Correspondence Yu Qian, Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC. Email: yuqian@sc.edu Summary A new strategy for the mass matrix lumping of enriched elements for explicit transient analysis is presented. It is shown that to satisfy the kinetic energy conservation, the use of zero or negative masses for enriched degrees of freedom of lumped mass matrix may be necessary. For a completely cracked element, by lumping the mass of each side of the interface into the finite element nodes located at the same side and assigning zero masses to the enriched degrees of freedom, the kinetic energy for rigid body translations is conserved without transferring spurious energy across the interface. The time integration is performed by adopting an explicit-implicit technique, where the regular and enriched degrees of freedom are treated explicitly and implicitly, respectively. The proposed method can be viewed as a general mass lumping scheme for the variants of the extended finite element methods because it can be used irrespective of the enrichment method. It also preserves the optimal critical time step of an intact finite element by treating the enriched degrees of freedom implicitly. The accuracy and efficiency of the proposed mass matrix are validated with several benchmark examples.

中文翻译：

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XFEM 变体的一般质量集总方案

通讯作者 Yu Qian，南卡罗来纳大学，哥伦比亚，南卡罗来纳大学土木与环境工程系。电子邮件：yuqian@sc.edu 摘要 提出了一种用于显式瞬态分析的富集元素的质量矩阵集总的新策略。结果表明，为了满足动能守恒，可能需要使用零质量或负质量来丰富集总质量矩阵的自由度。对于完全裂开的单元，通过将界面每一侧的质量集中到位于同一侧的有限元节点，并为丰富的自由度分配零质量，刚体平移的动能守恒，而不会传递虚假能量跨界面。时间积分采用显隐技术进行，其中规则和丰富的自由度分别被显式和隐式处理。所提出的方法可以被视为扩展有限元方法变体的一般质量集总方案，因为它可以与富集方法无关地使用。它还通过隐式处理丰富的自由度来保留完整有限元的最佳临界时间步长。所提出的质量矩阵的准确性和效率通过几个基准示例进行了验证。它还通过隐式处理丰富的自由度来保留完整有限元的最佳临界时间步长。所提出的质量矩阵的准确性和效率通过几个基准示例进行了验证。它还通过隐式处理丰富的自由度来保留完整有限元的最佳临界时间步长。所提出的质量矩阵的准确性和效率通过几个基准示例进行了验证。