结点域,即将常规扩展有限元法(standard-XFEM)的改进结点域增加一层作为corrected-XFEM的改进结点域,文中建议延拓corrected-XFEM的改进结点域,即在corrected-XFEM的改进结点域基础上再增加一层改进结点. 利用水平集函数表征材料内部的不连续界面,推导了XFEM求解的支配方程,给出了一种改进单元的数值积分方案以及改进单元处高精度应力的求解方法. 含夹杂问题的数值计算结果表明:建议的延拓corrected-XFEM改进结点域的方法能够明显提高XFEM的数值求解精度.

     

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出版历程
  • 收稿日期:  2012-04-17
  • 修回日期:  2012-08-09
  • 刊出日期:  2012-11-18

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