基于比例边界有限元法的坝库瞬态耦合分析
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摘要
将比例边界有限元法延伸至坝库耦合瞬态分析中,建立了模拟无限水库的比例边界有限元法与有限元法的耦合公式,利用坝库耦合作用中的耦合项,发展了坝库耦合瞬态分析的流固耦合解耦迭代算法,分析了水平向地震激励下的重力坝、垂直坝等坝库耦合瞬态响应.其中:有限域,如坝体和无限水库中的近场域,用有限元法模拟;无限域,如无限水库中的远场域,用比例边界有限元法描述.上述耦合公式和流固耦合解耦迭代算法继承了比例边界有限元法模拟无限域的优点,如离散单元少、精度高、矩阵对称、无须基本解等,数值结果验证了公式和算法的准确性和可行性.
The scaled boundary finite element method(SBFEM) was extended to transient coupling analyses of the dam-reservoir interaction,and a SBFEM and finite element method(FEM) coupling formulation was derived.Through using the coupling terms in the coupling formulation,a decoupling iteration algorithm was developed to analyze the transient responses of vertical dam and gravity dam-reservoir systems subjected to horizontal ground shock excitations,where FEM was chosen to model finite domain,while SBFEM was applied to describe the characteristics of semi-infinite reservoir.The SBFEM-FEM coupling formulation and its corresponding iteration algorithm keep the merits of the SBFEM in representing unbounded fluid medium such as little discretized elements,high accuracy,symmetrical matrix,and no requirement for fundamental solution.Numerical results show the accuracy and feasibility of the coupling formulation and iteration algorithm.
The scaled boundary finite element method(SBFEM) was extended to transient coupling analyses of the dam-reservoir interaction,and a SBFEM and finite element method(FEM) coupling formulation was derived.Through using the coupling terms in the coupling formulation,a decoupling iteration algorithm was developed to analyze the transient responses of vertical dam and gravity dam-reservoir systems subjected to horizontal ground shock excitations,where FEM was chosen to model finite domain,while SBFEM was applied to describe the characteristics of semi-infinite reservoir.The SBFEM-FEM coupling formulation and its corresponding iteration algorithm keep the merits of the SBFEM in representing unbounded fluid medium such as little discretized elements,high accuracy,symmetrical matrix,and no requirement for fundamental solution.Numerical results show the accuracy and feasibility of the coupling formulation and iteration algorithm.
引文
[1]Lee G C,Tsai C S.Time-domain analyses of dam-reservoir system,I:exact solution[J].Journal ofEngineering Mechanics,1991,117(9):1990-2006.
[2]Sharan S K.Finite element analysis of unbounded andincompressible fluid domains[J].International Jour-nal for Numerical Methods in Engineering,1985,21(9):1659-1669.
[3]邱流潮,金峰,王进廷.海绵吸收层法在坝库水瞬态动力相互作用分析中的应用[J].水利学报,2004,35(1):46-50.
[4]Saini S S,Bettess P,Zienkiewicz O C.Coupled hy-drodynamic response of concrete gravity dams usingfinite and infinite elements[J].Earthquake Engineer-ing and Structural Dynamics,1978,6(4):363-374.
[5]Gogoi I,Maity D.A non-reflecting boundary condi-tion for the finite element modeling of infinite reser-voir with layered sediment[J].Advances in WaterResources,2006,29(10):1515-1527.
[6]Fan S C,Li S M.Boundary finite-element methodcoupling finite-element method for steady-state analy-ses of dam-reservoir systems[J].Journal of Engi-neering Mechanics-ASCE,2008,134(2):133-142.
[7]Li S M,Liang H,Li A M.A semi-analytical solutionfor characteristics of a dam-reservoir system with ab-sorptive reservoir bottom[J].Journal of Hydrody-namics,2008,20(6):727-734.
[8]Li S M.Diagonalization procedure for scaled bounda-ry finite element method in modelling semi-infinitereservoir with uniform cross section[J].InternationalJournal for Numerical Methods in Engineering,2009,80(5):596-608.
[9]Tsai C S,Lee G C.Time-domain analyses of dam-reservoir system.II:substructure method[J].Jour-nal of Engineering Mechanics-ASCE,1991,117(9):2007-2026.
[2]Sharan S K.Finite element analysis of unbounded andincompressible fluid domains[J].International Jour-nal for Numerical Methods in Engineering,1985,21(9):1659-1669.
[3]邱流潮,金峰,王进廷.海绵吸收层法在坝库水瞬态动力相互作用分析中的应用[J].水利学报,2004,35(1):46-50.
[4]Saini S S,Bettess P,Zienkiewicz O C.Coupled hy-drodynamic response of concrete gravity dams usingfinite and infinite elements[J].Earthquake Engineer-ing and Structural Dynamics,1978,6(4):363-374.
[5]Gogoi I,Maity D.A non-reflecting boundary condi-tion for the finite element modeling of infinite reser-voir with layered sediment[J].Advances in WaterResources,2006,29(10):1515-1527.
[6]Fan S C,Li S M.Boundary finite-element methodcoupling finite-element method for steady-state analy-ses of dam-reservoir systems[J].Journal of Engi-neering Mechanics-ASCE,2008,134(2):133-142.
[7]Li S M,Liang H,Li A M.A semi-analytical solutionfor characteristics of a dam-reservoir system with ab-sorptive reservoir bottom[J].Journal of Hydrody-namics,2008,20(6):727-734.
[8]Li S M.Diagonalization procedure for scaled bounda-ry finite element method in modelling semi-infinitereservoir with uniform cross section[J].InternationalJournal for Numerical Methods in Engineering,2009,80(5):596-608.
[9]Tsai C S,Lee G C.Time-domain analyses of dam-reservoir system.II:substructure method[J].Jour-nal of Engineering Mechanics-ASCE,1991,117(9):2007-2026.
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