基于ABAQUS的粘弹性边界单元及在重力坝抗震分析中的应用
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摘要
考虑了2种不同的地震输入模型,即无质量地基模型和考虑辐射阻尼的粘弹性边界模型。以大型非线性有限元程序ABAQUS为平台,采用FORTRAN语言开发了用户单元子程序VSB_UEL.for,将粘弹性边界有效地嵌入到ABAQUS中。在尽量避免求解自由场的前提下,将离散的地震荷载转化为等效结点荷载,编写的计算程序可以方便地将等效荷载施加到人工边界结点上,并通过数值算例验证了粘弹性边界单元及波动输入程序的正确性,其求解效率和计算精度均令人满意,最后将该程序应用到在建的某水电站厂房坝段的抗震分析中。结果表明,与传统的固定边界无质量地基相比,考虑了粘弹性人工边界后,坝体的动力响应峰值减小了20%~40%;在进行结构动力响应分析时,考虑无限域地基的辐射阻尼影响是很有必要的。文中的用户子程序及波动输入程序很容易扩展至三维,为同类工程的抗震分析提供了简洁、合理的计算模式。
In this study,two different earthquake input models are presented,i.e.massless foundation model and viscous-spring boundary input model considering radiation damping.Based on the commercial nonlinear finite element code ABAQUS and the user element subroutine VSB_UEL.For,viscous-spring boundary element is developed by FORTRAN language,thus viscous-spring boundary is embedded into ABAQUS.For avoiding the free field being solved,the discrete seismic load is translated into equivalent nodal load,which could be applied to the nodes of artificial boundaries conveniently by the compiled computer program.The correctness of viscous-spring boundary element and wave input program are proved by a numerical example,their solution efficiency and calculation precision are both satisfied.Finally,the viscous-spring boundary element and wave input method are applied to the dynamic analysis of the power house section of a hydropower station which is being built.The results show that when viscous-spring boundary is considered and compared with the traditional fixed boundary of massless foundation,the peak value of dam's dynamic response is reduced by 20%~40%;when the structural dynamic analysis is studied,considering the radiation damping effect of infinite foundation is very necessary.The user element subroutine and wave input program could be extended to three-dimensional case easily,and offer a simple logical calculation method for the dynamic response analysis of analogous projects.
In this study,two different earthquake input models are presented,i.e.massless foundation model and viscous-spring boundary input model considering radiation damping.Based on the commercial nonlinear finite element code ABAQUS and the user element subroutine VSB_UEL.For,viscous-spring boundary element is developed by FORTRAN language,thus viscous-spring boundary is embedded into ABAQUS.For avoiding the free field being solved,the discrete seismic load is translated into equivalent nodal load,which could be applied to the nodes of artificial boundaries conveniently by the compiled computer program.The correctness of viscous-spring boundary element and wave input program are proved by a numerical example,their solution efficiency and calculation precision are both satisfied.Finally,the viscous-spring boundary element and wave input method are applied to the dynamic analysis of the power house section of a hydropower station which is being built.The results show that when viscous-spring boundary is considered and compared with the traditional fixed boundary of massless foundation,the peak value of dam's dynamic response is reduced by 20%~40%;when the structural dynamic analysis is studied,considering the radiation damping effect of infinite foundation is very necessary.The user element subroutine and wave input program could be extended to three-dimensional case easily,and offer a simple logical calculation method for the dynamic response analysis of analogous projects.
引文
[1]Clough R.W.Nonlinear mechanisms in the seismic response of arch dams[C].International Conference on Earthquake Engineering,Skopje,Yu-goslavia[s.n],1980.
[2]Lysmer J.,Kulemeyer R.L.Finite dynamic model for infinite media[J].Journal of Engineering Mechanics Division,ASCE,1969,95(4):759-877.
[3]Deeks A.J.,Randolph M.F.Axisymmetric time-domain transmitting boundaries[J].Journal of Engineering Mechanics Division,ASCE,1994,120(1):25-42.
[4]廖振鹏.工程波动理论导论[M].北京:科学出版社,2002.Liao Zhenpeng.Introduction to Wave Motion Theories in Engineering[M].Beijing:Science Press,2002.
[5]Andreas H.Nielsen.Absorbing boundary conditions for seismic analysis in ABAQUS[C].ABAQUS Users'Conference,Boston,Massachusetts,May 2006:359-376.
[6]刘晶波,谷音,杜义欣.一致粘弹性人工边界及粘弹性边界单元[J].岩土工程学报,2006,28(9):1070-1075.Liu Jingbo,Gu Yin,Du Yixin.Consistent viscous-spring artificial boundaries and viscous-spring boundary elements[J].Chinese Journal ofGeotechnical Engineering,2006,28(9):1070-1075.
[7]谢和平,冯夏庭.灾害环境下重大工程安全性的基础研究[M].北京:科学出版社,2009.Xie Heping,Feng Xiating.Basic Research on the Safety of Major Engineering Project in Hazardous Environments[M].Beijing:Science Press,2009.
