基于高阶双渐近透射边界的大坝-库水动力相互作用直接耦合分析模型
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摘要
高阶双渐近时域透射边界能够同时模拟行波和快衰波的传播,并且能够在全频范围内迅速逼近准确解,具有优良的收敛性能和计算效率.本文将动水压力波高阶双渐近透射边界直接嵌入到近场有限元方程中,建立了大坝-库水动力相互作用的直接耦合分析模型.该模型的整体控制方程保留了近场有限元方程系数矩阵对称稀疏的优势,可以方便地利用现有的通用有限元求解器求解.基于有限元开源软件框架体系OpenSees(Open System for Earthquake Engineering Simulation),编程实现了直接耦合分析模型,并将其应用于二维重力坝、三维拱坝与库水动力相互作用分析.数值算例表明,该直接耦合分析模型具有很高的精度和计算效率.
The high-order doubly asymptotic boundary is capable of accurately approximating the unbounded domain over the entire frequency range.It converges to the exact solution quickly as its order increases and has high computational efficiency.Embedding the high-order asymptotic boundary directly into finite element scheme,a seamless coupled model for dam-reservoir dynamic interaction analysis is established.Similar to the finite element equation of the near field structure,the coefficient matrices of the direct coupled model are sparse and symmetric,and the governing equation can be solved using general finite element solver.Based on the finite element open source code OpenSees,the direct coupled model is implemented and applied to gravity damreservoir and arch dam-reservoir dynamic interaction analysis.Numerical results show that the proposed model has high computational accuracy and efficiency.
The high-order doubly asymptotic boundary is capable of accurately approximating the unbounded domain over the entire frequency range.It converges to the exact solution quickly as its order increases and has high computational efficiency.Embedding the high-order asymptotic boundary directly into finite element scheme,a seamless coupled model for dam-reservoir dynamic interaction analysis is established.Similar to the finite element equation of the near field structure,the coefficient matrices of the direct coupled model are sparse and symmetric,and the governing equation can be solved using general finite element solver.Based on the finite element open source code OpenSees,the direct coupled model is implemented and applied to gravity damreservoir and arch dam-reservoir dynamic interaction analysis.Numerical results show that the proposed model has high computational accuracy and efficiency.
引文
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[11]李伟华,刘清华,赵成刚.饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法.地球物理学报,2010,53(10):2460-2469.Li W H,Liu Q H,Zhao C G,Three-dimensional viscousspring boundaries in time domain and dynamic analysis using explicit finite element method of saturated porous medium.Chinese J.Geophys.(in Chinese),2010,53(10):2460-2469.
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[16]邵秀民,蓝志凌.各向异性弹性介质中波动方程的吸收边界条件.地球物理学报,1995,38(S1):56-73.Shao X M,Lan Z L.Absorbing boundary conditions for anisotropic elastic wave equations.Chinese J.Geophys.(in Chinese),1995,38(S1):56-73.
[17]廖振鹏,周正华,张艳红.波动数值模拟中透射边界的稳定实现.地球物理学报,2002,45(4):533-545.Liao Z P,Zhou Z H,Zhang Y H.Stable implementation of transmitting boundary in numerical simulation of wave motion.Chinese J.Geophys.(in Chinese),2002,45(4):533-545.
[18]Chen J Y,Bording R P,Liu E R et al.The application of the nearly optimal sponge boundary conditions for seismic wave propagation in poroelastic media.Journal of Seismic Exploration,2010,19(1):1-19.
[19]Yang D H,Wang S Q,Zhang Z J et al.n-Times Absorbing Boundary Conditions for Compact Finite-Difference Modeling of Acoustic and Elastic Wave Propagation in the 2D TI Medium.Bulletin of the Seismological Society of America,2003,93(6):2389-2401.
[20]Zienkiewicz O C,Bettess P.Fluid-structure dynamic interaction and wave forces:An introduction to numerical treatment.International Journal for Numerical Methods in Engineering,1978,13(1):1-16.
[21]Küükarslan S,Coskun S B,TaskIn B.Transient analysis of dam-reservoir interaction including the reservoir bottom effects.Journal of Fluids and Structures,2005,20(8):1073-1084.
[22]Antes H,Von Estorff O.Analysis of absorption effects on the dynamic response of dam reservoir systems by boundary element methods.Earthquake Engineering&Structural Dynamics,1987,15(8):1023-1036.
[23]Soares Jr D,von Estorff O,Mansur W J.Efficient non-linear solid-fluid interaction analysis by an iterative BEM/FEM coupling.International Journal for Numerical Methods in Engineering,2005,64(11):1416-1431.
