P-SV波斜入射时成层半空间自由场的时域算法
|
摘要
刘晶波和王艳提出了一种弹性水平成层半空间中平面P-SV波斜入射时平面内自由波场时域计算的一维化有限元方法,该方法采用黏性人工边界条件近似地模拟下部基岩半空间的辐射阻尼,可导致平面P-SV波以大角度入射时自由场计算精度降低。本文提出一种精确模拟基岩半空间辐射阻尼的人工边界条件。由于基岩半空间中外行波是传播方向已知的平面P波和SV波,利用弹性介质的应力—位移本构关系建立了人工边界处应力与速度的阻抗边界条件;采用该人工边界条件替代黏性边界条件,改进了P-SV波斜入射时成层半空间自由场的时域算法。数值试验表明,与采用黏性边界条件的自由场算法相比,改进方法具有更高的计算精度,其计算结果与理论解吻合更好。
A 1D finite element method in time domain has been proposed by Liu and Wang for calculating the in-plane free wave field in elastic layered half space under the plane P and SV waves of oblique incidence(Engineering Mechanics,2007,24(7): 16-22(in Chinese) and Acta Mechanica Sinica,2007,23: 673-680).The viscous artificial boundary condition is used in this method to approximately model the radiation damping of underlying bedrock half space.This leads to the 1D finite element method with low accuracy.An artificial boundary condition is proposed in this paper,which can exactly model the radiation damping of bedrock half space.Due to that the outgoing waves in bedrock are the plane P and SV waves with known propagation directions,using the constitutive relation between stress and displacement in elastic media,the impedance boundary condition between stress and velocity on artificial boundary is developed.The 1D finite element method is further improved by using the new artificial boundary condition to replace the viscous boundary condition.Numerical examples indicate that the improved 1D finite element method has the higher accuracy than the original method,and the solution using the improved method is identical very well with the theoretical solution.
A 1D finite element method in time domain has been proposed by Liu and Wang for calculating the in-plane free wave field in elastic layered half space under the plane P and SV waves of oblique incidence(Engineering Mechanics,2007,24(7): 16-22(in Chinese) and Acta Mechanica Sinica,2007,23: 673-680).The viscous artificial boundary condition is used in this method to approximately model the radiation damping of underlying bedrock half space.This leads to the 1D finite element method with low accuracy.An artificial boundary condition is proposed in this paper,which can exactly model the radiation damping of bedrock half space.Due to that the outgoing waves in bedrock are the plane P and SV waves with known propagation directions,using the constitutive relation between stress and displacement in elastic media,the impedance boundary condition between stress and velocity on artificial boundary is developed.The 1D finite element method is further improved by using the new artificial boundary condition to replace the viscous boundary condition.Numerical examples indicate that the improved 1D finite element method has the higher accuracy than the original method,and the solution using the improved method is identical very well with the theoretical solution.
引文
[1]Wolf J P.Dynamic Soil-Structure Interaction[M].Engle-wood Cliffs:Prentice-Hall,1985.
[2]徐海滨,杜修力,赵密,等.地震波斜入射对高拱坝地震反应的影响[J].水力发电学报,2011,30(6):159-165.XU Hai-bin,DU Xiu-li,ZHAO Mi,et al.Effect of Oblique Incidence of Seismic Waves on Seismic Responses of High Arch Dam[J].Journal of Hydroelectric Engineering,2011,30(6):159-165.
[3]苑举卫,杜成斌,刘志明.地震波斜入射条件下重力坝动力响应分析[J].振动与冲击,2011,30(7):120-126.YUAN Wei-ju,DU Chen-bin,LIU Zhi-ming.Time-domain Seismic Response for Gravity Dam to Obliquely Incident and Seismic Waves[J].Journal of Vibration and Shock,2011,30(7):120-126.
[4]郜新军,赵成刚,刘秦.地震波斜入射下考虑局部地形影响和土结动力相互作用的多跨桥动力响应分析[J].工程力学,2011,28(11):237-243.GAO Xin-jun,ZHAO Cheng-gang,LIU Qin.Seismic Re-sponse Analysis of Multi-span Viaduct Considering Topo-graphic Effect and Soil-structure Dynamic Interaction Based onInclined Wave[J].Engineering Mechanics,2011,28(11):237-243.
[5]傅淑芳,刘宝诚.地震学教程[M].北京:地震出版社,1991.FU Shu-fang,LIU Bao-cheng.Seismology Tutoria[M]l.Bei-jing:Seismic Press,1991.
[6]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 Jing-bo,WANG Yan.A1-D Time-domain Method for2-D Wave Motion in Elastic Layered Half-space by AntiplaneWave Oblique Incidence[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(2):219-225.
[7]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 Jing-bo,WANG Yan.A1DTime-domain Method for In-plane Wave Motion of Free Field in Layered Media[J].Engi-neering Mechanics,2007,24(7):16-22.
[8]LIU Jing-bo,WANG Yan.A1DTime-domain Method for in-plane Wave Motions in A Layered Half-space[J].Acta Me-chanica Sinica,2007,23:673-680.
[9]王艳.非一致地震动场数值方法研究及在结构动力分析中的应用[D].北京:清华大学,2007.WANG Yan.Research on the Numerical Method for Asyn-chronous Seismic Wave Motions and Its Application in Dynamic Analysis of Structures[D].Beijing:Tsinghua University,2007.
