地震分析中的人工边界及其在LS-DYNA中的实现
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摘要
地震分析中的局部人工边界由于具有易于实现、稳定性较好的特点,目前在时域有限元法中得到广泛应用。基于球坐标系的膨胀波(P波)和剪切波(S波)理论,引入无限介质线弹性本构关系,并采用多个平面子波和远场散射波混合透射,推导一种新的三维黏弹性人工边界方程。在有限元分析中采用边界单元作等效处理,并将地震加速度记录转化为基底边界单元上的等效节点力进行输入,建立一种新的地震反应数值模拟技术。最后以人防工程结构的地震分析为例,利用有限元软件LS-DYNA分析弹性边界、透射边界及黏弹性边界对计算结果的影响。数值模拟表明,黏弹性人工边界简单实用,可解决地震动输入和自由场响应模拟问题,能更好地模拟人工边界外半无限介质的弹性恢复性能和能量辐射作用,并验证其有效性。
Local artificial boundary of seismic analysis is widely used in time-domain finite element method for its good feasibility and high numerical stability.A new equation for three-dimensional viscoelastic artificial boundary based on the theories of expansion wave(P-wave) motion and shear wave(S-wave) motion in spherical coordinate system is presented by introducing the constitutive relation of linear elastic infinite media and mixing the planar waves and the far-field scattered waves.A new numerical simulation technology for seismic responses is developed by introducing the equivalent boundary element into the finite element method and translating the seismic acceleration into the equivalent nodal force of boundary element on the bottom of the model.Finally,as a numerical example of seismic analysis for civil defense structure,the influences of elastic,transmission,viscoelastic boundary on the results are conducted by LS-DYNA.It is indicated that the viscoelastic artificial boundary is simple and can be easily used.The problems of seismic input and simulation of ground response are solved,and the elastic resume capability and energy radiation effectiveness of half infinite media outside the artificial boundary can be simulated very well.The validity of the proposed method is verified by the numerical example.
Local artificial boundary of seismic analysis is widely used in time-domain finite element method for its good feasibility and high numerical stability.A new equation for three-dimensional viscoelastic artificial boundary based on the theories of expansion wave(P-wave) motion and shear wave(S-wave) motion in spherical coordinate system is presented by introducing the constitutive relation of linear elastic infinite media and mixing the planar waves and the far-field scattered waves.A new numerical simulation technology for seismic responses is developed by introducing the equivalent boundary element into the finite element method and translating the seismic acceleration into the equivalent nodal force of boundary element on the bottom of the model.Finally,as a numerical example of seismic analysis for civil defense structure,the influences of elastic,transmission,viscoelastic boundary on the results are conducted by LS-DYNA.It is indicated that the viscoelastic artificial boundary is simple and can be easily used.The problems of seismic input and simulation of ground response are solved,and the elastic resume capability and energy radiation effectiveness of half infinite media outside the artificial boundary can be simulated very well.The validity of the proposed method is verified by the numerical example.
引文
[1]李彬.地铁地下结构抗震理论分析与应用研究[博士学位论文][D].北京:清华大学,2005.(LI Bin.Theoretical analysis of seismic response of underground subway structures and its application[Ph.D.Thesis][D].Beijing:Tsinghua University,2005.(in Chinese))
[2]廖振鹏.工程波动理论导论[M].2版.北京:科学出版社,2002.(LIAO Zhenpeng.Introduction to wave motion theories in enginee-ring[M].2nd ed.Beijing:Science Press,2002.(in Chinese))
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[4]LYSMER J,KUHLEMEYER R L.Finite dynamic model for infinite media[J].Journal of Engineering Mechanics,1969,95(4):759-777.
[5]DEEKS A J,RANDOLPH M F.Axisymmetric time-domain trans-mitting boundaries[J].Journal of Engineering Mechanics,1994,120(1):25-42.
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[7]CLAYTON R W,ENGQUIST B.Absorbing boundary conditions foracoustic and elastic wave equations[J].Bulletin of the Seismological Society of America,1977,67(6):1529-1540.
[8]HEIDARI A H,GUDDATI M N.Highly accurate absorbing boundary conditions for wide-angle wave equations[J].Geophysics,2006,71(3):85-97.
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[11]刘晶波,王艳.成层介质中平面内自由波场的一维化时域算法[J].工程力学,2007,24(7):16-22.(LIU Jingbo,WANG Yan.A1D time-domain method for in-plain wave motion of free field in layered media[J].Engineering Mechanics,2007,24(7):16-22.(in Chinese))
[12]朱志辉,尚守平,吴方伯.土-结构动力相互作用人工边界分析及试验验证[J].地震工程与工程振动,2007,27(3):137-143.(ZHU Zhihui,SHANG Shouping,WU Fangbo.Artificial boundary analysis of dynamic soil-sturcture interaction with test verification[J].Journal of Earthquake Engineering and Engineering Vibration,2007,27(3):137-143.(in Chinese))
[13]杜修力,赵密,王进廷.近场波动模拟的人工边界条件[J].力学学报,2006,38(1):49-56.(DU Xiuli,ZHAO Mi,WANG Jinting.A stress artificial fea for near-field wave problem[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):49-56.(in Chinese))
[14]ACHENBACH J D.Wave propagation in elastic solids[M].Amsterdam:North-Holland Pub.Co.,1973.
