非网格重剖分模拟宏观裂纹体的扩展有限单元法(2:数值实现)

探讨了扩展有限单元法的具体实现过程,包括裂纹体几何结构的拓扑分析、广义节点的选取及详细的单元数值计算。并针对前文提出的扩展有限单元平衡方程的统一矩阵实现模式,提出了采用虚拟层合元的思想来处理被裂纹横贯单元的子域积分问题,自然地解决了原方法中由于特殊的位移插值场在裂纹两侧不连续造成的单元刚度阵求解困难。同时依托比较成熟的虚拟层合单元法,可以方便地考虑域内及裂纹面上分布载荷影响。此外,一、二维算例较高精度的数值结果验证了本文算法的有效性和精度。

Extended finite element method for modeling cracks without remeshing ( 2: numerical implementation)

Some key procedures of numerical implementation for the extended finite element method are discussed in this paper,including topological analysis on the cracked body,selection of generalized nodes,and numerical calculation of various body elements.According to the unified constructing process of stiffness matrices for different extended finite elements presented in the previous paper,a new numerical technique,by combining the virtual laminated element(VLE) method,is given in detail to construct the structure stiffness matrices for the special finite elements intersecting with the existing crack,which can naturally resolve the difficulties due to the constructed functions of interposing displacement field are discontinuous across the crack faces.The relatively well-mature ideas of VLE also can provide convenience for the calculations of scattered loadings,inside of element body or on the crack surface.In addition,two typical applications are presented to demonstrate its validity and satisfactory accuracy.