一族无条件稳定和精度可控的时程积分显式算法
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- 英文论文题名：A family of explicit algorithms of time integration with unconditional stability and controllable accuracy
- 论文作者：李石 ; 杨迪雄
- 英文论文作者：Li Shi ; Yang Dixiong ; Department of Engineering Mechanics ; Dalian University of Technology State Key Laboratory of Structural Analysis for Industrial Equipment
- 年：2016
- 作者机构：大连理工大学工程力学系工业装备结构分析国家重点实验室;
- 论文关键词：结构动力学 ; 无条件稳定显式算法 ; 离散控制理论 ; 可控精度 ; 周期延长率
- 英文论文关键词：structural dynamics ; explicit unconditionally stable algorithm ; discrete control theory ; controllable period elongation ; period elongation
- 会议召开时间：2016-10-27
- 会议录名称：第九届全国防震减灾工程学术研讨会论文集
- 语种：中文
- 分类号：P315.9
- 学会代码：OGTY
- 会议名称：第九届全国防震减灾工程学术研讨会
- 会议地点：中国安徽合肥
- 主办单位：中国土木工程学会、中国工程院土木、水利与建筑工程学部、中国土木工程学会防震减灾工程技术推广委员会、合肥工业大学、安徽省住房和城乡建设厅
- 学会名称：中国土木工程学会
- 页数：9
- 文件大小：402k
- 原文格式：O
- 会议级别：全国
摘要
利用离散控制理论,针对结构动力学方程时程积分提出了一种新的无条件稳定、精度可控的显式算法。新算法采用显式位移、速度递推式,并利用Z变换获得相应的传递函数,将三个常用Newmark算法的极点带入特征方程。通过比较递推式的系数,引入正变量s,得到广义的系数。理论分析表明无条件稳定显式新算法具有二阶精度、零振幅衰减率和自起步特性,且周期延长率作为衡量算法精度的一个重要指标可以用变量s予以控制,而显式Newmark算法只是新算法的特例。此外,建立了线性和非线性系统的稳定性条件。最后,采用新算法进行弹塑性高层建筑结构地震响应分析,结果展示了新算法的有效性和精度可控性。
Using discrete control theory,this paper proposes a new family of unconditionally stable explicit algorithms with controllable accuracy for time integration of structural dynamics.New algorithms adopt the explicit recursive formula of velocity and displacement.Furthermore,based on discrete transfer function with the Z transformation,three poles of Newmark family of algorithms are assigned to the characteristic equation of new proposed algorithms.By comparing the formulation coefficients of new algorithms,a positive variable s is introduced to generalize the coefficients in recursive formula.Then,the theoretical analyses indicate that the new family of algorithms possesses the properties of second accuracy,zero amplitude decay and self—starting,and the period elongation as an important index to measure the algorithm accuracy which can be controlled by the variable s.The explicit Newmark method is only the special case of new algorithms.In addition,the stability conditions of linear and nonlinear systems are established.Finally,numerical results of example for analyzing the seismic responses of elasto—plastic tall building structure demonstrate the effectiveness and controllable accuracy of the new algorithms.
Using discrete control theory,this paper proposes a new family of unconditionally stable explicit algorithms with controllable accuracy for time integration of structural dynamics.New algorithms adopt the explicit recursive formula of velocity and displacement.Furthermore,based on discrete transfer function with the Z transformation,three poles of Newmark family of algorithms are assigned to the characteristic equation of new proposed algorithms.By comparing the formulation coefficients of new algorithms,a positive variable s is introduced to generalize the coefficients in recursive formula.Then,the theoretical analyses indicate that the new family of algorithms possesses the properties of second accuracy,zero amplitude decay and self—starting,and the period elongation as an important index to measure the algorithm accuracy which can be controlled by the variable s.The explicit Newmark method is only the special case of new algorithms.In addition,the stability conditions of linear and nonlinear systems are established.Finally,numerical results of example for analyzing the seismic responses of elasto—plastic tall building structure demonstrate the effectiveness and controllable accuracy of the new algorithms.
引文
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[3]Chung J,Hulbert GM.A time integration algorithm for structural dynamics with improved numerical dissipation:the generalized-αmethod[J].Journal of Applied Mechanics,1993,60(2):371-375.
[4]Chang SY.Explicit pseudodynamic algorithm with unconditional stability.Journal of Engineering Mechanics,2002,128(9):935-947.
[5]Chen C,Ricles JM.Development of direct integration algorithms for structural dynamics using discrete control theory[J].Journal of Engineering Mechanics,2008,134(8):676-683.
[6]Chang CY.A general technique to improve stability property for a structure-dependent integration method[J].International Journal for Numerical Methods in Engineering,2015,101(9):653-669.
[7]Kolay C,Ricles JM.Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation[J].Earthquake Engineering and Structural Dynamics,2014,43(9):1361-1380.
[8]Rezaiee-Pajand M,Hashemian M.Time integration method based on discrete transfer function[J J.International Journal of Structural Stability and Dynamics,2015,16;1550009.
[9]陈建兵,李杰.结构随机地震反应与可靠度的慨率密度演化分析研究进展[J].工程力学,2014(4):1-10.(Chen Jianbing,Li Jie.Probability density evolution method for stochastic seismic response and reliability of structures[J].Engineering Mechanics,2014(4):1-10(in Chinese)).
[2]Hilber HM,Hughes TJR,Taylor RL.Improved numerical dissipation for time integration algorithms in structural dynamics[J].Earthquake Engineering and Structural Dynamics,1977,5(3):283-292.
[3]Chung J,Hulbert GM.A time integration algorithm for structural dynamics with improved numerical dissipation:the generalized-αmethod[J].Journal of Applied Mechanics,1993,60(2):371-375.
[4]Chang SY.Explicit pseudodynamic algorithm with unconditional stability.Journal of Engineering Mechanics,2002,128(9):935-947.
[5]Chen C,Ricles JM.Development of direct integration algorithms for structural dynamics using discrete control theory[J].Journal of Engineering Mechanics,2008,134(8):676-683.
[6]Chang CY.A general technique to improve stability property for a structure-dependent integration method[J].International Journal for Numerical Methods in Engineering,2015,101(9):653-669.
[7]Kolay C,Ricles JM.Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation[J].Earthquake Engineering and Structural Dynamics,2014,43(9):1361-1380.
[8]Rezaiee-Pajand M,Hashemian M.Time integration method based on discrete transfer function[J J.International Journal of Structural Stability and Dynamics,2015,16;1550009.
[9]陈建兵,李杰.结构随机地震反应与可靠度的慨率密度演化分析研究进展[J].工程力学,2014(4):1-10.(Chen Jianbing,Li Jie.Probability density evolution method for stochastic seismic response and reliability of structures[J].Engineering Mechanics,2014(4):1-10(in Chinese)).