基于ABAQUS的动水压力波双渐近透射边界单元及应用
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摘要
高阶双渐近透射边界能够在全频范围内迅速逼近准确解,具有很高的计算精度和计算效率。基于大型通用有限元软件ABAQUS提供的用户子程序接口UEL开发了动水压力波双渐近透射边界单元,实现了有限元-双渐近透射边界时域耦合分析模型。双渐近透射边界单元的刚度矩阵和阻尼矩阵均为常矩阵,在分析计算中仅需计算一次,因此可以预先求解再读入ABAQUS以提高计算效率。通过数值算例验证了双渐近透射边界单元程序的正确性,并将其应用到大坝-库水动力相互作用分析。算例分析结果表明,双渐近透射边界单元具有良好的稳定性和计算精度,适用于实际大坝的地震响应分析。
The high order doubly asymptotic open boundary can converge to the exact solution over the whole frequency range. It has high computational accuracy and efficiency. Based on the user element subroutine interface UEL offered by the ABAQUS, a doubly asymptotic open boundary element for hydrodynamic pressure wave analysis was developed and the time-domain coupled analysis model by combining the finite element method and doubly asymptotic open boundary was realized. The stiffness matrix and damping matrix of the doubly asymptotic open boundary element are both constant matrices, which need to be solved only once during the analysis procedure. To increase the computational efficiency, they can be solved in advance and read into the ABAQUS during the analysis. The proposed element was verified by numerical examples and applied to the dynamic dam-reservoir interaction analysis. The numerical results demonstrate that the proposed user element is of good numerical stability and high computational accuracy. It is applicable to the seismic response analysis of realistic dams.
The high order doubly asymptotic open boundary can converge to the exact solution over the whole frequency range. It has high computational accuracy and efficiency. Based on the user element subroutine interface UEL offered by the ABAQUS, a doubly asymptotic open boundary element for hydrodynamic pressure wave analysis was developed and the time-domain coupled analysis model by combining the finite element method and doubly asymptotic open boundary was realized. The stiffness matrix and damping matrix of the doubly asymptotic open boundary element are both constant matrices, which need to be solved only once during the analysis procedure. To increase the computational efficiency, they can be solved in advance and read into the ABAQUS during the analysis. The proposed element was verified by numerical examples and applied to the dynamic dam-reservoir interaction analysis. The numerical results demonstrate that the proposed user element is of good numerical stability and high computational accuracy. It is applicable to the seismic response analysis of realistic dams.
引文
[ 1 ] Kü?üKARSLAN S,COSKUN S B,TASKIN B.Transient analysis of dam-reservoir interaction including the reservoir bottom effects[J].Journal of Fluids and Structures,2005,20(8):1073-1084.
[ 2 ] ANTES H,VON ESTORFF O.Analysis of absorption effects on the dynamic response of dam reservoir systems by boundary element methods[J].Earthquake Engineering & Structural Dynamics,1987,15(8):1023-1036.
[ 3 ] SOARES JR D,VON ESTORFF O,MANSUR W J.Efficient non-linear solid-fluid interaction analysis by an iterative BEM/FEM coupling[J].International Journal for Numerical Methods in Engineering,2005,64(11):1416-1431.
[ 4 ] SONG C,WOLF J P.The scaled boundary finite-element method-alias consistent infinitesimal finite-element cell method-for elastodynamics[J].Computer Methods in Applied Mechanics and Engineering,1997,147(3/4):329-355.
[ 5 ] 杜建国,林皋,谢清粮.一种新的求解坝面动水压力的半解析方法[J].振动与冲击,2009,28(3):31-34.DU Jianguo,LIN Gao,XIE Qingliang.A new semi-analytical method for solving hydrodynamic pressure on dams[J].Journal of Vibration and Shock,2009,28(3):31-34.
[ 6 ] LIN G,DU J,HU Z.Dynamic dam-reservoir interaction analysis including effect of reservoir boundary absorption[J].Science in China Series E:Technological Sciences,2007,50:1-10.
[ 7 ] LIN G,WANG Y,HU Z.An efficient approach for frequency-domain and time-domain hydrodynamic analysis of dam-reservoir systems[J].Earthquake Engineering & Structural Dynamics,2012,41(13):1725-1749.
[ 8 ] LI S M.Diagonalization procedure for scaled boundary finite element method in modeling semi-infinite reservoir with uniform cross-section[J].International Journal for Numerical Methods in Engineering,2009,80(5):596-608.
