高精度Fox-Goodwin时间积分法
Highly Accurate Fox-Goodwin Time Integration Method
DOI: 10.12677/IJM.2017.64017, PDF,    国家自然科学基金支持
作者: 邢修源：中国矿业大学(北京)附属中学，北京；张慧敏：北京航空航天大学，北京
关键词: Fox-Goodwin方法；高精度；时间积分法；精细积分法；Fox-Goodwin Method； High Accuracy； Time Integration Method； Precise Integration Method
摘要: 本文建立了高精度Fox-Goodwin时间积分法。这种方法采用等分步的思想，连乘每分步的Jacobi矩阵建立高精度Jacobi矩阵，然后利用高精度Jacobi矩阵进行递推求解。在构造高精度Jacobi矩阵的过程中，用指数矩阵运算技巧来达到降低计算量，用存贮增量矩阵策略来减小舍入误差的影响。性能分析表明，这种方法与精细积分法相比，具备较高的幅值和相位精度，且格式简单，便于应用。
Abstract: A Highly Accurate Fox-Goodwin time Integration Method (HAFIM) is presented in this paper. HAFIM creates the highly accurate Jacobi matrix by multi-sub-step notion and uses the highly ac-curate Jacobi matrix for recursive procedure. In the process of constructing the matrix, the exponential matrix operation techniques are employed to reduce the computational efforts and the computer rounding error. The analysis on properties indicates that the proposed method possesses higher amplitude and phase accuracy compared with the Precise time Integration Methods (PIMs). Moreover, the proposed method is very practical given its simplicity.
文章引用：邢修源, 张慧敏. 高精度Fox-Goodwin时间积分法[J]. 力学研究, 2017, 6(4): 161-172. https://doi.org/10.12677/IJM.2017.64017

参考文献

[1] Houbolt, J.C. (1950) A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft. Journal of Aeronautical Science, 17, 540-550. [Google Scholar] [CrossRef] 
[2] Newmark, N.M. (1959) A Method of Computation for Structural Dynamics. ASCE Journal of the Engineering Mechanics Divisions, 85, 67-94.
[3] Wilson, E.L. (1968) A Computer Program for Dynamic Stress Analysis of Underground Structures. SESM, University of California, Berkeley.
[4] Hilber, H.M., Hughes, T.J.R. and Taylor, R.L. (1977) Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics. Earthquake Engineering and Structural Dynamics, 5, 283-292. [Google Scholar] [CrossRef] 
[5] Wood, W.L., Bossak, M. and Zienkiewicz, O.C. (1980) An Alpha Modification of Newmark’s Method. International Journal for Numerical Methods in Engineering, 15, 1562-1566. [Google Scholar] [CrossRef] 
[6] Zhai, W.M. (1996) Two Simple Fast Integration Methods for Large-Scale Dynamic Problems in Engineering. International Journal for Numerical Methods in Engineering, 39, 4199-4214. [Google Scholar] [CrossRef] 
[7] Chung, L. and Hulbert, G.M. (1993) A Time Integration Algorithm for Structural Dynamics with Improved Numerical Dissipation: The Generalized-α Method. Journal of Applied Mechanics, 60, 371-375. [Google Scholar] [CrossRef] 
[8] Bathe, K.J. and Baig, M.M.I. (2005) On a Composite Implicit Time Integration Procedure for Nonlinear Dynamics. Computers and Structures, 83, 2513-2524. [Google Scholar] [CrossRef] 
[9] Zhou, X. and Tamma, K.K. (2004) Design, Analysis, and Synthesis of Generalized Single Step Single Solve and Optimal Algorithms for Structural Dynamics. International Journal for Numerical Methods in Engineering, 59, 597-668. [Google Scholar] [CrossRef] 
[10] 钟万勰. 结构动力方程的精细时程积分[J]. 大连理工大学学报, 1994, 34(2): 131-136.
[11] 钟万勰. 暂态历程的精细计算方法[J]. 计算结构力学及其应用, 1995, 12(1): 1-6.
[12] Lin, J.H., Shen, W.P. and Williams, F.M. (1997) Accurate High-Speed Computation of Nonstationary Random Seismic Response. Engineering Structures, 19, 586-593. [Google Scholar] [CrossRef] 
[13] 汪梦甫, 周锡元. 结构动力方程的更新精细积分方法[J]. 力学学报, 2004, 36(2): 191-195.
[14] 顾元宪, 陈飚松, 张洪武. 结构动力方程的增维精细积分法[J]. 力学学报, 2000, 32(4): 447-456.
[15] Wang, M.F. and Au, F.T.K. (2006) Assessment and Improvement of Precise Time Step Integration Method. Computers and Structures, 84, 779-786. [Google Scholar] [CrossRef] 
[16] Fox, L. and Goodwin, E.T. (1949) Some New Methods for the Numerical Integration of Ordinary Differential Equations. Proceedings of Cambridge Philosophical Society, 45, 373-388. [Google Scholar] [CrossRef] 

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