一种高精度圆柱形人工边界条件:水-柱体相互作用问题
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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。
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.
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.
引文
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[18]赵密,杜修力.时间卷积的局部高阶弹簧-阻尼-质量模型[J].工程力学,2009,26(5):8―18.Zhao Mi,Du Xiuli.High-order model of spring-dashpotmass model for localizing time convolution[J].Engineering Mechanics,2009,26(5):8―18.(in Chinese)
[19]赵密,杜修力,刘晶波.一种高阶精度人工边界条件:出平面外域波动问题[J].工程力学,2012,29(4):7―14.Zhao Mi,Du Xiuli,Liu Jingbo.A high-order accurate artificial boundary condition:out-of-plane exterior wave problem[J].Engineering Mechanics,2012,29(4):7―14.(in Chinese)
[20]Du X L,Zhao M.Stability and identification for rational approximation of frequency response function of unbounded soil[J].Earthquake Engineering and Structural Dynamics,2010,39(2):165―186.
[21]Du X L,Zhao M.A local time-domain transmitting boundary for simulating cylindrical elastic wave propagation in infinite media[J].Soil Dynamics and Earthquake Engineering,2010,30(10):937―946.
[22]Zhao M,Du X L,Liu J B,et al.Explicit finite element artificial boundary scheme for transient scalar waves in two-dimensional unbounded waveguide[J].International Journal for Numerical Methods in Engineering,2011,87(11):1073―1104.
[23]赵密.近场波动有限元模拟的应力型时域人工边界条件极其应用[D].北京:北京工业大学,2009.Zhao Mi.Stress-type time-domain artificial boundary condition for finite-element simulation of near-field wave motion and its engineering application[D].Beijing:Beijing University of Technology,2009.(in Chinese)
[24]Wang J T,Zhang C H,Du X L.An explicit integration scheme for solving dynamic problems of solid and porous media[J].Journal of Earthquake Engineering,2008,12(2):293―311.
[2]Zhang D,Zhang X,He J,et al.Offshore wind energy development in China:Current status and future perspective[J].Renewable and Sustainable Energy Reviews,2011,15(9):467―4684.
[3]闫静茹,路德春,杜修力,等.港珠澳大桥工程人工岛三维非线性地震反应分析[J].世界地震工程,2016,32(1):161―168.Yan Jingru,Lu Dechun,Du Xiuli,et al.Threedimensional nonlinear seismic response analysis of artificial island of Hong Kong-Zhuhai-Macao bridge project[J].World Earthquake Engineering,2016,32(1):161―168.(in Chinese)
[4]黄信,李忠献.动水压力作用对深水桥墩地震响应的影响[J].土木工程学报,2011,44(1):65―73.Huang Xin,Li Zhongxian.Influence of hydrodynamic pressure on seismic responses of bridge piers in deep water[J].China Civil Engineering Journal,2011,44(1):65―73.(in Chinese)
[5]李忠献,黄信.行波效应对深水连续刚构桥地震响应的影响[J].工程力学,2013,30(3):120―125.Li Zhongxian,Huang Xin.Influence of traveling wave effect on seismic responses of continuous rigid-framed bridge in deep water[J].Engineering Mechanics,2013,30(3):120―125.(in Chinese)
[6]张文学,黄荐,陈盈,等.渡槽结构考虑流固耦合的横向地震响应简化计算公式[J].工程力学,2017,34(8):69―75.Zhang Wenxue,Huang Jian,Chen Ying,et al.Asimplified formula for the calculation of the transverse seismic response of aqueducts considering fluid-structure interaction[J].Engineering Mechanics,2017,34(8):69―75.(in Chinese)
[7]Liaw C Y,Chopra A K.Dynamics of towers surrounded by water[J].Earthquake Engineering and Structural Dynamics,1974,3(1):33―49.
[8]Li Q,Yang W L.An improved method of hydrodynamic pressure calculation for circular hollow piers in deep water under earthquake[J].Ocean Engineering,2013,72:241―256.
[9]Du X L,Wang P G,Zhao M.Simplified formula of hydrodynamic pressure on circular bridge piers in the time domain[J].Ocean Engineering,2014,85:44―53.