[ 9 ] GIVOLI D.High-order local non-reflecting boundary conditions:a review[J].Wave Motion,2004,39(4):319-326.
[10] GEERS T.Singly and doubly asymptotic computational boundaries[C]//Proceedings of the IUTAM Symposium on Computational Methods for Unbounded Domains.Dordrecht:Kluwer Academic Publishers,1998.
[11] PREMPRAMOTE S,SONG C,TIN-LOI F,et al.High-order doubly asymptotic open boundaries for scalar wave equation[J].International Journal for Numerical Methods in Engineering,2009,79(3):340-374.
[12] WANG X,JIN F,PREMPRAMOTE S,et al.Time-domain analysis of gravity dam-reservoir interaction using high-order doubly asymptotic open boundary[J].Computers & Structures,2011,89(7/8):668-680.
[13] 王翔,金峰.动水压力波高阶双渐近时域平面透射边界I:理论推导[J].水利学报,2011,42(7):839-847.WANG Xiang,JIN Feng.High-order doubly asymptotic time-domain plane transmitting boundary for hydrodynamic pressure I:theoretical derivation[J] .Journal of Hydraulic Engineering,2011,42(7):839-847.
[14] GAO Y,JIN F,WANG X,et al.Finite element analysis of dam-reservoir interaction using high-order doubly asymptotic open boundary[J].Mathematical Problems in Engineering,2011,2011:201624.
[ 2 ] ANTES H,VON ESTORFF O.Analysis of absorption effects on the dynamic response of dam reservoir systems by boundary element methods[J].Earthquake Engineering & Structural Dynamics,1987,15(8):1023-1036.
[ 3 ] SOARES JR D,VON ESTORFF O,MANSUR W J.Efficient non-linear solid-fluid interaction analysis by an iterative BEM/FEM coupling[J].International Journal for Numerical Methods in Engineering,2005,64(11):1416-1431.
[ 4 ] SONG C,WOLF J P.The scaled boundary finite-element method-alias consistent infinitesimal finite-element cell method-for elastodynamics[J].Computer Methods in Applied Mechanics and Engineering,1997,147(3/4):329-355.
[ 5 ] 杜建国,林皋,谢清粮.一种新的求解坝面动水压力的半解析方法[J].振动与冲击,2009,28(3):31-34.DU Jianguo,LIN Gao,XIE Qingliang.A new semi-analytical method for solving hydrodynamic pressure on dams[J].Journal of Vibration and Shock,2009,28(3):31-34.
[ 6 ] LIN G,DU J,HU Z.Dynamic dam-reservoir interaction analysis including effect of reservoir boundary absorption[J].Science in China Series E:Technological Sciences,2007,50:1-10.
[ 7 ] LIN G,WANG Y,HU Z.An efficient approach for frequency-domain and time-domain hydrodynamic analysis of dam-reservoir systems[J].Earthquake Engineering & Structural Dynamics,2012,41(13):1725-1749.
[ 8 ] LI S M.Diagonalization procedure for scaled boundary finite element method in modeling semi-infinite reservoir with uniform cross-section[J].International Journal for Numerical Methods in Engineering,2009,80(5):596-608.
[ 9 ] GIVOLI D.High-order local non-reflecting boundary conditions:a review[J].Wave Motion,2004,39(4):319-326.
[10] GEERS T.Singly and doubly asymptotic computational boundaries[C]//Proceedings of the IUTAM Symposium on Computational Methods for Unbounded Domains.Dordrecht:Kluwer Academic Publishers,1998.
[11] PREMPRAMOTE S,SONG C,TIN-LOI F,et al.High-order doubly asymptotic open boundaries for scalar wave equation[J].International Journal for Numerical Methods in Engineering,2009,79(3):340-374.
[12] WANG X,JIN F,PREMPRAMOTE S,et al.Time-domain analysis of gravity dam-reservoir interaction using high-order doubly asymptotic open boundary[J].Computers & Structures,2011,89(7/8):668-680.
[13] 王翔,金峰.动水压力波高阶双渐近时域平面透射边界I:理论推导[J].水利学报,2011,42(7):839-847.WANG Xiang,JIN Feng.High-order doubly asymptotic time-domain plane transmitting boundary for hydrodynamic pressure I:theoretical derivation[J] .Journal of Hydraulic Engineering,2011,42(7):839-847.
[14] GAO Y,JIN F,WANG X,et al.Finite element analysis of dam-reservoir interaction using high-order doubly asymptotic open boundary[J].Mathematical Problems in Engineering,2011,2011:201624.
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