Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework
Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework
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DOI：
10.1002/nme.2798
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发表时间：
2010-07
影响因子：
2.9
通讯作者：
S. Natarajan;D. Mahapatra;S. Bordas
中科院分区：
文献类型：
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作者：
S. Natarajan;D. Mahapatra;S. Bordas
单位分割法，如扩展有限元法，允许不连续性模拟独立的网格（国际期刊编号。Meth.工程师1999; 45：601-620）。这消除了网格与不连续性对齐的需要，也消除了随着不连续性的发展而进行的繁琐的重新网格划分。然而，为了计算由不连续性包围的单元的刚度矩阵，通常采用将单元细分成与不连续性对齐的正交子单元。在本文中，我们使用一个简单的集成技术，提出了多边形域（国际期刊编号。Meth. Engng 2009; 80（1）：103-134。DOI：10.1002/nme.2589）来抑制对元素细分的需要。线弹性断裂力学和多材料问题中的几个基准问题的数值结果表明，所提出的方法产生准确的结果。由于其简单性，所提出的集成技术可以很容易地集成到任何现有的代码。版权所有© 2010约翰威利父子有限公司.
Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. J. Numer. Meth. Engng. 1999; 45:601–620). This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re‐meshing, as the discontinuity evolves. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted. In this paper, we use a simple integration technique, proposed for polygonal domains (Int. J. Numer. Meth. Engng 2009; 80(1):103–134. DOI: 10.1002/nme.2589) to suppress the need for element subdivision. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi‐material problem show that the proposed method yields accurate results. Owing to its simplicity, the proposed integration technique can be easily integrated in any existing code. Copyright © 2010 John Wiley & Sons, Ltd.