直接求解多维多点地震动方程的虚拟激励法
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摘要
为解决传统的虚拟激励法多维多点虚拟激励荷载输入繁琐及在通用有限元软件中实现困难的问题,通过在质量矩阵上"置大数"的方法快速实现地震动输入,更快捷地将一维多点激励扩展到多维多点虚拟激励,运用绝对位移直接求解运动方程。相比传统的多维多点虚拟激励法,不必将绝对位移分解为拟静力位移项和动力相对位移项,避免了求解静力影响矩阵的繁琐,能更高效的实现多自由度大跨结构多维多点虚拟激励荷载在通用有限元软件中的输入与分析,不需要编制专门的计算程序,使得虚拟激励法在理论上和工程中的应用得到进一步的拓展。
This work is concerned with the input and implementation issues of the pseudo load in the finite element software for a pseudo excitation method.The input of ground motion is achieved more expediently through a "place large numbers" approach.Therefore,the pseudo excitation is swiftly extended from one-dimensional and multi-supports(ODMS) to multi-dimensional and multi-supports(MDMS),and the motion equations are solved directly through absolute displacement.Compared to the traditional MDMS pseudo excitation method,the directly-solving method through the absolute displacement does not decompose the absolute displacement into quasi-static and dynamic relative displacement items,avoids solving the static influence matrix,more efficiently realizes the input of pseudo excitation loading and the analysis of multiple-degree-of-freedom structures in the finite element software,and does not require a special program.The pseudo excitation method is further expanded in theory and engineering applications.
This work is concerned with the input and implementation issues of the pseudo load in the finite element software for a pseudo excitation method.The input of ground motion is achieved more expediently through a "place large numbers" approach.Therefore,the pseudo excitation is swiftly extended from one-dimensional and multi-supports(ODMS) to multi-dimensional and multi-supports(MDMS),and the motion equations are solved directly through absolute displacement.Compared to the traditional MDMS pseudo excitation method,the directly-solving method through the absolute displacement does not decompose the absolute displacement into quasi-static and dynamic relative displacement items,avoids solving the static influence matrix,more efficiently realizes the input of pseudo excitation loading and the analysis of multiple-degree-of-freedom structures in the finite element software,and does not require a special program.The pseudo excitation method is further expanded in theory and engineering applications.
引文
[1]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2006:124―163.Lin Jiahao,Zhang Yahui.Pseudo excitation method forrandom vibration[M].Beijing:Science Press,2006:124―163.(in Chinese)
[2]Ernesto H Z,Vanmarcke E H.Seismic random vibrationanalysis of multi-support structural systems[J].Journalof Engineering Mechanics,ASCE,1994,120:1107―1128.
[3]Kiureghian A D,Neuenhofer A.A discussion on‘seismicrandom vibration analysis of multi-support structuralsystem’[J].Journal of Engineering Mechanics,ASCE,1995,121:1037.
[4]Ernesto H Z,Vanmarcke E H.Closure on the discussion[J].Journal of Engineering Mechanics,ASCE,1995,121:1038.
[5]李建俊,林家浩,张文首,张宏宝.大跨度结构受多点随机地震激励的响应[J].计算结构力学及其应用,1995,21(4):445―451.Li Jianjun,Lin Jiahao,Zhang Wenshou,Zhang Hongbao.Large-span structures seismic response subjected tomulti-support excitation[J].Computational StructuralMechanics and Applications,1995,21(4):445―451.(inChinese)
[6]赵灿晖,周志祥.多分量多点平稳随机地震响应的快速算法[J].西南交通大学学报,2007,42(1):55―60.Zhao Canhui,Zhou Zhixiang.Fast algorithm forstationary stochastic response subjected to multi-component multi-support seismic excitation[J].Journalof Southwest Jiaotong University,2007,42(1):55―60.(in Chinese)
[7]丁阳,林伟,李忠献.大跨度空间结构多维多点非平稳随机地震反应分析[J].工程力学,2007,24(3):97―103.Ding Yang,Lin Wei,Li Zhongxian.Non-stationaryrandom seismic analysis of long-span spatial structuresunder multi-support and multi-dimensional earthquakeexcitations[J].Engineering Mechanics,2007,24(3):97―103.(in Chinese)
[8]曹资,薛素铎.空间结构抗震理论与设计[M].北京:科学出版社,2006:113―225.Cao Zi,Xue Suduo.Seismic analysis and design ofspatial structures[M].Beijing:Science Press,2006:113―225.(in Chinese)
[9]江洋,石永久,王元清.实用多点输入虚拟激励法在通用有限元软件中的实现[J].地震工程与工程振动,2010,30(1):46―52.Jiang Yang,Shi Yongjiu,Wang Yuanqing.Practicalmulti-input pseudo-excitation method in general-purposefinite element software implementation[J].EarthquakeEngineering and Engineering Vibration,2010,30(1):46―52.(in Chinese)
[10]石永久,江洋,王元清.直接求解法在结构多点输入地震响应计算中的应用与改进[J].工程力学,2011,28(1):75―81.Shi Yongjiu,Jiang Yang,Wang Yuanqing.Applicationand improvement of direct solving method in seismicresponse analysis of structures under multi-supportexcitations[J].Engineering Mechanics.2011,28(1):75―81.(in Chinese)
[11]李永华,李思明.绝对位移直接求解的虚拟激励法[J].振动与冲击,2009,28(10):185―190.Li Yonghua,Li Siming.Absolute displacement directlysolve of the pseudo-excitation method[J].Vibration andShock,2009,28(10):185―190.(in Chinese)
[12]Clough R W,Penzien J.Dynamics of structures[M].3rded.Berkeley,USA:Computer&Structures,Inc,1995:427―538.