[15]吴艺,房营光.弹塑性地基中黏性与黏弹性人工边界条件有效性的验证[J].岩石力学与工程学报,2006,25(2):3468-3473.(WU Yi,FANG Yingguang.Validity of viscous and viscous-elastic artificial boundary conditions for elasto-plastic foundation[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(2):3468-3473.(in Chinese))
[16]AKI K,RICHARDS P G.Quantitative seismology theory and methods,vol.I:theory and methods(hardcover)[M].[S.l.]:W.H.Freeman and Company,1980.
[17]HUSHMAND B,SCOTT R F,CROUSE C B.Centrifuge lique-faction tests in a laminar box[J].Geotechnique,1988,38(2):253-262.
[18]HALLQUIST J Q.LS-DYNA theoretical manual[M].Livemore:Livermore Software Technology Corporation,1988.
[19]Livermore Software Technology Corporation.LS-DYNA keyword user′s manual(970V)[M].Livemore:Livermore Software Technology Corporation,2003.
[20]MALVAR L J,CRAWFORD J E,WESEVICH J W,et al.A plasticity concrete material model for DYNA3D[J].International Journal of Impact Engineering,1997,19(9/10):847-873.
[21]谷音,刘晶波,杜义欣.三维一致黏弹性人工边界及等效黏弹性边界单元[J].工程力学,2007,24(12):31-37.(GU Yin,LIU Jingbo,DU Yixin.3D consistent viscous-spring artificial boundary and viscous-spring boundary element[J].Engineering Mechanics,2007,24(12):31-37.(in Chinese))
[22]陈正发.黏性土地基中地铁隧道动力离心模型试验系统开发[硕士学位论文][D].北京:清华大学,2005.(CHEN Zhengfa.Development of the test system for dynamic centrifuge modeling of subway tunnel in clayey ground[M.S.Thesis][D].Beijing:Tsinghua University,2005.(in Chinese))
[23]刘光磊.饱和地基中地铁地下结构地震反应机制研究[博士学位论文][D].北京:清华大学,2007.(LIU Guanglei.Research on the seismic response mechanism of underground subway structures in saturated soil[Ph.D.Thesis][D].Beijing:Tsinghua University,2007.(in Chinese))
[24]刘军,林皋.地震作用下大体积混凝土结构损伤发展估计[J].大连理工大学学报,2007,47(2):228-232.(LIU Jun,LIN Gao.Prediction of damage evolution of massive concrete structure subjected to earthquake excitation[J].Journal of Dalian University of Technology,2007,47(2):228-232.(in Chinese))
[25]邱流潮,刘桦,金峰.二维土-结构地震动力相互作用时域有限元分析[J].工程力学,2006,23(9):114-119.(QIU Liuchao,LIU Hua,JIN Feng.Time-domain finite-element analysis of two dimensional seismic soil-structure interactions[J].Engineering Mechanics,2006,23(9):114-119.(in Chinese))
[26]邱流潮,金峰.地震分中人工边界处理与地震动入方法研究[J].岩土力学,2006,27(9):1501-1504.(QIU Liuchao,JIN Feng.Study on method of earthquake input and artificial boundary conditions for seismic soil-structure interaction analysis[J].Rock and Soil Mechanics,2006,27(9):1501-1504.(in Chinese))
[27]张克绪,谢君斐.土动力学[M].北京:地震出版社,1989.(ZHANG Kexu,XIE Junfei.Soil dynamics[M].Beijing:Earthquake Press,1989.(in Chinese))
[2]廖振鹏.工程波动理论导论[M].2版.北京:科学出版社,2002.(LIAO Zhenpeng.Introduction to wave motion theories in enginee-ring[M].2nd ed.Beijing:Science Press,2002.(in Chinese))
[3]赵密.黏弹性人工边界及其与透射人工边界的比较研究[硕士学位论文][D].北京:北京工业大学,2004.(ZHAO Mi.Study on the viscous-spring boundary and the transmitting boundary[M.S.Thesis][D].Beijing:Beijing University of Technology,2004.(in Chinese))
[4]LYSMER J,KUHLEMEYER R L.Finite dynamic model for infinite media[J].Journal of Engineering Mechanics,1969,95(4):759-777.
[5]DEEKS A J,RANDOLPH M F.Axisymmetric time-domain trans-mitting boundaries[J].Journal of Engineering Mechanics,1994,120(1):25-42.
[6]ANG H S,Newmark N M.Development of a transmitting boundary for numerical wave motion calculation[R].[S.l.]:Defense Atomic Support Agency,1972.
[7]CLAYTON R W,ENGQUIST B.Absorbing boundary conditions foracoustic and elastic wave equations[J].Bulletin of the Seismological Society of America,1977,67(6):1529-1540.
[8]HEIDARI A H,GUDDATI M N.Highly accurate absorbing boundary conditions for wide-angle wave equations[J].Geophysics,2006,71(3):85-97.
