复合单元法动力分析初步研究
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摘要
复合单元法是一种适用于不连续介质结构分析的数值计算方法,优点是建立网格时不用考虑结构中不连续面,计算时能离散模拟不连续面。在复合单元法静力计算模型的基础上,提出了复合单元的动力分析方法。给出了复合单元动力分析的质量矩阵和阻尼矩阵的具体表达式,通过质量矩阵、刚度矩阵和阻尼矩阵将分布于复合单元内部的惯性力和阻尼力分别转移到复合单元的广义节点上。建立了惯性力、阻尼力、动力荷载及弹性力作用下的复合单元动力系统的控制方程组。以一个基岩内含有两条断层的混凝土重力坝模型地震为例,采用复合单元法动力分析程序进行计算,其结果与有限单元法解吻合得较好,说明所提出方法的正确性和有效性。
Composite element method(CEM) is a numerical method suitable for discontinuous media structure.The main advantages of CEM are that the discontinuities can be ignored when creating grid,but the discontinuities can be explicitly simulated when calculating.Based on composite element model for static analysis,the composite element model for dynamic analysis is implemented.The formulas of mass matrix and damping matrix for dynamic analysis of CEM are presented.According to mass matrix,stiffness matrix and damping matrix,the inertial forces and the damping forces in composite element are converted to the generalized nodes.The control equations for dynamic system of CEM subjected to the inertia forces,the damping forces,the dynamic loads and the elastic forces are formulated.A seismic example of a concrete gravity dam on a rock base with two faults is computed by the CEM dynamic analysis program.The results meet well with the solution of finite element method(FEM).It shows the validity and effectiveness of the new method.
Composite element method(CEM) is a numerical method suitable for discontinuous media structure.The main advantages of CEM are that the discontinuities can be ignored when creating grid,but the discontinuities can be explicitly simulated when calculating.Based on composite element model for static analysis,the composite element model for dynamic analysis is implemented.The formulas of mass matrix and damping matrix for dynamic analysis of CEM are presented.According to mass matrix,stiffness matrix and damping matrix,the inertial forces and the damping forces in composite element are converted to the generalized nodes.The control equations for dynamic system of CEM subjected to the inertia forces,the damping forces,the dynamic loads and the elastic forces are formulated.A seismic example of a concrete gravity dam on a rock base with two faults is computed by the CEM dynamic analysis program.The results meet well with the solution of finite element method(FEM).It shows the validity and effectiveness of the new method.
引文
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[2]杜修力,陈厚群,侯顺载.拱坝-地基系统的三维非线性地震反应分析[J].水利学报,1997,(8):7-14.DU Xiu-li,CHEN Hou-qun,HOU Shun-zai.Thethree-dimensional nonlinear earthquake response analysisof arch dam-foundation system[J].Journal of HydraulicEngineering,1997,(8):7-14.
[3]张伯艳,陈厚群,杜修力,等.拱坝坝肩抗震稳定分析[J].水利学报,2000,(11):55-59.ZHANG Bo-yan,CHEN Hou-qun,DU Xiu-li,et al.Archdam abutment seismic stability analysis[J].Journal ofHydraulic Engineering,2000,(11):55-59.
[4]鲁军,张楚汉,王光伦,等.岩体动静力稳定分析的三维离散元数值模型[J].清华大学学报(自然科学版),1996,36(10):98-104.LU Jun,ZHANG Chu-han,WANG Guang-lun,et al.Three-dimensional distinct element numerical model forstatic and dynamic analysis of rock mass[J].Journal ofTsinghua University(Science and Technology),1996,36(10):98-104.
[5]SHI G H.Discontinuous deformation analysis:a newnumerical model for the statics and dynamics ofdeformable block structures[J].Engineering Computations,1992,9(2):157-168.
[6]卓家寿,张青.不连续介质力学问题的界面元法[M].北京:科学出版社,2000.
[7]郑惠峰,汪卫明,陈胜宏.块体单元法动力分析研究[J].岩石力学与工程学报,2007,26(3):608-613.ZHENG Hui-feng,WANG Wei-ming,CHEN Sheng-hong.Study on block element method for dynamic analysis[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(3):608-613.
[8]CHEN S H,QIANG S,CHEN S F,et al.Compositeelement analysis and justification for the rock massesreinforced by fully grouted bolt[J].Rock Mechanics andRock Engineering.2004,37(3):193-212.
[9]何则干,陈胜宏.加锚节理岩体的复合单元法研究[J].岩土力学,2007,28(8):1544-1549.HE Ze-gan,CHEN Sheng-hong.Study on bolteddiscontinuous rock mass by composite element method[J].Rock and Soil Mechanics,2007,28(8):1544-1549.
[10]CHEN S H,XU Q,HU J.Composite elements method forseepage analysis of geotechnical structures with drainagehole array[J].Journal of Hydrodynamics(Series B),2004,16(3):260-266.
[11]CHEN S H,QIANG S.Composite element model fordiscontinuous rock masses[J].International Journal ofRock Mechanics and Mining Sciences,2004,41(5):865-870.
[12]许桂生,陈胜宏.无压渗流分析的复合单元法[J].岩土力学,2005,26(5):745-749.XU Gui-sheng,CHEN Sheng-hong.Unconfined seepageanalysis with composite element method[J].Rock andSoil Mechanics,2005,26(5):745-749.
[13]薛娈鸾,陈胜宏.岩石裂隙渗流与法向应力耦合的复合单元模型[J].岩石力学与工程学报,2007,26(增刊1):2613-2619.XUE Luan-luan,CHEN Sheng-hong.Composite elementmodel of seepage-normal stress coupling for rockfractures[J].Chinese Journal of Rock Mechanics andEngineering,2007,26(Supp.1):2613-2619.
[14]QIANG S,ZHANG Y,CHEN S H.Research on thepre-process of three dimensional composite elementmethod for discontinuous rock[C]//Proceedings of theSixth European Conference on Numerical Methods inGeotechnical Engineering.London:Taylor and FrancisGroup,2006:283-288.
[15]朱伯芳.有限单元法原理与应用(第二版)[M].北京:中国水利水电出版社,1998.
[16]陆述远.高等水工结构[M].北京:中国电力出版社,1999.
[17]QIANG S,ZHANG Y,CHEN S H,et al.Application ofcomposite element method to Pubugou undergroundengineering[C]//Proceedings of the 4th Asian RockMechanics Symposium.Singapore:World ScientificPublishing Co.Pte.Ltd.,2006:169.
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