在不使用积分子单元的情况下集成强间断和弱间断及其在XFEM/GFEM框架中的示例应用
Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework
AI总结：
本文提出一种基于多边形域积分技术的简单方法，无需将单元细分为子单元即可计算XFEM/GFEM中由间断切割的单元刚度矩阵，并通过线弹性断裂力学和多材料问题的基准测试验证了其准确性。
摘要：
单位分解方法，如扩展有限元法（XFEM），允许独立于网格模拟间断[1]。这消除了网格与间断对齐或随着间断演化进行繁琐重网格化的需要。然而，为了计算被间断切割的单元的刚度矩阵，通常需要将单元细分为与间断对齐的积分子单元。在本文中，我们使用一种针对多边形域提出的简单积分技术[2]来避免单元细分。针对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，所提出的方法能够产生准确的结果。由于其简单性，所提出的积分技术可以轻松集成到任何现有代码中。
英文摘要：
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. 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 [2] 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
