求解结构地震响应位移输入模型存在的问题及其AMCE实效对策
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摘要
提出一种实效方法-刚性无质量束缚元AMCE(Appended Massless Constraint Element)法,以解决地震地面运动作用下求解结构响应的位移输入模型中容易而不容忽视的问题。首先对位移输入模型进行了详细分析,明确指出当前位移输入模型在理论上会导致计算结果具有不稳定性和不可靠性,进一步通过算例对此加以说明;针对此问题,提出了AMCE解决方法,并对本方法进行物理角度解释、理论分析和数值验证。结果表明,AMCE法不仅物理概念清晰、简单可行,而且具有足够的计算精度。
An effective method called Appended Massless Constraint Element(AMCE) method is presented and proposed,which is adopted to settle the problem,easy but not to be neglected,inherent in the displacement input model for calculating the structural responses under earthquake-induced ground motion.Based on the comprehensive and intensive analysis of the displacement input model in this paper,it points out explicitly that there is the unstability and extreme irrationality of the calculation results while adopting the displacement input model.To solve the problem,the RMCE method is presented.Then,the rationality and accuracy of the proposed method are further verified.Theoretical analysis and numerical results demonstrate that the proposed method is simple,feasible and possesses high accuracy.
An effective method called Appended Massless Constraint Element(AMCE) method is presented and proposed,which is adopted to settle the problem,easy but not to be neglected,inherent in the displacement input model for calculating the structural responses under earthquake-induced ground motion.Based on the comprehensive and intensive analysis of the displacement input model in this paper,it points out explicitly that there is the unstability and extreme irrationality of the calculation results while adopting the displacement input model.To solve the problem,the RMCE method is presented.Then,the rationality and accuracy of the proposed method are further verified.Theoretical analysis and numerical results demonstrate that the proposed method is simple,feasible and possesses high accuracy.
引文
[1]李宏男.结构多维抗震理论[M].北京:科学出版社,2006.(LI Hong-nan.Earthquake Resistant Theoryof Structures to Multi-Dimensional Excitations[M].Beijing:Science Press,2006.(in Chinese))
[2]胡聿贤.地震工程学(第二版)[M].北京:地震出版社,2006.(HU Yu-xian.Earthquake Engineering[M].Beijing:Earthquake Press,2006.(in Chinese))
[3]李杰,李国强.地震工程学导论[M].北京:地震出版社,1992.(LI Jie,LI Guo-qiang.Introduction toEarthquake Engineering[M].Beijing:EarthquakePress,1992.(in Chinese))
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[5]叶继红,孙建梅.多点激励反映谱法的理论研究[J].应用力学,2007,24(1):49-53.(YE Ji-hong,SUNJian-mei.Respense spectrum method for multi-Sup-port seismic excitations[J].Chinese Journal of Ap-plied Mechanics,2007,24(1):49-53.(in Chinese))
[6]薛素铎,王雪生,曹资.空间网格结构多维多点随机地震响应分析的高效算法[J].世界地震工程,2004,20(3):43-49.(XUE Su-duo,WANG Xue-sheng,CAOZi.An efficient algorithm for multi-dimensional andmulti-support random seismic analysis of spatial retic-ulated structures[J].World Earthquake Engineer-ing,2004,20(3):43-49.(in Chinese))
[7]全伟,李宏男.大跨结构多维多点输入抗震研究进展[J].防灾减灾工程学报,2006,26(3):343-349.(QUAN Wei,LI Hong-nan.State-of-the-Art reviewon multi-component multi-support Seismic responseanalysis of long-span structures[J].Journal of Dis-aster Prevention and Mitigation Engineering,2006,26(3):343-349.(in Chinese))
[8]潘旦光,楼梦麟,范立础.多点输入下大跨结构地震反应分析现状[J].同济大学学报,2001,29(10):1213-1219.(PAN Dan-guang,LOU Meng-lin,FANLi-chu.Status of seismic response analysis of long-span Structures under multiple support excitations[J].Journal of Tongji University,2001,29(10):1213:1219.(in Chinese))
[9]ANIL K.Chopra.Dynamics of Structures:Theoryand Applications to Earthquake Engineering(SecondEdition)[M].Prentice-Hall,Inc.,New Jersey,2001.
[10]WILSON E L.Static and Dynamic Analysis ofStructures:a Physical Approach with Emphasis onEarthquake Engineering[M].Computer and Struc-tures,Inc,Berkley,California,2004.
