成层介质中平面内自由波场的一维化时域算法
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摘要
提出了一种弹性水平成层半空间中平面内波动斜入射时自由波场时域计算的一维化有限元方法。首先,基于弹性波在斜入射情形下的传播特点对计算区域进行自动虚拟网格划分。然后将集中质量有限元法和中心差分法相结合建立节点的二维运动方程组,并根据采用的离散化准则和显式有限元法的特点将其转化为一维方程组。求解此方程组,即得到自由场中竖向一列节点的运动。最后根据行波的传播规律得到全部自由波场。以P波为例给出了理论分析和数值算例。结果表明,该方法不仅简单实用,而且具有较高的精度和良好的稳定性。
A 1D finite element method in time domain is developed, which is used to calculate the in-plane wave motion of free field in elastic layered semispace by oblique seismic incidence. First, the layered semispace is discretized virtually according to the propagation characteristic of elastic wave. Then, the finite element method with lumped mass and the central difference method are combined together to establish the 2D wave motion equations. On the basis of the discretization principle and by the advantage of the explicit finite element method, the 2D wave motion equations can be transformed into 1D equations. By solving the 1D equations, the displacement of nodes in one vertical line can be obtained. Finally, the wave motions of the whole free field are determined on the basis of the characteristic of traveling wave. As an example, P-wave is assumed as the incident wave. Theoretical analysis and numerical results demonstrate that the proposed method possesses high accuracy and good stability.
A 1D finite element method in time domain is developed, which is used to calculate the in-plane wave motion of free field in elastic layered semispace by oblique seismic incidence. First, the layered semispace is discretized virtually according to the propagation characteristic of elastic wave. Then, the finite element method with lumped mass and the central difference method are combined together to establish the 2D wave motion equations. On the basis of the discretization principle and by the advantage of the explicit finite element method, the 2D wave motion equations can be transformed into 1D equations. By solving the 1D equations, the displacement of nodes in one vertical line can be obtained. Finally, the wave motions of the whole free field are determined on the basis of the characteristic of traveling wave. As an example, P-wave is assumed as the incident wave. Theoretical analysis and numerical results demonstrate that the proposed method possesses high accuracy and good stability.
引文
[1]沈聚敏,周锡元,高小旺,刘晶波.抗震工程学[M].北京:中国建筑工业出版社,2000.Shen Jumin,Zhou Xiyuan,Gao Xiaowang,Liu Jingbo.Aseismic engineering[M].Beijing:China Architecture and Building Press,2000.(in Chinese)
[2]廖振鹏,郑天愉.工程地震学在中国的发展[J].地球物理学报,1997,40(S1):177～191.Liao Zhenpeng,Zheng Tianyu.Development of engineering seismology in China[J].Acta Geophysica Sinica,1997,40(S1):177～191.(in Chinese)
[3]Wolf J P,Obernhuber P.Effects of horizontally traveling waves in soil-structure interaction[J].Nuclear Engineering and Design,1979,57(2):221～244.
[4]李山有,廖振鹏,周正华.大型结构地震反应数值模拟中的波动输入[J].地震工程与工程振动,2001,6(2):1～5.Li Shanyou,Liao Zhenpeng,Zhou Zhenghua.Wave motion input in numerical simulation of seismic response for large-scale structure[J].Earthquake Engineering and Engineering Vibration,2001,6(2):1～5.(in Chinese)
[5]Pao Y H,Mow C C.The diffraction of elastic waves and dynamic stress concentration[M].New York:Crane&Russak,1973.
[6]Liu D K,Gai B Z,Tao G Y.Applications of the method of complex function to dynamic stress concentration[J].Wave Motion,1982,(4):293～304.
[7]Haskell N A.The dispersion of surface waves in multi-layered media[J].Bulletin of the Seismic Society of American,1953,43:17～34.
[8]Brekhovshikh L M.Waves in layered media[M].New York:Academic Press Inc.,1980.
[9]刘晶波,王艳.成层半空间出平面自由波场的一维化时域算法[J].力学学报,2006,38(2):219～225.Liu Jingbo,Wang Yan.A1D time-domain method for2D wave motion in elastic layered half-space by antiplane wave oblique incidence[J].Acta Mechanic Sinica,2006,38(2):219～225.(in Chinese)
[10]黎在良,刘殿魁.固体中的波[M].北京:科学出版社,1995.Li Zailiang,Liu Diankui.Wave motion in solid[M].Beijing:Science Press,1995.(in Chinese)
[11]廖振鹏.近场波动问题的有限元解法[J].地震工程与工程振动,1984,4(2):1～14.Liao Zhenpeng.The finite element solution of near-field wave motion problem[J].Earthquake Engineering and Engineering Vibration,1984,4(2):1～14.(in Chinese)
[12]廖振鹏.近场波动的数值模拟[J].力学进展,1997,27(2):193～212.Liao Zhenpeng.Numerical simulation of near-field wave motion[J].Advances in Mechanics,1997,27(2):193～212.(in Chinese)
[13]Lysmer J,Kulemeyer R L.Finite dynamic model for infinite media[J].Journal of Engineering Mechanics,ASCE,1969,95:759～877.
