一种新型裂尖加强函数的显式动态扩展有限元法

基于扩展有限元方法提出了一种新的裂尖加强函数，与传统三角函数基表征的加强函数相比，该裂尖加强函数通过组合传统的函数基，继承了传统附加函数的特性，同时使得结点的奇异附加自由度减少为2个，减少了总体劲度矩阵的规模，提高了计算效率。通过集中质量矩阵考虑结构的惯性效应，使用显式时间积分方法计算了含裂纹结构的瞬间受载问题，并应用相互作用积分得到裂尖端点处的动态应力强度因子。通过相关算例的对比分析，验证了所提出的裂尖加强函数的有效性，同时表明采用显式时间积分方法进行结构动态响应分析的可行性及准确性。

A NEW ENRICHMENT FUNCTION OF CRACK TIP IN XFEM DYNAMICS BY EXPLICIT TIME ALGORITHM

A new enrichment scheme of crack tip is proposed in the framework of extended finite element method. In the new enrichment scheme, the characteristic of enriched functions are preserved by combining the traditional function basis, and only two additional degrees of freedom are added at each node of the crack tip element to improve the computational efficiency and reduce the matrix size. The inertia effect is considered by using the lumped mass matrix, and explicit time algorithm is adopted to research the problem of stable crack with dynamic loading. The values of dynamic stress intensity factors are computed by the interaction integral approach. The numerical results show that the new enrichment scheme is effective, and the feasibility and accuracy of simulating the dynamic response of the structure by explicit time algorithm is verified.