稀疏求解的动力学显隐混合异步长交错计算方法
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国家重点研发计划项目(2017YFB0202701)和国家自然科学基金项目(51475287、11772192)


Explicit-Implicit Multi-time-step Computational Method for Structural Dynamics with Sparse Direct Solution
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    摘要:

    显隐混合方法是分析复杂精细结构动力学问题的经典方法。此类方法处理不同分区边界数据时常涉及插值过程,易造成计算不稳定,同时单一的时间步长会造成计算资源的浪费。基于多重边界网格,提出一种改进的显隐混合异步长计算方法。该方法采用节点分割将有限元模型划分为显式与隐式分区,不同分区采用兼容格式的预测校正Newmark积分格式。多重网格使得显式分区预测波形在边界重叠网格完整传递,显式分区节点数据直接求解。隐式分区采用稀疏存储行压缩CRS格式,节点数据由稀疏直接求解器求出。显式与隐式分区串行交替高效求解。数值算例表明,相比于显隐混合固定界面边界数据插值方法,本文方法精度较高,且进一步降低了动力学分析的计算时间。

    Abstract:

    Dynamic analysis of complex and fine structure often involves external load with different time scales. Meanwhile, a local refined mesh is needed at the analysis zone. The classical explicit-implicit mixed method was used to deal with such problems with the interpolation process of boundary data which was likely to cause computational instability. At the same time, a single time step would cause waste of computing resources. An improved explicit-implicit mixed asynchronous time step computing method was proposed with multiple boundary mesh. Node segmentation was used to divide the finite element model into explicit and implicit partitions. A compatible format predictive correction Newmark integration scheme was adopted in different partitions. A larger time step was used for implicit partition and a smaller time step for explicit region. The prediction waveform for explicit partition can be transmitted completely in the boundary mesh without truncation. Sparse storage row compression CRS format was used in the implicit partition and node data can be obtained by sparse direct solver. The node acceleration data for explicit and implicit partition were solved sequentially and efficiently. Numerical examples showed that the accuracy of the proposed method was higher than that of the traditional explicitimplicit mixed method and the computation time for dynamics analysis was further reduced.

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马志强,孔令爽,楼云锋,金先龙.稀疏求解的动力学显隐混合异步长交错计算方法[J].农业机械学报,2018,49(11):403-408.

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  • 收稿日期:2018-06-26
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  • 在线发布日期: 2018-11-10
  • 出版日期: 2018-11-10