工程力学 ›› 2019, Vol. 36 ›› Issue (1): 88-95.doi: 10.6052/j.issn.1000-4750.2017.10.0787

• 土木工程学科 • 上一篇    下一篇

一种高精度圆柱形人工边界条件:水-柱体相互作用问题

王丕光, 赵密, 李会芳, 杜修力   

  1. 北京工业大学城市与工程安全减灾教育部重点实验室, 北京 100124
  • 收稿日期:2017-10-26 修回日期:2018-01-31 出版日期:2019-01-29 发布日期:2019-01-10
  • 通讯作者: 赵密(1980-),男,吉林人,教授,博导,博士,主要从事重大工程抗震领域研究(E-mail:zhaomi@bjut.edu.cn). E-mail:zhaomi@bjut.edu.cn
  • 作者简介:王丕光(1985-),男,山东人,助理研究员,博士,主要从事桥梁结构抗震领域的研究(E-mail:wangpiguang1985@126.com);李会芳(1993-),女,河南人,博士生,主要从事人工边界方法的研究(E-mail:S201504005@emails.bjut.edu.cn);杜修力(1963-),男,四川人,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).
  • 基金资助:
    国家自然科学基金项目(51708010,51421005,51678015,51322813)

A HIGH-ACCURACY CYLINDRICAL ARTIFICIAL BOUNDARY CONDITION: WATER-CYLINDER INTERACTION PROBLEM

WANG Pi-guang, ZHAO Mi, LI Hui-fang, DU Xiu-li   

  1. Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China
  • Received:2017-10-26 Revised:2018-01-31 Online:2019-01-29 Published:2019-01-10

摘要: 针对水-柱体动力相互作用问题,提出一种用于模拟无限域水体的圆柱形高精度时域人工边界条件。首先,基于三维可压缩水体的波动方程和边界条件,采用分离变量法建立了时空全局的精确人工边界条件;然后,将其动力刚度表示为外域模型和波导模型人工边界条件动力刚度的嵌套形式;之后,应用时间局部化方法得到时间局部的高精度人工边界条件;最后,离散高精度人工边界条件,并将其与近场有限元方程耦合,形成一种能够采用显式时间积分方法求解的时间二阶常微分方程组。数值算例表明:提出的三维圆柱形高精度人工边界条件精确、高效、稳定。

关键词: 地震, 水-结构相互作用, 有限元法, 人工边界条件, 无限域

Abstract: A high-accuracy cylindrical artificial boundary condition (ABC) for water-cylinder dynamic interaction problem is presented to simulate the truncated infinite domain. Firstly, according to the wave equation and boundary conditions for the three-dimensional compressible water, an exact ABC that is global in time and space is developed by using the method of separation of variables. Secondly, the dynamic-stiffness of the cylindrical ABC is rewritten as a nested form of the two-dimensional linear and circular dynamic-stiffness. Thirdly, a high-accuracy ABC that is local in time but global in space is obtained by applying the temporal localization method. Fourthly, the resulted high-accuracy ABC is discretized using finite element method. Lastly, a symmetric second-order ordinary differential equations in time is developed by coupling the results with the finite element equation of the near field. The finite equation can be solved by explicit time integration algorithm. Numerical example demonstrates that the presented ABC is accurate, efficient and stable.

Key words: earthquake, fluid-structure interaction, finite element method, artificial boundary condition, unbounded domain

中图分类号: 

  • TU311.3
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