基于修正权函数的多裂纹无网格模拟

本文采用了一种基于不连续场修正权函数的无网格方法来处理二维平面多裂纹问题。相较于传统的无网格断裂不连续场和奇异场模拟方法，修正权函数法算法简便易实现。采用修正权函数处理多裂纹时，只需要对每一段裂纹周围节点的权函数进行修正，就能同时模拟多裂纹不连续位移场和多裂尖奇异场。本文采用基于不连续场修正权函数的无单元Galerkin方法（EFGM），对Y型裂纹板、十字型裂纹板和孔边双裂纹板进行了分析。数值结果表明，在不引入扩展基函数情况下，通过修正权函数法能够得到精度较高的应力强度因子解，能较好地拟合多裂纹的裂尖奇异场。

Meshless simulation of multi-crack problems based on modified weight function

In computational fracture mechanics, dealing with discontinuous displacement field cross the cracks and the approximation of the singular stress fields around the crack tips are two never-ending difficulties. Especially for the case of multiple cracks, these two issues become more challenging. In this paper, a modified weight function for discontinuous field is developed for meshless method to deal with two-dimensional multi-crack problems. According to the geometric characteristics of the cracks, the local coordinate system of the modified weight function method is established. The derivation process of the formula for the modified weight function is presented. The correction strategies and schemes for different calculation points in the multi-crack calculation domain are proposed with an optimized calculation scheme. Comparing with the traditional methods used for dealing with discontinuity and singular fields in fracture problems, the modified weight function is much simpler to be implemented. Only the weight functions of nodes around each crack segment need to be modified and both the discontinuous displacement fields across multiple cracks and the singular fields at multiple crack tips can be captured simultaneously. In this paper, the element-free Galerkin method (EFGM) based on the modified discontinuous weight function is used to numerically analyze plates with Y-shaped crack, cross-shaped crack and double cracks emanating from a hole, respectively. In these numerical examples, the convergence analysis of different computing parameters is carried out in detail. The results of stress intensity factor and Von-mises stress are given and compared. Numerical results show that without introducing enriched basis function with singular terms, the modified weight function can obtain solutions of stress intensity factor with high accuracy, and can satisfactorily fit the singular fields at multiple crack tips. The meshless simulation strategy for the multi-crack problems based on the modified weight function established in this paper can be further applied to the analysis of multi-crack propagation problems.