[13]屈铁军,王君杰,王前信.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55―62.Qu Tiejun,Wang Junjie,Wang Qianxin.Practical PSDground motion model with spatial effect[J].Journal ofEarthquake,1996,18(1):55―62.(in Chinese)
[2]Ernesto H Z,Vanmarcke E H.Seismic random vibrationanalysis of multi-support structural systems[J].Journalof Engineering Mechanics,ASCE,1994,120:1107―1128.
[3]Kiureghian A D,Neuenhofer A.A discussion on‘seismicrandom vibration analysis of multi-support structuralsystem’[J].Journal of Engineering Mechanics,ASCE,1995,121:1037.
[4]Ernesto H Z,Vanmarcke E H.Closure on the discussion[J].Journal of Engineering Mechanics,ASCE,1995,121:1038.
[5]李建俊,林家浩,张文首,张宏宝.大跨度结构受多点随机地震激励的响应[J].计算结构力学及其应用,1995,21(4):445―451.Li Jianjun,Lin Jiahao,Zhang Wenshou,Zhang Hongbao.Large-span structures seismic response subjected tomulti-support excitation[J].Computational StructuralMechanics and Applications,1995,21(4):445―451.(inChinese)
[6]赵灿晖,周志祥.多分量多点平稳随机地震响应的快速算法[J].西南交通大学学报,2007,42(1):55―60.Zhao Canhui,Zhou Zhixiang.Fast algorithm forstationary stochastic response subjected to multi-component multi-support seismic excitation[J].Journalof Southwest Jiaotong University,2007,42(1):55―60.(in Chinese)
[7]丁阳,林伟,李忠献.大跨度空间结构多维多点非平稳随机地震反应分析[J].工程力学,2007,24(3):97―103.Ding Yang,Lin Wei,Li Zhongxian.Non-stationaryrandom seismic analysis of long-span spatial structuresunder multi-support and multi-dimensional earthquakeexcitations[J].Engineering Mechanics,2007,24(3):97―103.(in Chinese)
[8]曹资,薛素铎.空间结构抗震理论与设计[M].北京:科学出版社,2006:113―225.Cao Zi,Xue Suduo.Seismic analysis and design ofspatial structures[M].Beijing:Science Press,2006:113―225.(in Chinese)
[9]江洋,石永久,王元清.实用多点输入虚拟激励法在通用有限元软件中的实现[J].地震工程与工程振动,2010,30(1):46―52.Jiang Yang,Shi Yongjiu,Wang Yuanqing.Practicalmulti-input pseudo-excitation method in general-purposefinite element software implementation[J].EarthquakeEngineering and Engineering Vibration,2010,30(1):46―52.(in Chinese)
[10]石永久,江洋,王元清.直接求解法在结构多点输入地震响应计算中的应用与改进[J].工程力学,2011,28(1):75―81.Shi Yongjiu,Jiang Yang,Wang Yuanqing.Applicationand improvement of direct solving method in seismicresponse analysis of structures under multi-supportexcitations[J].Engineering Mechanics.2011,28(1):75―81.(in Chinese)
[11]李永华,李思明.绝对位移直接求解的虚拟激励法[J].振动与冲击,2009,28(10):185―190.Li Yonghua,Li Siming.Absolute displacement directlysolve of the pseudo-excitation method[J].Vibration andShock,2009,28(10):185―190.(in Chinese)
[12]Clough R W,Penzien J.Dynamics of structures[M].3rded.Berkeley,USA:Computer&Structures,Inc,1995:427―538.
[13]屈铁军,王君杰,王前信.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55―62.Qu Tiejun,Wang Junjie,Wang Qianxin.Practical PSDground motion model with spatial effect[J].Journal ofEarthquake,1996,18(1):55―62.(in Chinese)
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