[10]Lysmer J,Kulemeyer R.Finite Dynamic Model for Infinite Media[J].Journal of Engineering Mechanics,ASCE,1969,95:759-877.
[11]LIU Jing-bo,LYan-dong.A Direct Method for Analysis of Dynamic Soil-structure Interaction Based on Interface Idea[A]//Proceedings of the Chinese-Swiss Workshop on Dy-namic Soil-Structure Interaction[C].Beijing:International Academic Publishers,1997.
[12]杜修力,赵密,王进廷.近场波动模拟的人工应力边界条件[J].力学学报,2006,38(1):49-56.DU Xiu-li,ZHAO Mi,WANG Jin-ting.A Stress ArtificialBoundary in FEA for Near-field Wave Problem[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):49-56.
[13]廖振鹏.工程波动理论导论(第二版)[M].北京:科学出版社,2002.LIAO Zhen-peng.Introduction to Wave Motion Theories for Engineering(Second Edition)[M].Beijing:Science Press,2002.
[14]DU Xiu-li,ZHAO Mi.A local Time-domain Transmitting Boundary for Simulating Cylindrical Elastic Wave Propaga-tion in Infinite Media[J].Soil Dynamics and Earthquake En-gineering,2010,30(10):937-946.
[15]ZHAO Mi,DU Xiu-li,LIU Jing-bo,et al.Explicit Finite El-ement Artificial Boundary Scheme for Transient Scalar Wavesin Two-dimensional Unbounded Waveguide[J].International Journal for Numerical Methods in Engineering,2011,87(11):1074-1104.
[2]徐海滨,杜修力,赵密,等.地震波斜入射对高拱坝地震反应的影响[J].水力发电学报,2011,30(6):159-165.XU Hai-bin,DU Xiu-li,ZHAO Mi,et al.Effect of Oblique Incidence of Seismic Waves on Seismic Responses of High Arch Dam[J].Journal of Hydroelectric Engineering,2011,30(6):159-165.
[3]苑举卫,杜成斌,刘志明.地震波斜入射条件下重力坝动力响应分析[J].振动与冲击,2011,30(7):120-126.YUAN Wei-ju,DU Chen-bin,LIU Zhi-ming.Time-domain Seismic Response for Gravity Dam to Obliquely Incident and Seismic Waves[J].Journal of Vibration and Shock,2011,30(7):120-126.
[4]郜新军,赵成刚,刘秦.地震波斜入射下考虑局部地形影响和土结动力相互作用的多跨桥动力响应分析[J].工程力学,2011,28(11):237-243.GAO Xin-jun,ZHAO Cheng-gang,LIU Qin.Seismic Re-sponse Analysis of Multi-span Viaduct Considering Topo-graphic Effect and Soil-structure Dynamic Interaction Based onInclined Wave[J].Engineering Mechanics,2011,28(11):237-243.
[5]傅淑芳,刘宝诚.地震学教程[M].北京:地震出版社,1991.FU Shu-fang,LIU Bao-cheng.Seismology Tutoria[M]l.Bei-jing:Seismic Press,1991.
[6]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 Jing-bo,WANG Yan.A1-D Time-domain Method for2-D Wave Motion in Elastic Layered Half-space by AntiplaneWave Oblique Incidence[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(2):219-225.
[7]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 Jing-bo,WANG Yan.A1DTime-domain Method for In-plane Wave Motion of Free Field in Layered Media[J].Engi-neering Mechanics,2007,24(7):16-22.
[8]LIU Jing-bo,WANG Yan.A1DTime-domain Method for in-plane Wave Motions in A Layered Half-space[J].Acta Me-chanica Sinica,2007,23:673-680.
[9]王艳.非一致地震动场数值方法研究及在结构动力分析中的应用[D].北京:清华大学,2007.WANG Yan.Research on the Numerical Method for Asyn-chronous Seismic Wave Motions and Its Application in Dynamic Analysis of Structures[D].Beijing:Tsinghua University,2007.
[10]Lysmer J,Kulemeyer R.Finite Dynamic Model for Infinite Media[J].Journal of Engineering Mechanics,ASCE,1969,95:759-877.
[11]LIU Jing-bo,LYan-dong.A Direct Method for Analysis of Dynamic Soil-structure Interaction Based on Interface Idea[A]//Proceedings of the Chinese-Swiss Workshop on Dy-namic Soil-Structure Interaction[C].Beijing:International Academic Publishers,1997.
[12]杜修力,赵密,王进廷.近场波动模拟的人工应力边界条件[J].力学学报,2006,38(1):49-56.DU Xiu-li,ZHAO Mi,WANG Jin-ting.A Stress ArtificialBoundary in FEA for Near-field Wave Problem[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):49-56.
[13]廖振鹏.工程波动理论导论(第二版)[M].北京:科学出版社,2002.LIAO Zhen-peng.Introduction to Wave Motion Theories for Engineering(Second Edition)[M].Beijing:Science Press,2002.
[14]DU Xiu-li,ZHAO Mi.A local Time-domain Transmitting Boundary for Simulating Cylindrical Elastic Wave Propaga-tion in Infinite Media[J].Soil Dynamics and Earthquake En-gineering,2010,30(10):937-946.
[15]ZHAO Mi,DU Xiu-li,LIU Jing-bo,et al.Explicit Finite El-ement Artificial Boundary Scheme for Transient Scalar Wavesin Two-dimensional Unbounded Waveguide[J].International Journal for Numerical Methods in Engineering,2011,87(11):1074-1104.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心