引用本文: 谢贵重, 王滔, 张世欣等. 基于单元分解的结构断裂扩展有限元法. 力学与实践, 2022, 44(6): 1375-1380.
Xie Guizhong, Wang Tao, Zhang Shixin, et al. Extension finite element method for structural fracture based on element decomposition. Mechanics in Engineering, 2022, 44(6): 1375-1380.
 Citation: Xie Guizhong, Wang Tao, Zhang Shixin, et al. Extension finite element method for structural fracture based on element decomposition. Mechanics in Engineering, 2022, 44(6): 1375-1380.

## EXTENSION FINITE ELEMENT METHOD FOR STRUCTURAL FRACTURE BASED ON ELEMENT DECOMPOSITION

• 摘要: 研究并提出了一种基于单元分解的扩展有限元方法，并将其用于求解结构断裂问题。首先，将不含加强节点的四边形单元剖分为四个三角形子域，通过加权平均获得单元中心处局部应变值；其次，基于三角形子域局部应变进一步构造单元刚度矩阵稳定项。最后，将该单元分解法应用到扩展有限元法的分析中。与传统扩展有限元方法相比，该方法可有效减少积分点数量、避免复杂等参变换且能保证裂纹尖端应力强度因子的求解精度。

Abstract: In this paper, an element decomposition based extended finite element method is proposed and employed to deal with the fracture analysis of structures. Firstly, the quadrilateral element with no enriched nodes is divided into four triangular sub-domains, and the local strain value at the center of the element is obtained by weighted average operation. Then, based on the local strain of the triangular sub-domain, the stability term of element stiffness matrix is further constructed. Finally, the element decomposition technique is applied to the analysis of the extended finite element method. Compared with the traditional extended finite element method, this method can effectively reduce the number of integration points, avoid complex isoparametric transformation and ensure higher accuracy for calculation of stress intensity factors.

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