EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

采用黏弹性人工边界单元时显式算法稳定性的改善研究

李述涛 刘晶波 宝鑫

李述涛, 刘晶波, 宝鑫. 采用黏弹性人工边界单元时显式算法稳定性的改善研究[J]. 力学学报, 2020, 52(6): 1838-1849. doi: 10.6052/0459-1879-20-224
引用本文: 李述涛, 刘晶波, 宝鑫. 采用黏弹性人工边界单元时显式算法稳定性的改善研究[J]. 力学学报, 2020, 52(6): 1838-1849. doi: 10.6052/0459-1879-20-224
Li Shutao, Liu Jingbo, Bao Xin. IMPROVEMENT OF EXPLICIT ALGORITHMS STABILITY WITH VISCO-ELASTIC ARTIFICIAL BOUNDARY ELEMENTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1838-1849. doi: 10.6052/0459-1879-20-224
Citation: Li Shutao, Liu Jingbo, Bao Xin. IMPROVEMENT OF EXPLICIT ALGORITHMS STABILITY WITH VISCO-ELASTIC ARTIFICIAL BOUNDARY ELEMENTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1838-1849. doi: 10.6052/0459-1879-20-224

采用黏弹性人工边界单元时显式算法稳定性的改善研究

doi: 10.6052/0459-1879-20-224
基金项目: 1) 国家自然科学基金(51878384);国家自然科学基金(U1839201);国家重点研发计划(2018YFC1504305);博士后创新人才支持计划(BX20200192);清华大学“水木学者”计划(2020SM005)
详细信息
    作者简介:

    2) 宝鑫,助理研究员,主要研究方向:地下结构抗爆抗震与海洋工程抗震. E-mail: baox@tsinghua.edu.cn

    通讯作者:

    宝鑫

  • 中图分类号: TU311,P315.9

IMPROVEMENT OF EXPLICIT ALGORITHMS STABILITY WITH VISCO-ELASTIC ARTIFICIAL BOUNDARY ELEMENTS

  • 摘要: 黏弹性人工边界单元是目前常用的处理半无限空间波动问题的数值模拟方法,可有效吸收计算区域内产生的外行波动.黏弹性人工边界单元具有与内部介质不同的质量密度、刚度和阻尼,受其影响,对整体模型进行显式时域逐步积分时,在边界区域易发生失稳现象,影响整体系统显式积分的计算效率. 针对该问题目前尚无行之有效的解决方法.本文针对二维黏弹性人工边界单元,建立可代表整体系统典型特征的侧边子系统和角点子系统,利用传递矩阵谱半径分析方法,基于传统中心差分格式,推导得到局部子系统稳定性条件的解析解.在此基础上通过研究解析解中各物理参数对稳定性条件的影响,给出通过增加人工边界单元的质量密度,以改善采用黏弹性人工边界单元时显式算法稳定性的方法.均匀和成层半空间波动问题算例分析表明,将内部单元质量密度设置为人工边界单元质量密度的上限,可以在保证黏弹性人工边界计算精度的前提下,有效改善整体系统显式时域逐步积分的数值稳定性,大幅提高计算效率.

     

