Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (6): 777-788.doi: https://doi.org/10.1007/s10483-011-1457-6

• Articles • 上一篇    下一篇

Stability and dispersion analysis of reproducing kernel collocation method for transient dynamics

罗汉中1 刘学文2 黄醒春1   

  1. 1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University,Shanghai 200240, P. R. China;
    2. Siemens Industry Software (China) Co., Ltd., 14F, Cloud-9 Office Tower, No. 1018, Changning Road, Shanghai 200042, P. R. China
  • 收稿日期:2010-06-04 修回日期:2011-04-09 出版日期:2011-06-01 发布日期:2011-06-01
  • 基金资助:

    Project supported by the Western Transport Technical Project of Ministry of Transport of China (No. 2009318000046)

Stability and dispersion analysis of reproducing kernel collocation method for transient dynamics

LUO Han-Zhong1, LIU Wue-Wen2, HUANG Xing-Chun1   

  1. 1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University,Shanghai 200240, P. R. China;
    2. Siemens Industry Software (China) Co., Ltd., 14F, Cloud-9 Office Tower, No. 1018, Changning Road, Shanghai 200042, P. R. China
  • Received:2010-06-04 Revised:2011-04-09 Online:2011-06-01 Published:2011-06-01
  • Supported by:

    Project supported by the Western Transport Technical Project of Ministry of Transport of China (No. 2009318000046)

摘要: A reproducing kernel collocation method based on strong formulation is introduced for transient dynamics. To study the stability property of this method, an algorithm based on the von Neumann hypothesis is proposed to predict the critical time step. A numerical test is conducted to validate the algorithm. The numerical critical time step and the predicted critical time step are in good agreement. The results are compared with those obtained based on the radial basis collocation method, and they are in good agreement. Several important conclusions for choosing a proper support size of the reproducing kernel shape function are given to improve the stability condition.

关键词: reproducing kernel collocation method (RKCM), stability analysis, dispersion analysis, transient dynamics

Abstract: A reproducing kernel collocation method based on strong formulation is introduced for transient dynamics. To study the stability property of this method, an algorithm based on the von Neumann hypothesis is proposed to predict the critical time step. A numerical test is conducted to validate the algorithm. The numerical critical time step and the predicted critical time step are in good agreement. The results are compared with those obtained based on the radial basis collocation method, and they are in good agreement. Several important conclusions for choosing a proper support size of the reproducing kernel shape function are given to improve the stability condition.

Key words: reproducing kernel collocation method (RKCM), stability analysis, dispersion analysis, transient dynamics

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