The Discontinuity‐Enriched Finite Element Method

The Discontinuity‐Enriched Finite Element Method
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不连续性丰富的有限元方法

DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Simone
A. Simone
中科院分区：
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文献类型：
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作者：
A. M. Aragón;A. Simone

文献摘要

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我们介绍了一种新的方法来模拟问题的弱和强不连续独立于有限元离散。与扩展/广义有限元法（X/GFEM）不同的是，这种新方法被命名为非连续性富集有限元法（DE - FEM），它只对网格中非连续性和元素边缘相交处创建的节点增加富集自由度。虽然是通用的，但该方法在断裂力学的背景下得到了证明，并通过一组无牵引和内聚裂纹实例说明了其通用性。我们发现DE - FEM在匹配网格的情况下恢复了与标准FEM相同的收敛速度，并将新方法与X/GFEM进行了比较。
We introduce a new methodology for modeling problems with both weak and strong discontinuities independently of the finite element discretization. At variance with the eXtended/Generalized Finite Element Method (X/GFEM), the new method, named the Discontinuity‐Enriched Finite Element Method (DE‐FEM), adds enriched degrees of freedom only to nodes created at the intersection between a discontinuity and edges of elements in the mesh. Although general, the method is demonstrated in the context of fracture mechanics, and its versatility is illustrated with a set of traction‐free and cohesive crack examples. We show that DE‐FEM recovers the same rate of convergence as the standard FEM with matching meshes, and we also compare the new approach to X/GFEM.