[24]Song C M,Wolf J P.The scaled boundary finite-element method-alias consistent infinitesimal finite-element cell method-for elastodynamics.Computer Methods in Applied Mechanics and Engineering,1997,147(3-4):329-355.
[25]Lin G,Du J G,Hu Z Q.Dynamic dam-reservoir interaction analysis including effect of reservoir boundary absorption.Science in China Series E:Technological Sciences,2007,50:1-10.
[26]Lin G,Wang Y,Hu Z Q.An efficient approach for frequency-domain and time-domain hydrodynamic analysis of dam-reservoir systems.Earthquake Engineering&Structural Dynamics,2012,41(13):1725-1749.
[27]Li S M.Diagonalization procedure for scaled boundary finite element method in modeling semi-infinite reservoir with uniform cross-section.International Journal for Numerical Methods in Engineering,2009,80(5):596-608.
[28]Givoli D.High-order local non-reflecting boundary conditions:a review.Wave Motion,2004,39(4):319-326.
[29]Geers T.Singly and doubly asymptotic computational boundaries.In:TL G,editor.Proceedings of the IUTAM Symposium on Computational Methods for Unbounded Domains.Dordrecht:Kluwer Academic Publishers;1998.p135-141.
[30]Prempramote S,Song C M,Tin-Loi F,et al.High-order doubly asymptotic open boundaries for scalar wave equation.International Journal for Numerical Methods in Engineering,2009,79(3):340-374.
[31]Wang X,Jin F,Prempramote S,et al.Time-domain analysis of gravity dam-reservoir interaction using high-order doubly asymptotic open boundary.Computers&Structures,2011,89(7-8):668-680.
[2]Humar J L,Jablonski A M.Boundary element reservoir model for seismic analysis of gravity dams.Earthquake Engineering&Structural Dynamics,1988,16(8):1129-1156.
[3]徐艳杰,张楚汉,金峰.非线性拱坝-地基动力相互作用的FE-BE-IBE模型.清华大学学报(自然科学版),1998,38(11):100-104.Xu Y J,Zhang C H,Jin F.Model of FE-BE-IBE coupling for soil-structure interaction on nonlinear response of arch dams.Journal of Tsinghua University(Sci&Tech).(in Chinese),1998,38(11):100-104
[4]Liu X,Xu Y,Wang G,et al.Seismic response of arch dams considering infinite radiation damping and joint opening effects.Earthquake Engineering and Engineering Vibration,2002,1(1):65-73.
[5]徐艳杰,牟海磊,张楚汉,et al.汶川地震中宝珠寺重力坝地震响应的三维有限元模拟.地球物理学报,2012,55(1):293-303.Xu Y J,Mu H L,Zhang C H,et al.3Dfinite element modeling of seismic response of Baozhusi gravity dam in Ms8.0Wenchuan Earthquake.Chinese J.Geophys.(in Chinese),2012,55(1):293-303
[6]程惠红,张怀,朱伯靖,et al.新丰江水库地震孔隙弹性耦合有限元模拟.中国科学:地球科学,2012,42(6):905-916.Cheng H H,Zhang H,Zhu B J,et al,Finite element investigation of the poroelastic effect on the Xinfengjiang Reservoir-Triggered earthquake.Sci China Earth Sci,(in Chinese),2012,42(6):905-916.
[7]Westergaard H M.Water pressure on dams during earthquakes.Transactions of the American Society of Civil Engineering,1933,98:418-433.
[8]杜修力,王进廷.动水压力及其对坝体地震反应影响的研究进展.水利学报,2001,(7):13-21.Du X L,Wang J T.Review of studies on the hydrodynamic pressure and its effects on the seismic response of dams.Journal of Hydraulic Engineering(in Chinese),2001,(7):13-21.
[9]徐世浙.地球物理中的有限单元法.北京:科学出版社,1994:260-277.Xu S Z,The finite element method in Geophysics(in Chinese),Beijing:Science Press,1994:260-277.
[10]冯德山,陈承申,王洪华.基于混合边界条件的有限单元法GPR正演模拟.地球物理学报,2012,55(11):3774-3785.Feng D S,Chen C S,Wang H H,Finite element method GPR forward simulation based on mixed boundary condition.Chinese J.Geophys.(in Chinese),2012,55(11):3774-3785.
[11]李伟华,刘清华,赵成刚.饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法.地球物理学报,2010,53(10):2460-2469.Li W H,Liu Q H,Zhao C G,Three-dimensional viscousspring boundaries in time domain and dynamic analysis using explicit finite element method of saturated porous medium.Chinese J.Geophys.(in Chinese),2010,53(10):2460-2469.
