An explicit dynamics extended finite element method. Part 2: Element-by-element stable-explicit/explicit dynamic scheme
An explicit dynamics extended finite element method. Part 2: Element-by-element stable-explicit/explicit dynamic scheme
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DOI：
10.1016/j.cma.2009.02.018
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发表时间：
2009-06
影响因子：
7.2
通讯作者：
A. Gravouil;T. Elguedj;H. Maigre
中科院分区：
文献类型：
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作者：
A. Gravouil;T. Elguedj;H. Maigre
本文提出了一种通用的显式时间积分格式，用于采用标准临界时间步长的扩展有限元法进行动力学模拟。我们使用本文第一部分中提出的广义质量集总技术。这种技术使我们能够考虑任意丰富功能的X-FEM显式动力学模拟。在这第二部分中，所提出的方法允许使用标准的有限元临界时间步长估计。为此，我们发展了一种经典的逐单元策略，将标准中心差分格式与Chang [S.Y.] Chang，一种具有改进稳定性的显式方法，Int. J. Numer.方法Engrg. 77（8）（2008）1100-1120]。该方案与X-FEM相结合，使我们能够独立于所考虑的富集函数恢复FE临界时间步长。此外，在X-FEM框架下，研究了这种新显式格式的稳定性，包括固定富集和随时间演化的富集。一些算例说明了新的显式数值时间格式的良好性质，并给出了它在动态裂纹扩展中的应用。
This paper presents a general explicit time integration scheme for dynamics simulations using the eXtended Finite Element Method with standard critical time step. We use the generalized mass lumping technique proposed in Part I of this paper. This technique allows us to consider arbitrary enrichment functions in the X-FEM for explicit dynamics simulations. In this second part, the proposed approach allows the use of standard finite elements critical time step estimates. For that purpose, we develop a classical element-by-element strategy that couples the standard central difference scheme with the unconditionally stable-explicit scheme proposed by Chang [S.Y. Chang, An explicit method with improved stability property, Int. J. Numer. Methods Engrg. 77 (8) (2008) 1100–1120]. This scheme coupled with X-FEM allows us to recover FE critical time steps independently of the enrichment functions considered. Furthermore, a study of the stability property of this new explicit scheme is proposed in the X-FEM framework, both with fixed enrichments and evolving enrichments with time. Some examples illustrate the good properties of the new explicit numerical time scheme and some applications to dynamics crack growth are given.