One of the most important tasks in the numerical analysis of the fracture problem is to achieve a high-precision approximation of the singular stress fields at crack tips. Partially or fully enriched basis functions are often used as enhancements on the whole problem domain or just near the crack tips when constructing the meshless shape functions to simulate the singularity fields at crack tips, namely: global enhancement with fully enriched basis, global enhancement with partially enriched basis, local enhancement with fully enriched basis and local enhancement with partially enriched basis. The scheme of the enriched basis has been extensively and successfully employed in handling problems with a single crack, but its applicability in the branched crack problem remains to be studied. In this paper, the stress intensity factors, the displacement field and the stress field near crack tip are calculated by these four schemes, respectively, and the singular field at the crack tip of a branching crack is also considered. The numerical results show that: for the problems with a single crack, the accuracy of the stress intensity factor obtained by the meshless method with different kinds of enriched basis is basically the same, but the accuracy of the crack tip field variables is obviously different; for the problems with branched crack, the accuracy of the stress intensity factors differs depending on the problems.

中文翻译：

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裂缝尖端奇异场的无网格数值模拟

断裂问题数值分析中最重要的任务之一是实现裂纹尖端奇异应力场的高精度近似。部分或完全丰富的基函数在构造无网格形状函数以模拟裂纹尖端的奇异场时，通常用作整个问题域或仅靠近裂纹尖端的增强，即：具有完全丰富的基的全局增强，具有部分的全局增强丰富的基础、完全丰富的基础的局部增强和部分丰富的基础的局部增强。丰富基的方案已被广泛并成功地应用于处理单裂纹问题，但其在分支裂纹问题中的适用性仍有待研究。在本文中，应力强度因子，分别通过这四种方案计算了裂尖附近的位移场和应力场，并考虑了分支裂缝裂尖处的奇异场。数值结果表明：对于单一裂纹问题，不同类型富集基的无网格法得到的应力强度因子精度基本相同，但裂纹尖端场变量精度明显不同；对于分支裂纹问题，应力强度因子的精度因问题而异。不同富集基的无网格法得到的应力强度因子精度基本相同，但裂纹尖端场变量的精度明显不同；对于分支裂纹问题，应力强度因子的精度因问题而异。不同富集基的无网格法得到的应力强度因子精度基本相同，但裂纹尖端场变量的精度明显不同；对于分支裂纹问题，应力强度因子的精度因问题而异。