一族无条件稳定的显式结构动力学算法

郭豪鑫1,吴春利2

振动与冲击 ›› 2020, Vol. 39 ›› Issue (12) : 48-56.

PDF(1407 KB)
PDF(1407 KB)
振动与冲击 ›› 2020, Vol. 39 ›› Issue (12) : 48-56.
论文

一族无条件稳定的显式结构动力学算法

  • 郭豪鑫1,吴春利2
作者信息 +

A family of unconditionally stable explicit algorithms for structural dynamics

  • GUO Haoxin1,WU Chunli2
Author information +
文章历史 +

摘要

利用离散控制理论分析HHT- 算法,提出了一族具有可控数值阻尼的无条件稳定显式结构动力学算法—显式HHT- 法,用于线性和非线性结构动力学分析。新算法采用显式的位移、速度递推式。研究了所提算法的精度,稳定性,数值色散和能量耗散特性。研究表明该算法对于线弹型和刚度软化型非线性系统是无条件稳定的,算法数值阻尼由单个参数控制,对于特定的参数值,所提算法不会产生数值能量耗散。此外所提出的显式算法的数值色散和能量耗散特性与隐式HHT- 算法相同。数值算例验证了理论分析的正确性。

Abstract

The implicit dissipative HHT-  method is analyzed using discrete control theory, a one-parameter family of explicit structural dynamics algorithms with controllable numerical energy dissipation, referred to as the explicit HHT-  method, is developed for linear and nonlinear structural dynamic numerical analysis applications. New algorithm adopts the recursive formula of velocity and displacement of explicit algorithm. Accuracy stability, numerical dispersion, and energy dissipation characteristics of the proposed algorithms are studied. It is shown that the algorithms are unconditionally stable for linear elastic and stiffness softening-type nonlinear systems. The amount of numerical damping is controlled by a single parameter, for a specific value of this parameter, the resulting algorithm is shown to produce no numerical energy dissipation. It is further shown that the numerical dispersion and energy dissipation characteristics of the proposed explicit algorithms are the same as that of the implicit HHT-  method. A numerical example is presented to verify the correctness of theoretical analysis.

关键词

直接积分算法 / 显式 / 无条件稳定 / 数值能量耗散 / 动力分析 / 离散传递函数

Key words

direct integration algorithm / explicit / unconditional stability / numerical energy dissipation / dynamic analysis / discrete transfer function

引用本文

导出引用
郭豪鑫1,吴春利2. 一族无条件稳定的显式结构动力学算法[J]. 振动与冲击, 2020, 39(12): 48-56
GUO Haoxin1,WU Chunli2. A family of unconditionally stable explicit algorithms for structural dynamics[J]. Journal of Vibration and Shock, 2020, 39(12): 48-56

