粘弹性人工边界的虚位移原理
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摘要
该文将结构及其近场地基作为动力平衡系统,将在人工边界上的波动分解为自由波和散射波,并将输入地震波动转化为作用于人工边界上的等效荷载以实现波动输入。基于以上假设通过分析结构及其近场地基系统的动力平衡关系和自由场的传播机制,给出了自由场的位移表达式、速度表达式,以及在人工边界上由自由场产生的等效荷载一般表达形式,最后建立了粘弹性人工边界统一的动力学积分弱解形式,同时基于有限元程序自动生成系统(FEPG)开发了粘弹性边界条件元件程序。经过计算验证:该文建立的具有粘弹性人工边界的动力学问题的积分弱解方程粘弹性边界条件元件程序可靠、正确。利用这些元件程序,在前处理中可像加位移或应力边界条件一样简便快捷地施加粘弹性边界条件。
The paper takes the structure and near-field foundation as a dynamic equilibrium system and decomposes the input wave on artificial boundaries into free waves and dispersion waves that are mutually independent.Based on the above assumptions,the paper analyzes the dynamic equilibrium relation between the structure and near-field foundation and promulgation mechanism of free fields,deduces uniform expressions of the displacement,velocity and equipollent loads acting on artificial boundaries,and then sets up the dynamical integral week equations of viscous-spring artificial boundaries.Meanwhile,based on Finite Element Program Generator(FEPG),boundary element codes are developed for viscous-spring boundary conditions.Thus viscous-spring boundary conditions can be simply and rapidly applied like general displacements and stress conditions.The computational results show that element codes are accurate and reliable.
The paper takes the structure and near-field foundation as a dynamic equilibrium system and decomposes the input wave on artificial boundaries into free waves and dispersion waves that are mutually independent.Based on the above assumptions,the paper analyzes the dynamic equilibrium relation between the structure and near-field foundation and promulgation mechanism of free fields,deduces uniform expressions of the displacement,velocity and equipollent loads acting on artificial boundaries,and then sets up the dynamical integral week equations of viscous-spring artificial boundaries.Meanwhile,based on Finite Element Program Generator(FEPG),boundary element codes are developed for viscous-spring boundary conditions.Thus viscous-spring boundary conditions can be simply and rapidly applied like general displacements and stress conditions.The computational results show that element codes are accurate and reliable.
引文
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[15]邱流潮,金峰.无限介质中波动分析的显式时域辐射边界[J].清华大学学报(自然科学版),2003,43(11):1530―1533.Qiu Liuchao,Jin Feng.Explicit time-domain radiationboundaries for analysis of wave propagation inunbounded media[J].Journal of Tsinghua University(Science and Technology),2003,43(11):1530―1533.(in Chinese)
[16]杜修力,赵密,王进廷.近场波动模拟的人工粘弹性边界条件[J].力学学报,2006,38(1):50―56.Du Xiuli,Zhao Mi,Wang Jinting.A Stress artificialboundary in FEA for near-field wave problem[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):50―56.(in Chinese)
[17]刘云贺,张伯艳,陈厚群.拱坝地震输入模型中粘弹性边界和粘性边界的比较[J].水利学报,2006,37(6):758―763.Liu Yunhe,Zhang Boyan,Chen Houqun.Comparison ofviscous-spring boundary with viscous boundary for archdam seismic input model[J].Journal of HydraulicEngineering,2006,37(6):758―763.(in Chinese)
[18]程恒,张燎军,张汉云.等效三维一致粘弹性边界单元及其在拱坝抗震分析中的应用[J].水力发电学报,2009,28(5):169―173.Cheng Heng,Zhang Liaojun,Zhang Hanyun.Applicationof 3D consistent equivalent viscous-spring boundaryelement to seismic analysis of arch dams[J].Journal ofHydroelectric Engineering,2009,28(5):169―173.(inChinese)
[19]梁国平.有限元语言[M].北京:科学出版社,2008:1―74.Liang Guoping.The finite element language[M].Beijing:Science Press,2008:1―74.(in Chinese)
[20]梁国平.有限元程序自动生成系统与有限元语言[J].力学进展,1990,20(2):199―204.Liang Guoping.Finite element program generator andfinite element language[J].Advances in Mechanics,1990,20(2):199―204.(in Chinese)
[2]Zienkievicz O C,Bettess P.Infinite element in study offluid-structure interaction problems[C]//Lions J L,Glowinski R.Computing Methods in Applied Sciences:Second International Symposium,IRIA,Versailles.France:Springer,1975:133―172.
[3]Zhang Boyan.The calculation of the free field responseof a canyon[J].Japan Society of Civil Engineers,1993,10(3):129―137.
[4]ChopraAK,Tan H.Modeling dam-foundation interactionin analysis of arch dams[C]//Alfonso Lopez Arroyo,Rafael Blazquez.Proc.10th WCEE,Rotterdam:A.A.Balkema,1992-1994:4623―4626.