[11]ANIL K Chopra.结构动力学理论及其在地震工程中的应用(第二版)[M].谢礼立,吕大刚,译.北京:科学出版社,2006.(ANIL K,Chopra.Dynamics ofStructures Theory and Applications to EarthquakeEngineering(Second Edition)[M].XIE Li-li,L Da-gang,translated.Beijing:Higher EducationPress,2007.(in Chinese))
[12]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社.2004.(LIN Jia-hao,ZHANG Ya-hui.Pseudo-Excitation Method for Random Vibration[M].Beijing:Science Press,2004.(in Chinese))
[13]田玉基,杨庆山.地震地面运动作用下结构反应的分析模型[J].工程力学,2005,22(6):170-174.(TIANYu-ji,YANG Qing-shan.Analysis models and meth-ods for structural seismic responses[J].EngineeringMechanics,2005,22(6):170-174.(in Chinese))
[14]柳国环,李宏男,林海.结构地震响应计算模型的分析与应用[J].工程力学,2009,26(2):10-15.(LIUGuo-huan,LI Hong-nan,LIN Hai.Model Compari-sion and analysis for structural seismic responses[J].Engineering Mechanics,2009,26(2):10-15.(in Chi-nese))
[15]HUGHES T.The Finite Element Method-LinearStatic and Dynamic Finite Element Analysis[M].Prentice Hall,Inc.,New Jersey,1987.(in Chinese))
[16]CLOUGH R W,PENZIEN J.Dynamics of Struc-tures(Second Edition)[M].Computers and Struc-tures,Inc.,2004.
[2]胡聿贤.地震工程学(第二版)[M].北京:地震出版社,2006.(HU Yu-xian.Earthquake Engineering[M].Beijing:Earthquake Press,2006.(in Chinese))
[3]李杰,李国强.地震工程学导论[M].北京:地震出版社,1992.(LI Jie,LI Guo-qiang.Introduction toEarthquake Engineering[M].Beijing:EarthquakePress,1992.(in Chinese))
[4]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 Zhong-xian.A-nalysis models and methods for structural seismic re-sponses[J].Engineering Mechanics,2007,24(3):97-103.(in Chinese))
[5]叶继红,孙建梅.多点激励反映谱法的理论研究[J].应用力学,2007,24(1):49-53.(YE Ji-hong,SUNJian-mei.Respense spectrum method for multi-Sup-port seismic excitations[J].Chinese Journal of Ap-plied Mechanics,2007,24(1):49-53.(in Chinese))
[6]薛素铎,王雪生,曹资.空间网格结构多维多点随机地震响应分析的高效算法[J].世界地震工程,2004,20(3):43-49.(XUE Su-duo,WANG Xue-sheng,CAOZi.An efficient algorithm for multi-dimensional andmulti-support random seismic analysis of spatial retic-ulated structures[J].World Earthquake Engineer-ing,2004,20(3):43-49.(in Chinese))
[7]全伟,李宏男.大跨结构多维多点输入抗震研究进展[J].防灾减灾工程学报,2006,26(3):343-349.(QUAN Wei,LI Hong-nan.State-of-the-Art reviewon multi-component multi-support Seismic responseanalysis of long-span structures[J].Journal of Dis-aster Prevention and Mitigation Engineering,2006,26(3):343-349.(in Chinese))
[8]潘旦光,楼梦麟,范立础.多点输入下大跨结构地震反应分析现状[J].同济大学学报,2001,29(10):1213-1219.(PAN Dan-guang,LOU Meng-lin,FANLi-chu.Status of seismic response analysis of long-span Structures under multiple support excitations[J].Journal of Tongji University,2001,29(10):1213:1219.(in Chinese))
[9]ANIL K.Chopra.Dynamics of Structures:Theoryand Applications to Earthquake Engineering(SecondEdition)[M].Prentice-Hall,Inc.,New Jersey,2001.
[10]WILSON E L.Static and Dynamic Analysis ofStructures:a Physical Approach with Emphasis onEarthquake Engineering[M].Computer and Struc-tures,Inc,Berkley,California,2004.
[11]ANIL K Chopra.结构动力学理论及其在地震工程中的应用(第二版)[M].谢礼立,吕大刚,译.北京:科学出版社,2006.(ANIL K,Chopra.Dynamics ofStructures Theory and Applications to EarthquakeEngineering(Second Edition)[M].XIE Li-li,L Da-gang,translated.Beijing:Higher EducationPress,2007.(in Chinese))
[12]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社.2004.(LIN Jia-hao,ZHANG Ya-hui.Pseudo-Excitation Method for Random Vibration[M].Beijing:Science Press,2004.(in Chinese))
[13]田玉基,杨庆山.地震地面运动作用下结构反应的分析模型[J].工程力学,2005,22(6):170-174.(TIANYu-ji,YANG Qing-shan.Analysis models and meth-ods for structural seismic responses[J].EngineeringMechanics,2005,22(6):170-174.(in Chinese))
[14]柳国环,李宏男,林海.结构地震响应计算模型的分析与应用[J].工程力学,2009,26(2):10-15.(LIUGuo-huan,LI Hong-nan,LIN Hai.Model Compari-sion and analysis for structural seismic responses[J].Engineering Mechanics,2009,26(2):10-15.(in Chi-nese))
[15]HUGHES T.The Finite Element Method-LinearStatic and Dynamic Finite Element Analysis[M].Prentice Hall,Inc.,New Jersey,1987.(in Chinese))
[16]CLOUGH R W,PENZIEN J.Dynamics of Struc-tures(Second Edition)[M].Computers and Struc-tures,Inc.,2004.
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