[14]廖振鹏,黄孔亮,杨柏坡.暂态波透射边界[J].中国科学A辑,1984,14(6):556～564.Liao Zhenpeng,Huang Kongliang,Yang Baipo.A transmitting boundary for transient wave analysis[J].Science in China(Series A),1984,27(10):1063～1076.(in English)
[15]廖振鹏.透射边界与无穷远辐射条件[J].中国科学E辑,2001,31(3):254～262.Liao Zhenpeng.Transmitting boundary and radiation conditions at infinity[J].Science in China(Series E),2001,44(2):177～186.(in English)
[16]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,Lu Yandong.A direct method for analysis of dynamic soil-structure interaction[J].China Civil Engineering Journal,1998,31(3):55～64.(in Chinese)
[17]Liu Jingbo,Liao Zhenpeng.In-plane wave motion in finite element model[J].Acta Mechanica Sinica,1992,8(1):80～87.
[18]傅淑芳,刘宝诚.地震学教程[M].北京:地震出版社,1991.Fu Shufang,Liu Baocheng.Seismology tutorial[M].Beijing:Seismic Press,1991.(in Chinese)
[2]廖振鹏,郑天愉.工程地震学在中国的发展[J].地球物理学报,1997,40(S1):177～191.Liao Zhenpeng,Zheng Tianyu.Development of engineering seismology in China[J].Acta Geophysica Sinica,1997,40(S1):177～191.(in Chinese)
[3]Wolf J P,Obernhuber P.Effects of horizontally traveling waves in soil-structure interaction[J].Nuclear Engineering and Design,1979,57(2):221～244.
[4]李山有,廖振鹏,周正华.大型结构地震反应数值模拟中的波动输入[J].地震工程与工程振动,2001,6(2):1～5.Li Shanyou,Liao Zhenpeng,Zhou Zhenghua.Wave motion input in numerical simulation of seismic response for large-scale structure[J].Earthquake Engineering and Engineering Vibration,2001,6(2):1～5.(in Chinese)
[5]Pao Y H,Mow C C.The diffraction of elastic waves and dynamic stress concentration[M].New York:Crane&Russak,1973.
[6]Liu D K,Gai B Z,Tao G Y.Applications of the method of complex function to dynamic stress concentration[J].Wave Motion,1982,(4):293～304.
[7]Haskell N A.The dispersion of surface waves in multi-layered media[J].Bulletin of the Seismic Society of American,1953,43:17～34.
[8]Brekhovshikh L M.Waves in layered media[M].New York:Academic Press Inc.,1980.
[9]刘晶波,王艳.成层半空间出平面自由波场的一维化时域算法[J].力学学报,2006,38(2):219～225.Liu Jingbo,Wang Yan.A1D time-domain method for2D wave motion in elastic layered half-space by antiplane wave oblique incidence[J].Acta Mechanic Sinica,2006,38(2):219～225.(in Chinese)
[10]黎在良,刘殿魁.固体中的波[M].北京:科学出版社,1995.Li Zailiang,Liu Diankui.Wave motion in solid[M].Beijing:Science Press,1995.(in Chinese)
[11]廖振鹏.近场波动问题的有限元解法[J].地震工程与工程振动,1984,4(2):1～14.Liao Zhenpeng.The finite element solution of near-field wave motion problem[J].Earthquake Engineering and Engineering Vibration,1984,4(2):1～14.(in Chinese)
[12]廖振鹏.近场波动的数值模拟[J].力学进展,1997,27(2):193～212.Liao Zhenpeng.Numerical simulation of near-field wave motion[J].Advances in Mechanics,1997,27(2):193～212.(in Chinese)
[13]Lysmer J,Kulemeyer R L.Finite dynamic model for infinite media[J].Journal of Engineering Mechanics,ASCE,1969,95:759～877.
[14]廖振鹏,黄孔亮,杨柏坡.暂态波透射边界[J].中国科学A辑,1984,14(6):556～564.Liao Zhenpeng,Huang Kongliang,Yang Baipo.A transmitting boundary for transient wave analysis[J].Science in China(Series A),1984,27(10):1063～1076.(in English)
[15]廖振鹏.透射边界与无穷远辐射条件[J].中国科学E辑,2001,31(3):254～262.Liao Zhenpeng.Transmitting boundary and radiation conditions at infinity[J].Science in China(Series E),2001,44(2):177～186.(in English)
[16]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,Lu Yandong.A direct method for analysis of dynamic soil-structure interaction[J].China Civil Engineering Journal,1998,31(3):55～64.(in Chinese)
[17]Liu Jingbo,Liao Zhenpeng.In-plane wave motion in finite element model[J].Acta Mechanica Sinica,1992,8(1):80～87.
[18]傅淑芳,刘宝诚.地震学教程[M].北京:地震出版社,1991.Fu Shufang,Liu Baocheng.Seismology tutorial[M].Beijing:Seismic Press,1991.(in Chinese)
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