| 凌道盛,徐小敏,陈云敏.数学网格和物理网格分离的有限单元法(I):基本理论[J].计算力学学报,2009,26(3):401~406 |
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| 数学网格和物理网格分离的有限单元法(I):基本理论 |
| An enhanced finite element method with separate mathematical and physical mesh |
| 投稿时间：2008-08-08 |
| DOI：10.7511/jslx20093021 |
| 中文关键词: 有限单元法 移动边界 非连续变形 位移插值 |
| 英文关键词:finite element method discontinuous deformation movable boundary displacement interpolation |
| 基金项目:国家"973"重点基础研究课题(2007CB714200);国家自然科学基金(50778163)资助项目. |
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| 中文摘要: |
| 常规有限单元法在复杂边界问题的网格剖分、可移动边界和非连续变形问题的数值模拟等方面存在困难。本文将常规的有限单元分离为几何上相互独立的数学单元和物理单元,基于数学单元构造近似函数,引入位移模式关联法则以确定物理单元的位移模式,提出了在现有有限单元法框架内、基于数学网格和物理网格分离的强化有限单元法(FEM++)。与常规有限单元法(SFEM)比较表明,强化有限单元法不仅很好地克服了常规有限单元法网格剖分上的困难,而且提供了一条更简便、更自然的分析移动边界问题和非连续变形问题的新途径。最 |
| 英文摘要: |
| For standard finite element method (SFEM), mesh generation of domain with complex boundary and problems with movable boundary or discontinuous deformation are cumbersome to deal with. In this paper, conventional element is separated into two kinds of elements, mathematical element and physical element, which are geometrically independent. The mathematical element and physical element are applied for approximating construction and physical domain description, respectively. By introducing correlation rule between mathematical and physical element, the approximate displacement of physical element is determined. Basing on separated mathematical and physical meshes, an enhanced finite element method (FEM++), which is in the framework of SFEM, is then put forwards. A typical correlation rule, named extension of mathematical displacement mode for regular mathematical element, is proposed with corresponding formulas. The most important advantage of FEM++ is that it provides a new simple way to simulate problems with movable boundary or strong／weak discontinuous deformation. Finally, its applicability and validity are verified through a numerical example. |
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