[8]杜修力,赵密.基于粘弹性边界的拱坝地震反应分析方法[J].水利学报,2006,37(9):1063-1069.Du Xiuli,Zhao Mi.Analysis method for seismic response of arch dams in time domain based on viscous-spring artificial boundary condition[J].Journal of Hydraulic Engineering,2006,37(9):1063-1069.
[9]贺向丽.高混凝土坝抗震分析中远域能量逸散时域模拟方法研究[D].南京:河海大学,2006.He Xiangli.Study on time-domain simulating method of far field energy dissipation in seismic analysis of high concrete dams[D].Nanjing:HohaiUniversity,2006.
[10]DL5073-2000,水工建筑物抗震设计规范[S].DL5073-2000,Seismic Design of Hydraulic Structures[S].
[11]姚艳华,彭刚,陈灯红.拟合水工设计反应谱的人工地震波的生成与Huang变换校正[J].西北地震学报,2008,30(3):255-260.Yao Yanhua,Peng Gang,Chen Denghong.Synthesis and Huang transform correction of simulated earthquake wave for hydraulic design responsespectrum[J].Northwestern Seismological Journal,2008,30(3):255-260.
[12]陈灯红,彭刚,姚艳华,等.地震波时域数值优化研究及应用[J].世界地震工程,2008,24(4):130-135.Chen Denghong,Peng Gang,Yao Yanhua,et al.Research and application on the numerical optimization of the earthquake wave time-domain[J].World Earthquake Engineering,2008,24(4):130-135.
[13]陈厚群.坝址地震动输入机制探讨[J].水利学报,2006,37(12):1417-1423.Chen Houqun.Discussion on seismic input mechanism at dam site[J].Journal of Hydraulic Engineering,2006,37(12):1417-1423.
[2]Lysmer J.,Kulemeyer R.L.Finite dynamic model for infinite media[J].Journal of Engineering Mechanics Division,ASCE,1969,95(4):759-877.
[3]Deeks A.J.,Randolph M.F.Axisymmetric time-domain transmitting boundaries[J].Journal of Engineering Mechanics Division,ASCE,1994,120(1):25-42.
[4]廖振鹏.工程波动理论导论[M].北京:科学出版社,2002.Liao Zhenpeng.Introduction to Wave Motion Theories in Engineering[M].Beijing:Science Press,2002.
[5]Andreas H.Nielsen.Absorbing boundary conditions for seismic analysis in ABAQUS[C].ABAQUS Users'Conference,Boston,Massachusetts,May 2006:359-376.
[6]刘晶波,谷音,杜义欣.一致粘弹性人工边界及粘弹性边界单元[J].岩土工程学报,2006,28(9):1070-1075.Liu Jingbo,Gu Yin,Du Yixin.Consistent viscous-spring artificial boundaries and viscous-spring boundary elements[J].Chinese Journal ofGeotechnical Engineering,2006,28(9):1070-1075.
[7]谢和平,冯夏庭.灾害环境下重大工程安全性的基础研究[M].北京:科学出版社,2009.Xie Heping,Feng Xiating.Basic Research on the Safety of Major Engineering Project in Hazardous Environments[M].Beijing:Science Press,2009.
[8]杜修力,赵密.基于粘弹性边界的拱坝地震反应分析方法[J].水利学报,2006,37(9):1063-1069.Du Xiuli,Zhao Mi.Analysis method for seismic response of arch dams in time domain based on viscous-spring artificial boundary condition[J].Journal of Hydraulic Engineering,2006,37(9):1063-1069.
[9]贺向丽.高混凝土坝抗震分析中远域能量逸散时域模拟方法研究[D].南京:河海大学,2006.He Xiangli.Study on time-domain simulating method of far field energy dissipation in seismic analysis of high concrete dams[D].Nanjing:HohaiUniversity,2006.
[10]DL5073-2000,水工建筑物抗震设计规范[S].DL5073-2000,Seismic Design of Hydraulic Structures[S].
[11]姚艳华,彭刚,陈灯红.拟合水工设计反应谱的人工地震波的生成与Huang变换校正[J].西北地震学报,2008,30(3):255-260.Yao Yanhua,Peng Gang,Chen Denghong.Synthesis and Huang transform correction of simulated earthquake wave for hydraulic design responsespectrum[J].Northwestern Seismological Journal,2008,30(3):255-260.
[12]陈灯红,彭刚,姚艳华,等.地震波时域数值优化研究及应用[J].世界地震工程,2008,24(4):130-135.Chen Denghong,Peng Gang,Yao Yanhua,et al.Research and application on the numerical optimization of the earthquake wave time-domain[J].World Earthquake Engineering,2008,24(4):130-135.
[13]陈厚群.坝址地震动输入机制探讨[J].水利学报,2006,37(12):1417-1423.Chen Houqun.Discussion on seismic input mechanism at dam site[J].Journal of Hydraulic Engineering,2006,37(12):1417-1423.
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