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竖向成层介质中标量波传播问题的高精度人工边界条件

李会芳 赵密 杜修力

李会芳, 赵密, 杜修力. 竖向成层介质中标量波传播问题的高精度人工边界条件[J]. 工程力学, 2022, 39(5): 55-64. doi: 10.6052/j.issn.1000-4750.2021.02.0112
引用本文: 李会芳, 赵密, 杜修力. 竖向成层介质中标量波传播问题的高精度人工边界条件[J]. 工程力学, 2022, 39(5): 55-64. doi: 10.6052/j.issn.1000-4750.2021.02.0112
LI Hui-fang, ZHAO Mi, DU Xiu-li. HIGH-PRECISION ARTIFICIAL BOUNDARY CONDITION FOR SCALAR WAVE PROPAGATION IN VERTICAL STRATIFIED MEDIA[J]. Engineering Mechanics, 2022, 39(5): 55-64. doi: 10.6052/j.issn.1000-4750.2021.02.0112
Citation: LI Hui-fang, ZHAO Mi, DU Xiu-li. HIGH-PRECISION ARTIFICIAL BOUNDARY CONDITION FOR SCALAR WAVE PROPAGATION IN VERTICAL STRATIFIED MEDIA[J]. Engineering Mechanics, 2022, 39(5): 55-64. doi: 10.6052/j.issn.1000-4750.2021.02.0112

竖向成层介质中标量波传播问题的高精度人工边界条件

doi: 10.6052/j.issn.1000-4750.2021.02.0112
基金项目: 国家重点研发计划项目(2018YFC1504305);国家自然科学基金联合基金项目(U1839201);国家自然科学基金重点项目(51738001)
详细信息
    作者简介:

    李会芳(1993−),女,河南安阳人,博士生,主要从事人工边界方法和隧道地震反应研究(E-mail: lihuifang2021@126.com)

    杜修力(1963−),男,四川广安人,长江学者特聘教授,博士,博导,主要从事地震工程领域的研究(E-mail: duxiuli@bjut.edu.cn)

    通讯作者:

    赵 密(1980−),男,吉林公主岭人,教授,博士,博导,主要从事重大工程抗震领域研究(E-mail: zhaomi@bjut.edu.cn)

  • 中图分类号: TU311.3

HIGH-PRECISION ARTIFICIAL BOUNDARY CONDITION FOR SCALAR WAVE PROPAGATION IN VERTICAL STRATIFIED MEDIA

  • 摘要: 为了实现含竖向成层介质以及表面不规则地形场地中标量波传播问题的高效且高精度求解,该文基于连分式展开和扩展的一致边界,建立了一种频域下折线形高精度人工边界条件。通过在每个竖向地层内引入独立的斜角坐标变换,新的人工边界条件可以用于多起伏地表地形条件。新的折线形人工边界在频域下推导,仅含有连分式阶数一个待定实参数,用于调整计算精度,该参数不随外行波的频率和传播角度改变。人工边界条件可以与内域有限元方程无缝耦合,应用简单方便。由于新边界条件的高精度,内域尺寸可以取较小甚至可以直接将人工边界加在结构周围或者地表,从而极大提高计算效率。通过典型数值算例,将人工边界计算模型与有限元大模型的解进行了对比分析,验证了该文提出的折线形人工边界条件的有效性和高精度。
  • 图  1  竖向成层且地表起伏的半空间场地中标量波传播问题

    Figure  1.  Scalar wave propagation in half space including vertical stratified media and irregular topography

    图  2  Ricker波的时程和频谱曲线

    Figure  2.  Time history and Fourier spectrum of Ricker wavelet impulse

    图  3  含竖直地层半空间场地中标量波传播问题

    Figure  3.  Scalar wave propagation in half space field with one vertical layer

    图  4  水平地表场地中观察点位移时程结果

    Figure  4.  Time histories of displacement solutions at observation points in a flat surface site

    图  5  含竖向成层介质且地表起伏的半空间场地中标量波传播问题

    Figure  5.  Scalar wave propagation in half space field with vertical stratified media and irregular topography

    图  6  折线地表场地中观察点位移时程结果

    Figure  6.  Time histories of displacement solutions at observation points in a zigzag terrain site

    图  7  含竖向成层介质的阶梯地形半空间场地中标量波传播问题

    Figure  7.  Scalar wave propagation in step-shaped half space field with vertical stratified media

    图  8  阶梯地形场地中观察点位移时程结果

    Figure  8.  Time histories of displacement solutions at observation points in a stepped terrain site

    图  9  含地下结构的复杂地形地质半空间场地中标量波传播问题

    Figure  9.  Scalar wave propagation in complex topographical geological half space field including an underground structure

    图  10  含地下结构场地中观察点位移时程结果

    Figure  10.  Time histories of displacement solutions at observation points in a site containing underground structure

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出版历程
  • 收稿日期:  2021-02-01
  • 修回日期:  2021-05-10
  • 网络出版日期:  2021-06-18
  • 刊出日期:  2022-05-01

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