[12]Lan H,Zhang Z.Three-Dimensional Wave-Field Simulation in Heterogeneous Transversely Isotropic Medium with Irregular Free Surface.Bulletin of the Seismological Society of America,2011,101(3):1354-1370.
[13]Lan H Q,Zhang Z J.Comparative study of the free-surface boundary condition in two-dimensional finite-difference elastic wave field simulation.Journal of Geophysics and Engineering,2011,8(2):275.
[14]兰海强,刘佳,白志明,VTI介质起伏地表地震波场模拟,地球物理学报,2011,54(8):2072-2084,Lan H.Q.,Liu J.,Bai Z.M.,Wave-field simulation in VTI media with irregular free surface.Chinese J.Geophys.(in Chinese),2011,54(8):2072-2084.
[15]Givoli D.Non-reflecting boundary conditions.Journal of Computational Physics,1991,94(1):1-29.
[16]邵秀民,蓝志凌.各向异性弹性介质中波动方程的吸收边界条件.地球物理学报,1995,38(S1):56-73.Shao X M,Lan Z L.Absorbing boundary conditions for anisotropic elastic wave equations.Chinese J.Geophys.(in Chinese),1995,38(S1):56-73.
[17]廖振鹏,周正华,张艳红.波动数值模拟中透射边界的稳定实现.地球物理学报,2002,45(4):533-545.Liao Z P,Zhou Z H,Zhang Y H.Stable implementation of transmitting boundary in numerical simulation of wave motion.Chinese J.Geophys.(in Chinese),2002,45(4):533-545.
[18]Chen J Y,Bording R P,Liu E R et al.The application of the nearly optimal sponge boundary conditions for seismic wave propagation in poroelastic media.Journal of Seismic Exploration,2010,19(1):1-19.
[19]Yang D H,Wang S Q,Zhang Z J et al.n-Times Absorbing Boundary Conditions for Compact Finite-Difference Modeling of Acoustic and Elastic Wave Propagation in the 2D TI Medium.Bulletin of the Seismological Society of America,2003,93(6):2389-2401.
[20]Zienkiewicz O C,Bettess P.Fluid-structure dynamic interaction and wave forces:An introduction to numerical treatment.International Journal for Numerical Methods in Engineering,1978,13(1):1-16.
[21]Küükarslan S,Coskun S B,TaskIn B.Transient analysis of dam-reservoir interaction including the reservoir bottom effects.Journal of Fluids and Structures,2005,20(8):1073-1084.
[22]Antes H,Von Estorff O.Analysis of absorption effects on the dynamic response of dam reservoir systems by boundary element methods.Earthquake Engineering&Structural Dynamics,1987,15(8):1023-1036.
[23]Soares Jr D,von Estorff O,Mansur W J.Efficient non-linear solid-fluid interaction analysis by an iterative BEM/FEM coupling.International Journal for Numerical Methods in Engineering,2005,64(11):1416-1431.
[24]Song C M,Wolf J P.The scaled boundary finite-element method-alias consistent infinitesimal finite-element cell method-for elastodynamics.Computer Methods in Applied Mechanics and Engineering,1997,147(3-4):329-355.
[25]Lin G,Du J G,Hu Z Q.Dynamic dam-reservoir interaction analysis including effect of reservoir boundary absorption.Science in China Series E:Technological Sciences,2007,50:1-10.
[26]Lin G,Wang Y,Hu Z Q.An efficient approach for frequency-domain and time-domain hydrodynamic analysis of dam-reservoir systems.Earthquake Engineering&Structural Dynamics,2012,41(13):1725-1749.
[27]Li S M.Diagonalization procedure for scaled boundary finite element method in modeling semi-infinite reservoir with uniform cross-section.International Journal for Numerical Methods in Engineering,2009,80(5):596-608.
[28]Givoli D.High-order local non-reflecting boundary conditions:a review.Wave Motion,2004,39(4):319-326.
[29]Geers T.Singly and doubly asymptotic computational boundaries.In:TL G,editor.Proceedings of the IUTAM Symposium on Computational Methods for Unbounded Domains.Dordrecht:Kluwer Academic Publishers;1998.p135-141.
[30]Prempramote S,Song C M,Tin-Loi F,et al.High-order doubly asymptotic open boundaries for scalar wave equation.International Journal for Numerical Methods in Engineering,2009,79(3):340-374.
[31]Wang X,Jin F,Prempramote S,et al.Time-domain analysis of gravity dam-reservoir interaction using high-order doubly asymptotic open boundary.Computers&Structures,2011,89(7-8):668-680.