[10]黄信,李忠献.考虑水底柔性反射边界的深水桥墩地震动水压力分析[J].工程力学,2012,29(7):102―116.Huang Xin,Li Zhongxian.Earthquake induced hydrodynamic pressure of bridge pier in deep water with flexible reflecting boundary[J].Engineering Mechanics,2012,29(7):102―116.(in Chinese)
[11]赖伟,王君杰,胡世德.地震下桥墩动水压力分析[J].同济大学学报,2004,32(1):1―5.Lai Wei,Wang Junjie,Hu Shide.Earthquake induced hydrodynamic pressure on bridge pier[J].Journal of Tongji University,2004,32(1):1―5.(in Chinese)
[12]Williams A N.Analysis of the base-excited response of intake-outlet towers by a Green’s function approach[J].Engineering Structures,1991,13(1):43―53.
[13]Jiang H,Wang B,Bai X,et al.Simplified expression of hydrodynamic pressure on deep water cylindrical bridge piers during earthquakes[J].Journal of Bridge Engineering,2017,22(6):04017014.
[14]Liaw C Y,Chopra A K.Earthquake analysis of axisymmetric towers partially submerged in water[J].Earthquake Engineering and Structural Dynamics,1975,3(3):233―248.
[15]刘浪,杨万理,李乔.深水桥梁墩水耦合抗震分析方法[J].西南交通大学学报,2015,50(3):449―453.Liu Lang,Yang Wanli,Li Qiao.Seismic analysis method of deep-water bridge pier and water coupling[J].Journal of Southwest Jiaotong University,2015,50(3):449―453.(in Chinese)
[16]刘晶波,王振宇,杜修力,等.波动问题中的三维时域粘弹性人工边界[J].工程力学,2005,22(6):46―51.Liu Jingbo,Wang Zhenyu,Du Xiuli,et al.Threedimensional visco-elastic artificial boundaries in time domain for wave motion problems[J].Engineering Mechanics,2005,22(6):46―51.(in Chinese)
[17]杜修力,赵密.一种新的高阶弹簧-阻尼-质量边界-无限域圆柱对称波动问题[J].力学学报,2009,41(2):207―215.Du Xiuli,Zhao Mi.A novel high-order spring-dashpotmass boundary for cylindrical-symmetry wave motions in infinite domain[J].Chinese Journal of Theoretical and Applied Mechanics,2009,41(2):207―215.(in Chinese)
[18]赵密,杜修力.时间卷积的局部高阶弹簧-阻尼-质量模型[J].工程力学,2009,26(5):8―18.Zhao Mi,Du Xiuli.High-order model of spring-dashpotmass model for localizing time convolution[J].Engineering Mechanics,2009,26(5):8―18.(in Chinese)
[19]赵密,杜修力,刘晶波.一种高阶精度人工边界条件:出平面外域波动问题[J].工程力学,2012,29(4):7―14.Zhao Mi,Du Xiuli,Liu Jingbo.A high-order accurate artificial boundary condition:out-of-plane exterior wave problem[J].Engineering Mechanics,2012,29(4):7―14.(in Chinese)
[20]Du X L,Zhao M.Stability and identification for rational approximation of frequency response function of unbounded soil[J].Earthquake Engineering and Structural Dynamics,2010,39(2):165―186.
[21]Du X L,Zhao M.A local time-domain transmitting boundary for simulating cylindrical elastic wave propagation in infinite media[J].Soil Dynamics and Earthquake Engineering,2010,30(10):937―946.
[22]Zhao M,Du X L,Liu J B,et al.Explicit finite element artificial boundary scheme for transient scalar waves in two-dimensional unbounded waveguide[J].International Journal for Numerical Methods in Engineering,2011,87(11):1073―1104.
[23]赵密.近场波动有限元模拟的应力型时域人工边界条件极其应用[D].北京:北京工业大学,2009.Zhao Mi.Stress-type time-domain artificial boundary condition for finite-element simulation of near-field wave motion and its engineering application[D].Beijing:Beijing University of Technology,2009.(in Chinese)
[24]Wang J T,Zhang C H,Du X L.An explicit integration scheme for solving dynamic problems of solid and porous media[J].Journal of Earthquake Engineering,2008,12(2):293―311.