全部

力学与实践 ›› 2010, Vol. 32 ›› Issue (2): 76-81.doi: 10.6052/1000-0879-2008-598

• 应用研究 • 上一篇    下一篇

大型结构动力响应的状态方程的Krylov精细时程积分法

陈臻林   

  1. 成都理工大学,土木与环境工程学院
  • 收稿日期:2009-03-20 修回日期:2009-09-28 出版日期:2010-04-08 发布日期:2010-04-08

KRYLOV PRECISE TIME-STEP INTEGRATION ALGORITHM FOR LARGE-SCALE STRUCTURE DYNAMIC EQUATION

Chen ZhenLin   

  • Received:2009-03-20 Revised:2009-09-28 Online:2010-04-08 Published:2010-04-08

摘要: 提出了一种新的精细时程积分法来求解大型动力系统. 结合Krylov子空间法、培德级数 近似以及一般载荷的维数扩展法,进一步提高精细时程积分法的计算效率. 利用维数扩展法 避免计算微分方程特解,并可处理任意载荷. 对于大型动力系统,通过Krylov子空间的降维 分析将问题转化到一个子空间,计算效率得到极大提高. 对于迭代次数$N$ 的选择作了详细讨论,进一步提高了计算效率.

关键词: 精细时程积分, Krylov子空间法, 培德级数近似

Abstract: An efficient precise time-step integration algorithm to solve large-scale transient problems is presented. The Krylov subspace method, the Pad\'{e} approximations and the dimensional expanding method of ordinary excitations are applied to modify the original precise time-step integration algorithm in order to improve the computational efficiency. The problems of arbitrary complex excitations can also be solved. For a large-scale system, the efficiency of the algorithm would be influenced because the dimension of system extended by the dimension expanding method becomes higher, especially, for the complex excitations. The present algorithm can solve the large-scale system without difficulty by using the decreasing dimension analysis of the Krylov subspace method. The efficiency of the new algorithm can be improved by analyzing the exponentional matrix in a subspace instead of the original large space. More computational cost can be saved by selecting the parameter $N$ carefully.

Key words: Precise time-step integration (PTI) algorithm, Krylov subspace method, Padé approximations