基于单位分解的扩展径向点插值无网格法

An enriched radial point interpolation meshless method based on partition of unity

针对线弹性断裂力学问题,提出扩展径向点插值无网格法(X-RPIM)。该方法基于单位分解思想,在传统径向点插值无网格法的位移模式中加入扩展项来描述裂纹两侧的不连续位移场和裂尖奇异场。由于其形函数具有Kronecker函数性质,易于施加本质边界条件。详细描述了X-RPIM不连续位移模式的建立,支配方程的离散形式以及J积分计算混合模式裂纹的应力强度因子的实现过程,讨论了不同积分区域对应力强度因子的影响。数值算例分析证明了该方法在求解断裂问题时的可行性和有效性,同时说明扩展径向点插值无网格法在模拟裂纹扩展问题时具有良好的前景。

An enriched radial point interpolation meshless method（X-RPIM） was presented for the linear elastic fracture problem. In order to represent the discontinuous displacement field along crack face and stress singularity around the crack tip, enriched functions were added in the approximation of traditional radial point interpolation meshless method （RPIM） based on the ideas of partition of unity. The merit of presented method is that the shape functions have the properties ofKronecker δ functions, which would make the essential boundary be implemented easily. The construction of discontinuous approximation function, the discrete format of governing equation and the evaluated process of the mixed-mode stress intensity factors by using the J integral method are introduced in detail in X-RPIM. The impact for the computational results of stress intensity factors using different integral domains of crack tip is discussed. Analyses of numerical examples demonstrate that the enriched radial point interpolation meshless method can effectively solve fracture problem, and has practical merits for modeling crack growth problem.