  • [1] Alterman ZS, Aboudi J, Karal FC. Pulse propagation in a laterally heterogeneous solid elastic sphere. Geophysical Journal of the Royal Astronomical Society, 1970,21(3):243-260
    [2] 杜修力, 赵密, 王进廷. 近场波动模拟的人工应力边界条件. 力学学报, 2006,38(1):49-56
    [2] ( Du Xiuli, Zhao Mi, Wang Jinting. A stress artificial boundary in fea for near field wave problem. Chinese Journal of Theoretical and Applied Mechanics, 2006,38(1):49-56 (in Chinese))
    [3] 邢浩洁, 李鸿晶. 透射边界条件在波动谱元模拟中的实现:一维波动. 力学学报, 2017,49(2):367-379
    [3] ( Xing Haojie, Li Hongjing. Implementation of multi-transmitting boundary condition for wave motion simulation by spectral element method: one dimension case. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(2):367-379 (in Chinese))
    [4] 刘晶波, 宝鑫, 谭辉 等. 波动问题中流体介质的动力人工边界. 力学学报, 2017,49(6):1418-1427
    [4] ( Liu Jingbo, Bao Xin, Tan Hui, et al. Dynamical artificial boundary for fluid medium in wave motion problems. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(6):1418-1427 (in Chinese))
    [5] 章小龙, 李小军, 陈国兴 等. 黏弹性人工边界等效载荷计算的改进方法. 力学学报, 2016,48(5):1126-1135
    [5] ( Zhang Xiaolong, Li Xiaojun, Chen Guoxing, et al. An improved method of the calculation of equivalent nodal forces in viscous-elastic artificial boundary. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(5):1126-1135. (in Chinese))
    [6] 刘晶波, 谷音, 杜义欣. 一致黏弹性人工边界及黏弹性边界单元. 岩土工程学报, 2006,28(9):1070-1075
    [6] ( Liu Jingbo, Gu Yin, Du Yixin. Consistent viscous-spring artificial boundaries and viscous-spring boundary elements. Chinese Journal of Geotechnical Engineering, 2006,28(9):1070-1075 (in Chinese))
    [7] 谷音, 刘晶波, 杜义欣. 三维一致黏弹性人工边界及等效黏弹性边界单元. 工程力学, 2007,24(12):31-37
    [7] ( Gu Yin, Liu Jingbo, Du Yixin. 3D consistent viscous-spring artificial boundary and viscous-spring boundary element. Engineering Mechanics, 2007,24(12):31-37 (in Chinese))
    [8] 王启云, 张家生, 孟飞 等. 高速铁路路基模型列车振动荷载模拟. 振动与冲击, 2013(6):48-51, 77
    [8] ( Wand Qiyun, Zhang Jiasheng, Meng Fei, et al. Simulation of train vibration load on the subgrade testing model of high-speed railway. Journal of Vibration and Shock, 2013(6):48-51, 77 (in Chinese))
    [9] 尹尚之, 叶丹, 梁应军 等. 二维弧形一致黏弹性边界单元在 ABAQUS 中的应用. 世界地震工程, 2017,33(1):69-74
    [9] ( Yin Shangzhi, Ye Dan, Liang Yingjun, et al. Application of 2D arc consistent viscous-spring artificial boundary element in ABAQUS. World Earthquake Engineering, 2017,33(1):69-74 (in Chinses))
    [10] 贾磊, 解咏平, 李慎奎. 爆破振动对邻近隧道衬砌安全的数值模拟分析. 振动与冲击, 2015(11):181-185, 219
    [10] ( Jia Lei, Xie Yongping, Li Shenkui. Numerical simulation for impact of blasting vibration on nearby tunnel lining safety. Journal of Vibration and Shock, 2015(11):181-185, 219 (in Chinese))
    [11] Bao X, Liu JB, Wang DY, et al. Modification research of the internal substructure method for seismic wave input in deep underground structure-soil systems. Shock and Vibration, 2019: 1-13
    [12] Liu JB, Bao X, Wang DY, et al. The internal substructure method for seismic wave input in 3D dynamic soil-structure interaction analysis. Soil Dynamic and Earthquake Engineering, 2019,127:1-12
    [13] 刘晶波, 谭辉, 宝鑫 等. 土-结构动力相互作用分析中基于人工边界子结构的地震波动输入方法. 力学学报, 2018,50(1):32-43
    [13] ( Liu Jingbo, Tan Hui, Bao Xin, et al. The seismic wave input method for soil-structure dynamic interaction analysis based on the substructure of artificial boundaries. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(1):32-43 (in Chinese))
    [14] Li ST, Liu JB, Yang Z, et al. Multiscale method for seismic response of near-source sites. Advances in Civil Engineering, 2020: 1-25
    [15] 刘恒, 廖振鹏. 波动数值模拟的一种显式方法-二维波动. 力学学报, 2010,42(6):1104-1116
    [15] ( Liu Heng, Liao Zhenpeng. An explicit method for numerical simulation of wave motion-2D wave motion. Chinese Journal of Theoretical and Applied Mechanics, 2010,42(6):1104-1116 (in Chinese))
