弹性波三维散射快速多极子间接边界元法求解

王冬, 刘中宪, 武凤娇, 刘蕾

王冬, 刘中宪, 武凤娇, 刘蕾. 弹性波三维散射快速多极子间接边界元法求解[J]. 工程力学, 2017, 34(1): 33-44. DOI: 10.6052/j.issn.1000-4750.2015.05.0435
引用本文: 王冬, 刘中宪, 武凤娇, 刘蕾. 弹性波三维散射快速多极子间接边界元法求解[J]. 工程力学, 2017, 34(1): 33-44. DOI: 10.6052/j.issn.1000-4750.2015.05.0435
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WANG Dong, LIU Zhong-xian, WU Feng-jiao, LIU Lei. THE FMM-IBEM SOLUTION OF THREE-DIMENSIONAL SCATTERING OF ELASTIC WAVES[J]. Engineering Mechanics, 2017, 34(1): 33-44. DOI: 10.6052/j.issn.1000-4750.2015.05.0435
Citation: WANG Dong, LIU Zhong-xian, WU Feng-jiao, LIU Lei. THE FMM-IBEM SOLUTION OF THREE-DIMENSIONAL SCATTERING OF ELASTIC WAVES[J]. Engineering Mechanics, 2017, 34(1): 33-44. DOI: 10.6052/j.issn.1000-4750.2015.05.0435
shu

弹性波三维散射快速多极子间接边界元法求解

  • 1.

    天津城建大学, 天津市土木建筑结构防护与加固重点实验室, 天津 300384;

  • 2.

    河北建研科技有限公司, 河北, 石家庄 050021

基金项目: 国家自然科学基金项目（51278327）；国家科技支撑计划项目（2012BAJO7B05）；天津市科技支撑重大项目（15ZXCXSF0070）
详细信息
    作者简介:

    王冬(1988-),男,四川人,硕士生,主要从事动力边界元法研究(E-mail:wang_dong_0832@163.com);武凤娇(1989-),女,内蒙人,硕士生,主要从事弹性波散射研究(E-mail:wudiwufengjiao@163.com);刘蕾(1987-),女,河南人,硕士生,主要从事地震波散射研究(E-mail:liulei870905@163.com)

    通讯作者:

    刘中宪(1982-),男,河南人,副教授,博士后,硕导,主要从事地震工程和工程波动领域研究(E-mail:zhongxian1212@163.com)

  • 中图分类号: O347.41

THE FMM-IBEM SOLUTION OF THREE-DIMENSIONAL SCATTERING OF ELASTIC WAVES

  • 1.

    Tianjin ChengJian University, Tianjin Key Laboratory of Civil Structure Protection and Reinforcement, Tianjin 300384, China;

  • 2.

    Hebei Building Research Technical Co., Ltd, Shijiazhuang, Hebei 050021, China

摘要

    摘要
  • 摘要: 边界元方法对于无限域中弹性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大规模实际工程中的应用。为此，基于单层位势理论，结合快速多极子展开技术，通过对球面压缩波和剪切波势函数的泰勒级数展开，建立一种新的快速多极间接边界元方法，以实现大规模弹性波三维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弹性波三维散射问题的快速精确求解。最后以全空间椭球形孔洞群对平面P波、SV波的散射为例，揭示了三维孔洞群周围稳态位移场和应力场的若干分布规律。该文方法对低无量纲频率（ka<5.0）的大规模多体散射问题尤为适合。
    Abstract: Boundary element method has unique advantages to solve elastic wave scattering problems, while the asymmetric and dense matrix equation greatly restrict the application of traditional boundary element in practical engineering. 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 Taylor series expansion of compressible and shear wave potential function for solving large scale elastic wave scattering problems efficiently and accurately. It is verified that this method greatly improves the computing speed and reduces the calculation storage. Then the elastic wave scattering problem for millions of DOFs can be solved effectively and accurately on an ordinary personal workstation. Finally, the scattering problem of P wave by ellipsoidal cavities group in elastic full-space is solved, and some important characteristics for the displacement and stress fields in steady state are discussed based on the numerical results. This method is especially suitable for solving the multiple scattering problems at low dimensionless frequency (ka<5.0).
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出版历程
  • 收稿日期:  2015-05-18
  • 修回日期:  2016-04-03
  • 刊出日期:  2017-01-24

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