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稀疏求解的動力學(xué)顯隱混合異步長交錯計算方法
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國家重點研發(fā)計劃項目(2017YFB0202701)和國家自然科學(xué)基金項目(51475287、11772192)


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

    顯隱混合方法是分析復(fù)雜精細(xì)結(jié)構(gòu)動力學(xué)問題的經(jīng)典方法。此類方法處理不同分區(qū)邊界數(shù)據(jù)時常涉及插值過程,易造成計算不穩(wěn)定,同時單一的時間步長會造成計算資源的浪費?;诙嘀剡吔缇W(wǎng)格,提出一種改進的顯隱混合異步長計算方法。該方法采用節(jié)點分割將有限元模型劃分為顯式與隱式分區(qū),不同分區(qū)采用兼容格式的預(yù)測校正Newmark積分格式。多重網(wǎng)格使得顯式分區(qū)預(yù)測波形在邊界重疊網(wǎng)格完整傳遞,顯式分區(qū)節(jié)點數(shù)據(jù)直接求解。隱式分區(qū)采用稀疏存儲行壓縮CRS格式,節(jié)點數(shù)據(jù)由稀疏直接求解器求出。顯式與隱式分區(qū)串行交替高效求解。數(shù)值算例表明,相比于顯隱混合固定界面邊界數(shù)據(jù)插值方法,本文方法精度較高,且進一步降低了動力學(xué)分析的計算時間。

    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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馬志強,孔令爽,樓云鋒,金先龍.稀疏求解的動力學(xué)顯隱混合異步長交錯計算方法[J].農(nóng)業(yè)機械學(xué)報,2018,49(11):403-408. MA Zhiqiang, KONG Lingshuang, LOU Yunfeng, JIN Xianlong. Explicit-Implicit Multi-time-step Computational Method for Structural Dynamics with Sparse Direct Solution[J]. Transactions of the Chinese Society for Agricultural Machinery,2018,49(11):403-408.

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  • 收稿日期:2018-06-26
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  • 在線發(fā)布日期: 2018-11-10
  • 出版日期: 2018-11-10