参考文献

[1] Chopra A K. Dynamics of Structures. Theory and Applications to[J]. Earthquake Engineering, 2017.
[2] Dokainish M, Subbaraj K. A survey of direct time-integration methods in computational structural dynamics—I. Explicit methods[J]. Computers & Structures, 1989, 32(6): 1371-1386.
[3] Newmark N M. A method of computation for structural dynamics[J]. Journal of the engineering mechanics division, 1959, 85(3): 67-94.
[4] 张继锋, 邓子辰, 张凯.结构动力方程求解的改进精细Runge-Kutta方法[J]. 应用数学和力学, 2015, 36(04): 378-385.( Zhang Ji-feng, Deng Zi-chen,Zhang Kai, An Improved Precise Runge-Kutta Method for Structural Dynamic Equations[J].Applied Mathematics and Mechanics,2015, 36(04): 378-385.(in chinese))
[5] 张晓志, 程岩, 谢礼立. 结构动力反应分析的三阶显式方法[J]. 地震工程与工程振动, 2002, (03): 1-8.( Zhang Xiao-zhi,Cheng Yan,Xie Li -li,A new explicit solution of dynamic response analysis[J].Earthquake Engineering And Engineering Vibration,2002,(03):1-8. (in chinese))
[6] 陈学良, 金星, 陶夏新. 求解加速度反应的显式积分格式研究[J]. 地震工程与工程振动, 2006, (05): 60-67.(Chen Xue liang, Jin Xing, Tao Xiaxin,Study on explicit in tegration formula for dynam ic acceleration response[J]Earthquake Engineering And Engineering Vibration,2006,(05):60-67. (in chinese))
[7] 杨超, 肖守讷, 鲁连涛. 基于双步长的显式积分算法[J]. 振动与冲击, 2015, 34(01): 29-32+38.( YANG Chao,XIAO Shou-ne,LU Lian-tao Explicit integration algorithm based on double time steps[J] Journal of Vibration and Shock, 2015, 34(01): 29-32+38(in chinese))
[8] Wilson E L. A computer program for the dynamic stress analysis of underground structures[R]. California Univ Berkeley Structural Engineering Lab, 1968.
[9] Hilber H M, Hughes T J, Taylor R L. Improved numerical dissipation for time integration algorithms in structural dynamics[J]. Earthquake Engineering & Structural Dynamics, 1977, 5(3): 283-292.
[10] Chung J, Hulbert G. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method[J]. Journal of applied mechanics, 1993, 60(2): 371-375.
[11] Dahlquist G G. A special stability problem for linear multistep methods[J]. BIT Numerical Mathematics, 1963, 3(1): 27-43.
[12] Chang S-Y. Explicit pseudodynamic algorithm with unconditional stability[J]. Journal of Engineering Mechanics, 2002, 128(9): 935-947.
[13] Chang S-Y. Enhanced, unconditionally stable, explicit pseudodynamic algorithm[J]. Journal of Engineering Mechanics, 2007, 133(5): 541-554.
[14] Chang S Y. An explicit method with improved stability property[J]. International Journal for Numerical Methods in Engineering, 2009, 77(8): 1100-1120.
[15] Chen C, Ricles J M. Development of Direct Integration Algorithms for Structural Dynamics Using Discrete Control Theory[J]. Journal of Engineering Mechanics, 2008, 134(8): 676-683.
[16] Kolay C, Ricles J M. Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation[J]. Earthquake Engineering & Structural Dynamics, 2014, 43(9): 1361-1380.
[17] 杜晓琼, 杨迪雄, 赵永亮. 一种无条件稳定的结构动力学显式算法[J]. 力学学报, 2015, 47(02): 310-319.(Du Xiaoqiong,Yang Dixiong,Zhao Yongliang.An Unconditionally Stable Explicit Algorithm For Structural Dynamics[J].Chinese Journal of Theoretical and Applied Mechanics,2015, 47(02): 310-319.(in chinese))
[18] Gui Y, Wang J-T, Jin F, et al. Development of a family of explicit algorithms for structural dynamics with unconditional stability[J]. Nonlinear Dynamics, 2014, 77(4): 1157-1170.
[19] 桂耀.一族双显式算法及其在实时耦联动力试验中的应用[D].清华大学, 2014.( Gui Yao.A Family of Dual Explicit Algorithms with Application in Real-Time Dynamic Hybrid Testing[D].Tsinghua university,2014(in chinese))
[20] Hughes T J. The finite element method: linear static and dynamic finite element analysis[M].  Courier Corporation, 2012.
[21] 张雄, 王天舒.计算动力学[M].  清华大学出版社, 2007. (Zhang Xiong, Wang Tianshu. Computational Dynamics. Beijing: Tsinghua University Press, 2007 (in Chinese))
[22] Rezaiee-Pajand M, Hashemian M. Time Integration Method Based on Discrete Transfer Function[M]. 2015: 1550009.
[23] 刘春生, 吴庆宪. 现代控制工程基础[M]. 科学出版社, 2011. (Liu Chunsheng, Wu Qingxian. Fundamentals of Modern Control Engineering. Beijing: Science Press, 2011 (in Chinese))
[24] Ogata K. Discrete-time control systems[M]. 2.  Prentice Hall Englewood Cliffs, NJ, 1995.
[25] Chang S-Y. Explicit pseudodynamic algorithm with improved stability properties[J]. Journal of engineering mechanics, 2009, 136(5): 599-612.
 

PDF(1407 KB)

443

Accesses

0

Citation

Detail

段落导航
相关文章

/