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The Stable Explicit Time Stepping Analysis with a New Enrichment Scheme by XFEM

Xue-cong Liu1, Qing Zhang1,*, Xiao-zhou Xia1

Department of Engineering Mechanics, Hohai University, Nanjing 211100, P R China.

*Corresponding Author. E-mail: email (Qing Zhang).

Computers, Materials & Continua 2017, 53(3), 187-206. https://doi.org/10.3970/cmc.2017.053.203

Abstract

This paper focuses on the study of the stability of explicit time integration algorithm for dynamic problem by the Extended Finite Element Method (XFEM). A new enrichment scheme of crack tip is proposed within the framework of XFEM. Then the governing equations are derived and evolved into the discretized form. For dynamic problem, the lumped mass and the explicit time algorithm are applied. With different grid densities and different forms of Newmark scheme, the Dynamic Stress Intensity Factor (DSIF) is computed by using interaction integral approach to reflect the dynamic response. The effectiveness of the proposed scheme is demonstrated through the numerical examples, and the critical time stepping in different situations are listed and analyzed to illustrate the factors that affect the numerical stability.

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Cite This Article

X. . Liu, Q. . Zhang and O. . Xia, "The stable explicit time stepping analysis with a new enrichment scheme by xfem," Computers, Materials & Continua, vol. 53, no.3, pp. 187–206, 2017. https://doi.org/10.3970/cmc.2017.053.203



cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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