平面框架结构地震力的设计敏度和海森矩阵的计算
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摘要
提出一种平面框架结构地震力的设计敏度和海森矩阵的精确计算方法.在有限单元法和纽马克-β法的基础上推导了平面框架结构地震力的设计敏度和海森矩阵的计算公式,用matlab语言编制了平面框架结构地震力的设计敏度和海森矩阵的计算程序,实现了平面框架结构地震力的设计敏度和海森矩阵的精确计算.最后给出一个二层平面框架结构算例,数值结果表明本文所提的地震力的设计敏度和海森矩阵的计算方法是有效的和高效的.
This paper presented an accurate method of calculating the earthquake force design sensitivity and Hessian matrix of the planar frame. The formulas for the earthquake force design sensitivity and Hessian matrix of the planar frame were deduced based on the finite element method and Newmark-β method,and the corresponding calculating program was implemented with matlab language. Finally,a two-story planar frame was demonstrated as an example. The results indicate the method is effective.
This paper presented an accurate method of calculating the earthquake force design sensitivity and Hessian matrix of the planar frame. The formulas for the earthquake force design sensitivity and Hessian matrix of the planar frame were deduced based on the finite element method and Newmark-β method,and the corresponding calculating program was implemented with matlab language. Finally,a two-story planar frame was demonstrated as an example. The results indicate the method is effective.
引文
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7潘振宽,丁洁玉,王钰.基于隐式微分代数方程的多体系统动力学设计灵敏度分析方法.动力学与控制学报,2004,2(2):66～69(Pan Zhenkuan,Ding Jieyu,Wang Yu.Design sensitivity analysis of multibody system dynamics described by implicit differential/algebraic equations.Jour-nal ofDynamics and Control,2004,2(2):66～69(in Chi-nese))
8丁洁玉,潘振宽,陈立群.基于微分/代数方程的多体系统动力学设计灵敏度分析的伴随变量方法.动力学与控制学报,2006,4(3):205～209(Ding Jieyu,Pan Zhen-kuan,Chen Liqun.Adjoint variable method for multibody system dynamics described by differential/algebraic equa-tions.Journal ofDynamics and Control,2006,4(3):205～209(in Chinese))
9G VReklaitis,ARavindran,KMRagsdell.Engineering Op-timization Methods and Applications.NewYork:John Wiley&Sons,1983:98～119
10朱伯芳.有限单元法原理与应用.北京:中国水利水电出版社,1998:459～467(Zhu Bofang.Finite element meth-od principle and application.Beijing:China Water Power Press,1998:459～467(in Chinese))
11Anil K Chopra.结构动力学理论及其在地震工程中的应用(第2版).北京:清华大学出版社,2005:609～627(Anil K Chopra.Structural dynamics theory and application in earthquake engineering(the second edition).Beijing:Ts-inghua University Press,2005:609～627(in Chinese))
12刘尔烈,崔恩第,徐振铎.有限单元法及程序设计.天津:天津大学出版社,2004:4～72(Liu Erlie,Cun Endi,Xu Zhenduo.Finite element method and programmer.Tian-jin:Tianjin University Press,2004:4～72(in Chinese))
2MBogomolni,UKirsch,I Sheinman.Efficient design sensi-tivities of structures subjected to dynamic loading.Interna-tional Journal ofSolids and Structures,2006,43:5485～5500
3林家浩.结构动力优化中的灵敏度分析.振动与冲击,1985,4(1):1～6(Lin Jiahao.Sensitivity analysis in struc-tural dynamic optimization.Journal ofVibration and Shock,1985,4(1):1～6(in Chinese))
4林树枝,程耿东.动力响应灵敏度分析的振形空间法.地震工程与工程振动,1990,10(3):57～64(Lin Shuzhi,Cheng Gengdong.Mode shape space method of dynamic re-sponse sensitivity analysis.Earthquake Engineering and En-gineering Vibration,1990,10(3):57～64(in Chinese))
5张传立,邹时智,宋天霞.结构动力响应灵敏度分析的Laplace变换法.华中理工大学学报,1995,23(7):27～30(Zhang chuanli,Zou Shizhi,Song Tianxia.A method of Laplace transformation for sensitivity analysis of the struc-tural dynamic response.Journal ofHuazhong University of Science and Technology,1995,23(7):27～30(in Chi-nese))
6邹时智,宋天霞.非线性结构动力响应中的灵敏度分析.华中理工大学学报,1996,24(9):71～74(Zou Shizhi,Song Tianxia.A sensitivity analysis of the nonlinear struc-tural dynamic response.Journal ofHuazhong University of Science and Technology,1996,24(9):71～74(in Chi-nese))
7潘振宽,丁洁玉,王钰.基于隐式微分代数方程的多体系统动力学设计灵敏度分析方法.动力学与控制学报,2004,2(2):66～69(Pan Zhenkuan,Ding Jieyu,Wang Yu.Design sensitivity analysis of multibody system dynamics described by implicit differential/algebraic equations.Jour-nal ofDynamics and Control,2004,2(2):66～69(in Chi-nese))
8丁洁玉,潘振宽,陈立群.基于微分/代数方程的多体系统动力学设计灵敏度分析的伴随变量方法.动力学与控制学报,2006,4(3):205～209(Ding Jieyu,Pan Zhen-kuan,Chen Liqun.Adjoint variable method for multibody system dynamics described by differential/algebraic equa-tions.Journal ofDynamics and Control,2006,4(3):205～209(in Chinese))
9G VReklaitis,ARavindran,KMRagsdell.Engineering Op-timization Methods and Applications.NewYork:John Wiley&Sons,1983:98～119
10朱伯芳.有限单元法原理与应用.北京:中国水利水电出版社,1998:459～467(Zhu Bofang.Finite element meth-od principle and application.Beijing:China Water Power Press,1998:459～467(in Chinese))
11Anil K Chopra.结构动力学理论及其在地震工程中的应用(第2版).北京:清华大学出版社,2005:609～627(Anil K Chopra.Structural dynamics theory and application in earthquake engineering(the second edition).Beijing:Ts-inghua University Press,2005:609～627(in Chinese))
12刘尔烈,崔恩第,徐振铎.有限单元法及程序设计.天津:天津大学出版社,2004:4～72(Liu Erlie,Cun Endi,Xu Zhenduo.Finite element method and programmer.Tian-jin:Tianjin University Press,2004:4～72(in Chinese))
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