A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis
A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis
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DOI：
10.3970/cmes.2011.073.331
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发表时间：
2011-03
影响因子：
2.4
通讯作者：
N. Vu-Bac;H. Nguyen-Xuan;Lei Chen;S. Bordas;P. Kerfriden;R. Simpson;Guirong Liu;T. Rabczuk
中科院分区：
文献类型：
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作者：
N. Vu-Bac;H. Nguyen-Xuan;Lei Chen;S. Bordas;P. Kerfriden;R. Simpson;Guirong Liu;T. Rabczuk
将节点光滑有限元法（NS-FEM）与扩展有限元法（XFEM）相结合，形成一种分析二维弹性断裂问题的新的数值方法（NS-XFEM）。NS-FEM采用应变平滑技术在与节点相关的平滑域上计算系统刚度矩阵，这导致直接使用沿平滑域边界沿着的形函数值进行线积分。因此，我们避免了在裂纹尖端的应力奇异性的积分。用边界积分代替内部积分时，不需要对裂缝单元进行剖分，简化了间断近似的积分。与XFEM-T3单元相比，NS-XFEM的主要优势在于它提供了更精确的解决方案。我们将通过两个数值例子表明，NS-XFEM在能量范数和应力强度因子方面显着改善了结果。对于所研究的例子，我们得到了超收敛结果
This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration by boundary integration, simplifying integration of the discontinuous approximation. The key advantage of the NS-XFEM is that it provides more accurate solutions compared to the XFEM-T3 element. We will show for two numerical examples that the NS-XFEM significantly improves the results in the energy norm and the stress intensity factors. For the examples studied, we obtain super-convergent results