[9]CHEN S H,LIU Y J.A unified boundary element method for the analysis of sound and shell-like structure interactions II.efficient solution techniques[J].Journal of the Acoustical Society of America,2000,108(6):2738-2745.
[10]王振宇,刘晶波.成层地基非线性波动问题人工边界与波动输入研究[J].岩石力学与工程学报,2004,23(7):1169-1173.(WANG Zhenyu,LIU Jingbo.Study on wave motion input and artificial boundary for problem of nonlinear wave motion in layered soil[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(7):1169-1173.(in Chinese))
[11]刘晶波,王艳.成层介质中平面内自由波场的一维化时域算法[J].工程力学,2007,24(7):16-22.(LIU Jingbo,WANG Yan.A1D time-domain method for in-plain wave motion of free field in layered media[J].Engineering Mechanics,2007,24(7):16-22.(in Chinese))
[12]朱志辉,尚守平,吴方伯.土-结构动力相互作用人工边界分析及试验验证[J].地震工程与工程振动,2007,27(3):137-143.(ZHU Zhihui,SHANG Shouping,WU Fangbo.Artificial boundary analysis of dynamic soil-sturcture interaction with test verification[J].Journal of Earthquake Engineering and Engineering Vibration,2007,27(3):137-143.(in Chinese))
[13]杜修力,赵密,王进廷.近场波动模拟的人工边界条件[J].力学学报,2006,38(1):49-56.(DU Xiuli,ZHAO Mi,WANG Jinting.A stress artificial fea for near-field wave problem[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):49-56.(in Chinese))
[14]ACHENBACH J D.Wave propagation in elastic solids[M].Amsterdam:North-Holland Pub.Co.,1973.
[15]吴艺,房营光.弹塑性地基中黏性与黏弹性人工边界条件有效性的验证[J].岩石力学与工程学报,2006,25(2):3468-3473.(WU Yi,FANG Yingguang.Validity of viscous and viscous-elastic artificial boundary conditions for elasto-plastic foundation[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(2):3468-3473.(in Chinese))
[16]AKI K,RICHARDS P G.Quantitative seismology theory and methods,vol.I:theory and methods(hardcover)[M].[S.l.]:W.H.Freeman and Company,1980.
[17]HUSHMAND B,SCOTT R F,CROUSE C B.Centrifuge lique-faction tests in a laminar box[J].Geotechnique,1988,38(2):253-262.
[18]HALLQUIST J Q.LS-DYNA theoretical manual[M].Livemore:Livermore Software Technology Corporation,1988.
[19]Livermore Software Technology Corporation.LS-DYNA keyword user′s manual(970V)[M].Livemore:Livermore Software Technology Corporation,2003.
[20]MALVAR L J,CRAWFORD J E,WESEVICH J W,et al.A plasticity concrete material model for DYNA3D[J].International Journal of Impact Engineering,1997,19(9/10):847-873.
[21]谷音,刘晶波,杜义欣.三维一致黏弹性人工边界及等效黏弹性边界单元[J].工程力学,2007,24(12):31-37.(GU Yin,LIU Jingbo,DU Yixin.3D consistent viscous-spring artificial boundary and viscous-spring boundary element[J].Engineering Mechanics,2007,24(12):31-37.(in Chinese))
[22]陈正发.黏性土地基中地铁隧道动力离心模型试验系统开发[硕士学位论文][D].北京:清华大学,2005.(CHEN Zhengfa.Development of the test system for dynamic centrifuge modeling of subway tunnel in clayey ground[M.S.Thesis][D].Beijing:Tsinghua University,2005.(in Chinese))
[23]刘光磊.饱和地基中地铁地下结构地震反应机制研究[博士学位论文][D].北京:清华大学,2007.(LIU Guanglei.Research on the seismic response mechanism of underground subway structures in saturated soil[Ph.D.Thesis][D].Beijing:Tsinghua University,2007.(in Chinese))
[24]刘军,林皋.地震作用下大体积混凝土结构损伤发展估计[J].大连理工大学学报,2007,47(2):228-232.(LIU Jun,LIN Gao.Prediction of damage evolution of massive concrete structure subjected to earthquake excitation[J].Journal of Dalian University of Technology,2007,47(2):228-232.(in Chinese))
[25]邱流潮,刘桦,金峰.二维土-结构地震动力相互作用时域有限元分析[J].工程力学,2006,23(9):114-119.(QIU Liuchao,LIU Hua,JIN Feng.Time-domain finite-element analysis of two dimensional seismic soil-structure interactions[J].Engineering Mechanics,2006,23(9):114-119.(in Chinese))
[26]邱流潮,金峰.地震分中人工边界处理与地震动入方法研究[J].岩土力学,2006,27(9):1501-1504.(QIU Liuchao,JIN Feng.Study on method of earthquake input and artificial boundary conditions for seismic soil-structure interaction analysis[J].Rock and Soil Mechanics,2006,27(9):1501-1504.(in Chinese))
[27]张克绪,谢君斐.土动力学[M].北京:地震出版社,1989.(ZHANG Kexu,XIE Junfei.Soil dynamics[M].Beijing:Earthquake Press,1989.(in Chinese))
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