    [16] 马天宝, 任会兰, 李健 等. 爆炸与冲击问题的大规模高精度计算. 力学学报, 2016,48(3):599-608
    [16] ( Ma Tianbao, Ren Huilan, Li Jian, et al. Large scale high precision computation for explosion and impact problems. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(3):599-608 (in Chinese))
    [17] 何涛. 基于 ALE 有限元法的流固耦合强耦合数值模拟. 力学学报, 2018,50(2):395-404
    [17] ( He Tao. A partitioned strong coupling algorith for fluid-structure interaction using arbitrary lagrangian-eulerian finite eleent forulation. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(2):395-404 (in Chinese))
    [18] 李鸿晶, 梅雨辰, 任永亮. 一种结构动力时程分析的积分求微方法. 力学学报, 2019,51(5):1507-1516
    [18] ( Li Hongjing, Mei Yuchen, Ren Yongliang. An integral differentiation procedure for dynamic time-history response analysis of structures. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(5):1507-1516 (in Chinese))
    [19] 谢志南, 廖振鹏. 透射边界高频失稳机理及其消除方法-SH波动. 力学学报, 2012,44(4):745-752
    [19] ( Xie Zhinan, Liao Zhenpeng. Mechanism of high frequency instability caused by transmitting boundary and method of its elimination-SH wave. Chinese Journal of Theoretical and Applied Mechanics, 2012,44(4):745-752 (in Chinese))
    [20] 关慧敏, 廖振鹏. 时域局部人工边界的稳定性分析方法概述. 世界地震工程, 1997(2):1-7
    [20] ( Guan Huimin, Liao Zhenpeng. Overview of stability analysis methods for local artificial boundaries in the time domain. World Earthquake Engineering, 1997(2):1-7 (in Chinese))
    [21] 关慧敏, 廖振鹏. 局部人工边界稳定性的一种分析方法. 力学学报, 1996,28(3):376-380
    [21] ( Guan Huimin, Liao Zhenpeng. A method for the stability analysis of local artificial boundaries. Chinese Journal of Theoretical and Applied Mechanics, 1996,28(3):1601-1606 (in Chinese))
    [22] 李小军, 杨宇. 透射边界稳定性控制措施探讨. 岩土工程学报, 2012(4):641-645
    [22] ( Li Xiaojun, Yang Yu. Measures for stability control of transmitting boundary. Journal of Geotechnical Engineering, 2012(4):641-645 (in Chinese))
    [23] Liao ZP, Liu JB. Numerical instabilites of a local transmitting boundary. Earthq Eng Struct Dyn, 1992,21:65-77
    [24] 关慧敏, 廖振鹏. 一种改善多次透射边界稳定性的措施. 地震工程与工程震动, 1997(4):2-9
    [24] ( Guan Huimin, Liao Zhenpeng. A measure to improve the stability of multiple transmission boundary. Earthquake Engineering and Engineering Vibration, 1997(4):2-9 (in Chinese))
    [25] Liu J, Sharan SK. Analysis of dynamic contact of cracks in viscoelastic media. Computer Methods in Applied Mechanics and Engineering, 1995,121(1-4):187-200
    [26] Kamel AH. A stability checking procedure for finite-difference schemes with boundary conditions in acoustic media. Bull Seism Soc Am, 1989,79(5):1601-1606
    [27] 李述涛, 刘晶波, 宝鑫 等. 采用黏弹性人工边界单元时显式算法稳定性分析. 工程力学, 2020, doi: 10.6052/j.issn.1000-4750.2019.12.0755
    [27] ( Li Shutao, Liu Jingbo, Bao Xin, et al. Stability analysis of explicit algorithms with visco-elastic artificial boundary elements. Engineering Mechanics, 2020, doi: 10.6052/j.issn.1000-4750.2019.12.0755 (in Chinses))
    [28] Hughes TJR. Analysis of transient algorithms with particular reference to stability behavior. Computational Methods for Transient Analysis, 1983,I:67-156
    [29] 王勖成, 邵敏. 有限单元法基本原理和数值方法. 北京: 清华大学出版社, 1997: 66-67
    [29] ( Wang Xucheng, Shao Min. Basic Principle and Numerical Method of Finite Element Method. Beijing: Tsinghua University Press, 1997: 66-67(in Chinese))
    [30] 申志强, 夏军, 宋殿义 等. 基于高阶剪切变形理论的四边形求积元板单元及其应用. 力学学报, 2018,50(5):1093-1103
    [30] ( Shen Zhiqiang, Xia Jun, Song Dianyi, et al. A quadrilateral quadrature plate element based on reddy's higher-order shear deformation theory and its application. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(5):1093-1103 (in Chinese))
    [31] Abaqus Analysis User's Manual (version 6.14). ABAQUS, INC., 2013
  • 加载中
计量
  • 文章访问数:  1083
  • HTML全文浏览量:  253
  • PDF下载量:  102
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-06-02
  • 刊出日期:  2020-12-10

目录

    /

    返回文章
    返回