[5]Dominguez J,Maeso O.Model for the seismic analysisof arch dams including interaction effects[C]//AlfonsoLopez Arroyo,Rafael Blazquez.Proc.10th WCEE,Rotterdam:A.A.Balkema,1992-1994:4601―4606.
[6]Zhang Chuhan,Jin Feng,Pekau O A.Time Domainprocedure of FE-BE-IBE coupling for seismic interactionof arch dams and canyon[J].Earthquake Engineeringand Structural Dynamic,1995,24:1651―1666.
[7]Yan Junyi,Jin Feng,Xu Yanjie,Wang Guanglun,ZhangChuhan.A seismic free field input model FE-SBFEcoupling in time domain[J].Earthquake Engineering andEngineering Vibration,2003,2(1):51―58.
[8]陈健云,李建波,林皋,马秀平.结构-地基动力相互作用时域数值分析的显-隐式分区异步长递归算法[J].岩石力学与工程学报,2007,26(12):2481―2487.Chen Jianyun,Li Jianbo,Lin Gao,Ma Xiuping.Asub-regional explicit-implicit recursive method withmixed step-size strategy in time domain for dynamicstructure-foundation interaction analysis[J].ChineseJournal of Rock Mechanics and Engineering,2007,26(12):2481―2487.(in Chinese)
[9]Li J B,Yang J,Lin G.A stepwise damping-solventextraction method for large-scale dynamic soil-structureinteraction analysis in time domain[J].InternationalJournal for Numerical and Analytical Methods inGeomechanics,2008,32:415―436.
[10]刘晶波,吕彦东.结构-地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998,31(3):55―64.Liu Jingbo,LüYandong.A direct method for analysis ofdynamic soil-structure interaction[J].Journal of CivilEngineering,1998,31(3):55―64.(in Chinese)
[11]Deeks A J,Randolph M F.Axisymmetric time-domaintransmitting boundaries[J].Journal of EngineeringMechanics,1994,120(1):25―42.
[12]廖振鹏.工程波动理论导论[M].第2版.北京:科学出版社,2002:136―187.Liao Zhenpeng.Introduction to wave motion theories inengineering[M].2nd ed.Beijing:Science Press,2002:136―187.(in Chinese)
[13]赵建锋,杜修力,韩强,李立云.外源波动问题数值模拟的一种实现方式[J].工程力学,2007,24(4):52―58.Zhao Jianfeng,Du Xiuli,Han Qiang,Li Liyun.Anapproach to numerical simulation for external sourcewave motion[J].Engineering Mechanics,2007,24(4):52―58.(in Chinese)
[14]刘晶波,王振宇,杜修力,杜义欣.波动问题中的三维时域粘弹性人工边界[J].工程力学,2005,22(6):46―51.Liu Jingbo,Wang Zhenyu,Du Xiuli,Du Yixin.Three-dimensional visco-elastic artificial boundaries intime domain for wave motion problems[J].EngineeringMechanics,2005,22(6):46―51.(in Chinese)
[15]邱流潮,金峰.无限介质中波动分析的显式时域辐射边界[J].清华大学学报(自然科学版),2003,43(11):1530―1533.Qiu Liuchao,Jin Feng.Explicit time-domain radiationboundaries for analysis of wave propagation inunbounded media[J].Journal of Tsinghua University(Science and Technology),2003,43(11):1530―1533.(in Chinese)
[16]杜修力,赵密,王进廷.近场波动模拟的人工粘弹性边界条件[J].力学学报,2006,38(1):50―56.Du Xiuli,Zhao Mi,Wang Jinting.A Stress artificialboundary in FEA for near-field wave problem[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):50―56.(in Chinese)
[17]刘云贺,张伯艳,陈厚群.拱坝地震输入模型中粘弹性边界和粘性边界的比较[J].水利学报,2006,37(6):758―763.Liu Yunhe,Zhang Boyan,Chen Houqun.Comparison ofviscous-spring boundary with viscous boundary for archdam seismic input model[J].Journal of HydraulicEngineering,2006,37(6):758―763.(in Chinese)
[18]程恒,张燎军,张汉云.等效三维一致粘弹性边界单元及其在拱坝抗震分析中的应用[J].水力发电学报,2009,28(5):169―173.Cheng Heng,Zhang Liaojun,Zhang Hanyun.Applicationof 3D consistent equivalent viscous-spring boundaryelement to seismic analysis of arch dams[J].Journal ofHydroelectric Engineering,2009,28(5):169―173.(inChinese)
[19]梁国平.有限元语言[M].北京:科学出版社,2008:1―74.Liang Guoping.The finite element language[M].Beijing:Science Press,2008:1―74.(in Chinese)
[20]梁国平.有限元程序自动生成系统与有限元语言[J].力学进展,1990,20(2):199―204.Liang Guoping.Finite element program generator andfinite element language[J].Advances in Mechanics,1990,20(2):199―204.(in Chinese)
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