基于比例边界有限元法动态刚度矩阵的坝库耦合分析方法
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摘要
针对坝体在水平向激励下的瞬态耦合问题和基于比例边界有限元法,推导了等横截面半无限水库的动态刚度矩阵,其值用贝赛尔函数计算。基于该动态刚度矩阵,建立了有限元法与比例边界有限元法的耦合方程,分析了水平向激励下任意几何形状的半无限水库的瞬态响应。其中,半无限水库分解成用有限元离散的任意几何形状的近场域和用比例边界有限元法模拟的远场域即等横截面半无限水库。通过比较动态刚度矩阵和动态质量矩阵模拟等横截面半无限水库的计算效率,发现它们计算精度相同,但动态刚度矩阵效率更高。数值算例表明了所发展的动态刚度矩阵与其耦合方程的正确性。
For dam transient analysis subjected to horizontal ground excitations and based on the scaled boundary finite element method(SBFEM),a dynamic stiffness of semi-infinite reservoir with constant cross section was proposed,which was evaluated by the Bessel function.Based on the dynamic stiffness,a SBFEM and finite element method(FEM) coupling equation was developed to analyze transient responses of semi-infinite reservoir with arbitrary geometry under horizontal ground excitations,where the semi-infinite reservoir was divided into two parts: near field and far field(semi-infinite reservoir with constant cross section).The near field with arbitrary geometry was discretized by FEM,while the far field was modeled by the SBFEM.Through comparing the calculation efficiency of the dynamic stiffness matrix and that of the dynamic mass matrix,it was found that the calculation efficiency of the dynamic stiffness matrix was higher than that of the dynamic mass matrix,and both of them had the same accuracy.Numerical examples showed the accuracy of the developed dynamic stiffness matrix and its coupled equation.
For dam transient analysis subjected to horizontal ground excitations and based on the scaled boundary finite element method(SBFEM),a dynamic stiffness of semi-infinite reservoir with constant cross section was proposed,which was evaluated by the Bessel function.Based on the dynamic stiffness,a SBFEM and finite element method(FEM) coupling equation was developed to analyze transient responses of semi-infinite reservoir with arbitrary geometry under horizontal ground excitations,where the semi-infinite reservoir was divided into two parts: near field and far field(semi-infinite reservoir with constant cross section).The near field with arbitrary geometry was discretized by FEM,while the far field was modeled by the SBFEM.Through comparing the calculation efficiency of the dynamic stiffness matrix and that of the dynamic mass matrix,it was found that the calculation efficiency of the dynamic stiffness matrix was higher than that of the dynamic mass matrix,and both of them had the same accuracy.Numerical examples showed the accuracy of the developed dynamic stiffness matrix and its coupled equation.
引文
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[2]Wolf J P.The scaled boundary finite element method[M].Chichester:Wiley,2003:51―54.
[3]Lin G,Du J G,Hu Z Q.Dynamic dam-reservoirinteraction analysis including effect of reservoirboundary absorption[J].Science in China Series E:Technological Sciences,2007,50:1―10.
[4]Lin G,Wang Y,Hu Z Q.Hydrodynamic pressure on archdam and gravity dam including absorption effect ofreservoir sediments[C].WCCM/APCOM 2010,IOPConference series:Material Science and Engineering,10012234:1―10.
[5]Fan S C,Li S M.Boundary finite element methodcoupling finite element method for steady-state analysesof dam-reservoir systems[J].Journal of EngineeringMechanics,2008,134(2):133―142.
[6]Li S M,Liang H,Li A M.A semi-analytical solution forcharacteristics of a dam-reservoir system with absorptivereservoir bottom[J].Journal of Hydrodynamics,2008,20(6):727―734.
[7]Ekevid T,Wiberg N E.Wave propagation related tohigh-speed train-A scaled boundary FE-approach forunbounded domains[J].Computer Methods in AppliedMechanics and Engineering,2002,191:3947―3964.
[8]Fan S C,Li S M,Yu G Y.Dynamic fluid-structureinteraction analysis using boundary finite elementmethod-finite element method[J].Journal of AppliedMechanics,ASME,2005,72:591―598.
[9]Li S M.Coupled finite element-scaled boundary finiteelement method for transient analysis of dam-reservoirinteraction[C].Lecture Notes in Computer Science,2011,Part IV,LNCS 6785:26―34.
[10]Bazyar M H,Song C M.A continued-fraction-basedhigh-order transmitting boundary for wave propagationin unbounded domains of arbitrary geometry[J].International Journal for Numerical Methods inEngineering,2008,74:209―237.
[11]Wang X,Jin F,Prempramote S,Song C M.Time-domainanalysis of gravity dam-reservoir interaction usinghigh-order doubly asymptotic open boundary[J].Computers and Structures,2011,89:668―680.
[12]Li S M.Diagonalization procedure for scaled boundaryfinite element method in modelling semi-infinitereservoir with uniform cross section[J].InternationalJournal for Numerical Methods in Engineering,2009,80(5):596―608.
[13]Lee G C,Tsai C S.Time-domain analyses ofdam-reservoir system,I:Exact solution[J].Journal ofEngineering Mechanics,1991,117(9):1990―2006.
[14]Tsai C S,Lee G C.Time-domain analyses ofdam-reservoir system.II:Substructure method[J].Journal of Engineering Mechanics,ASCE,1991,117(9):2007―2026.
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