弹性半空间SH波散射快速边界积分方程法求解
详细信息 本馆镜像全文    |  推荐本文 | | 获取馆网全文
摘要
边界积分方程法对于半无限空间中地震波散射求解具有独特优势,但求解矩阵的非对称稠密特征极大限制了该方法在高频与多体散射中的应用。为此,基于单层位势理论,结合快速多极子展开技术,通过对二维SH波势函数的多极展开,建立一种新的快速多极间接边界积分方程法,以实现弹性半空间中高自由度地震波散射的精确高效模拟。算例分析表明所提方法能够大幅度降低计算时间和存储量,可在目前普通计算机上快速实现上百万自由度SH波二维散射问题的精确求解。方法可进一步拓展到P,SV波的散射分析。
The boundary integral equation method has unique advantage to solve the scattering of seismic wave in half-space,while the asymmetric and dense matrix equations greatly restrict the application of traditional boundary element in high frequency and multi-body scattering. Therefore,based on the single-layer potential theory,combined with the fast multipole expansion technique,a new rapid indirect boundary element method is developed by using the multipole expansion of two-dimensional SH wave's potential function for solving the high DOF's scattering of seismic waves in elastic half-space efficiently and accurately. It is verified that this method greatly improves the computing speed and reduces the calculate storage,and then the two-dimensional scattering problems of SH waves for millions of DOF's can be solved effectively and accurately on an ordinary personal computer. This method can also be applied to the analysis of the scattering of P,SV waves.
引文
[1]Yuan X M,Liao Z P.Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section[J].Earthquake Engineering and Structural Dynamics,1995,24(10):1303-1313.
    [2]陈少林,张莉莉,李山有.半圆柱型沉积盆地对SH波散射的数值分析[J].工程力学,2014,31(4):218-224.CHEN Shaolin,ZHANG Lili,LI Shanyou.Numerical analysis of the plane SH waves scattering by semi-cylindrical alluvial valley[J].Engineering Mechanics,2014,31(4):218-224.(in Chinese)
    [3]杜修力,熊建国.波动问题的级数解边界元法[J].地震工程与工程振动,1988,3(8):39-49.DU Xiuli,XIONG Jianguo.Application of boundary element method to wave propagation by using series solution[J].Earthquake Engineering and Engineering Dynamics,1988,3(8):39-49.(in Chinese)
    [4]梁建文,巴振宁,等.弹性层状半空间中沉积谷地对入射平面SH波的放大作用[J].地震工程与工程振动,2007,27(3):1-9.LIANG Jianwen,BA Zhenning,et al.Surface motion of an alluvial valley in layered half-space for incident plane SH waves[J].Journal of Earthquake Engineering and Engineering Vibration,2007,27(3):1-9.
    [5]Sanchez-Sesma F J,Esquivel J A.Ground motion on alluvial valleys under incident plane SH waves[J].Bulletin of the Seismological Society of America,1979,69(4):1107-1120.
    [6]Dravinski M,Mossessian T K.Application of a hybrid method for scattering of P,SV and Rayleigh waves by near-surface irregularities[J].Bulletin of the Seismological Society of America,1987,77(5):1784-1803.
    [7]姚振汉,王海涛.边界元法[M].北京:高等教育出版社,2009.YAO Zhenhan,WANG Haitao.Boundary element methods[M],Beijing:Higher Education Press,2009.(in Chinese)
    [8]Liu Y.Fast multipole boundary element method:theory and applications in engineering[M].Cambridge University Press,2009.
    [9]Trifunac M D.Scattering of plane SH waves by a aemi-cylindrical canyon[J].Earthquake Engineering&Structural Dynamics,1972,1(3):267-281.

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