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基于分区径向基函数配点法的大变形分析

王莉华 李溢铭 褚福运

王莉华, 李溢铭, 褚福运. 基于分区径向基函数配点法的大变形分析[J]. 力学学报, 2019, 51(3): 743-753. doi: 10.6052/0459-1879-19-005
引用本文: 王莉华, 李溢铭, 褚福运. 基于分区径向基函数配点法的大变形分析[J]. 力学学报, 2019, 51(3): 743-753. doi: 10.6052/0459-1879-19-005
Lihua Wang, Yiming Li, Fuyun Chu. FINTE SUBDOMAIN RADIAL BASIS COLLOCATION METHOD FOR THE LARGE DEFORMATION ANALYSIS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 743-753. doi: 10.6052/0459-1879-19-005
Citation: Lihua Wang, Yiming Li, Fuyun Chu. FINTE SUBDOMAIN RADIAL BASIS COLLOCATION METHOD FOR THE LARGE DEFORMATION ANALYSIS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 743-753. doi: 10.6052/0459-1879-19-005

基于分区径向基函数配点法的大变形分析

doi: 10.6052/0459-1879-19-005
基金项目: 1) 国家自然科学基金项目(11572229)和中央高校基本科研业务费项目(22120180063)资助.
详细信息
    通讯作者:

    王莉华

  • 中图分类号: O34;

FINTE SUBDOMAIN RADIAL BASIS COLLOCATION METHOD FOR THE LARGE DEFORMATION ANALYSIS

  • 摘要: 无网格法因为不需要划分网格, 可以避免网格畸变问题,使得其广泛应用于大变形和一些复杂问题. 径向基函数配点法是一种典型的强形式无网格法,这种方法具有完全不需要任何网格、求解过程简单、精度高、收敛性好以及易于扩展到高维空间等优点,但是由于其采用全域的形函数, 在求解高梯度问题时 存在精度较低和无法很好地反应局部特性的缺点. 针对这个问题,本文引入分区径向基函数配点法来求解局部存在高梯度的大变形问题. 基于完全拉格朗日格式,采用牛顿迭代法建立了分区径向基函数配点法在大变形分析中的增量求解模式.这种方法将求解域根据其几何特点划分成若干个子域, 在子域内构建径向基函数插值, 在界面上施加所有的界面连续条件,构建分块稀疏矩阵统一求解. 该方法仍然保持超收敛性, 且将原来的满阵转化成了稀疏矩阵, 降低了存储空间,提高了计算效率. 相比较于传统的径向基函数配点法和有限元法, 这种方法能够更好地反应局部特性和求解高梯度问题.数值分析表明该方法能够有效求解局部存在高梯度的大变形问题.

     

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出版历程
  • 收稿日期:  2018-01-04
  • 刊出日期:  2019-05-18

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