块体单元法动力分析研究
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摘要
将块体单元法引入结构动力分析,同时给出动力分析的块体单元法中质量矩阵和阻尼矩阵的具体表达式,建立块体系统在惯性力、阻尼力、动力荷载及弹性力作用下的动力平衡方程。最后分析2个算例,通过将块体单元法与其他方法计算结果进行对比,验证块体单元法动力分析的准确性和合理性。块体单元法对于岩体中含大量不连续面的复杂结构在前处理工作上有较大的优越性,因此可广泛应用于水工及岩土工程结构动力及地震作用下的变形与稳定性分析。
Dynamic analysis of structures is one of main issues of structural design,especially for structures of rock masses containing various discontinuities.Numerical analysis is an important method for the problem.Block element method(BEM)is an effective numerical method for the analysis of rock masses.BEM is employed to expand the dynamic analysis of structures.At first,the formulas of mass matrix and damping matrix for dynamic analysis of BEM are presented;then,the dynamic equilibrium equations of the block system subjected to the inertia forces,the damping forces,the dynamic loads and the elastic forces are formulated.Finally,two examples are studied with the method.Both of the results are very close to those calculated by other methods.BEM has advantages in pretreatment of large numbers of discontinuities contained in rock masses;so it is expected to be widely used in stability analysis of complicated rock masses under dynamic or seismic loadings.
Dynamic analysis of structures is one of main issues of structural design,especially for structures of rock masses containing various discontinuities.Numerical analysis is an important method for the problem.Block element method(BEM)is an effective numerical method for the analysis of rock masses.BEM is employed to expand the dynamic analysis of structures.At first,the formulas of mass matrix and damping matrix for dynamic analysis of BEM are presented;then,the dynamic equilibrium equations of the block system subjected to the inertia forces,the damping forces,the dynamic loads and the elastic forces are formulated.Finally,two examples are studied with the method.Both of the results are very close to those calculated by other methods.BEM has advantages in pretreatment of large numbers of discontinuities contained in rock masses;so it is expected to be widely used in stability analysis of complicated rock masses under dynamic or seismic loadings.
引文
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[15]王文亮.结构动力学[M].上海:复旦大学出版社,1993.(WANG Wenliang.Structural dynamics[M].Shanghai:Fudan University Press,1993.(in Chinese))
[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 Xiuli,CHEN Houqun,HOU Shunzai.The three-dimensional nonlinear earthquake response analysis of arch dam-foundation system[J].Journal of Hydraulic Engineering,1997,(8):7-14.(in Chinese))
[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 Boyan,CHEN Houqun,DU Xiuli,et al.Arch dam abutment asiesmatic stability analysis[J].Journal of Hydraulic Engineering,2000,(11):55-59.(in Chinese))
[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 Chuhan,WANG Guanglun,et al.Three-dimensional distinct element numerical model for static and dynamic analysis of rock mass[J].Journal of Tsinghua University(Science and Technology),1996,36(10):98-104.(in Chinese))
[5]SHI G H.Discontinuous deformation analysis:a new numerical model for the statics and dynamics of deformable 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.(ZHUO Jiashou,ZHANG Qing.Interface element method for discontinuum mechanics[M].Beijing:Science Press,2000.(in Chinese))
[7]陈胜宏.高坝复杂岩石地基及岩石高边坡稳定分析[M].北京:中水利水电出版社,2002.(CHEN Shenghong.Stability analysis of complicated rock foundation of high dam and high rock slope[M].Beijing:China Water Power Press,2002.(in Chinese))
[8]LI Y M,CHEN S H.A dynamic formulation of block element method[J].Chinese Journal of Geotechnical Engineering,2003,25(5):647-650.
[9]朱伯芳.有限单元法原理与应用[M].2版.北京:中水利水电出版社,1998.(ZHU Bofang.Finite element method theory and applications[M].2nd ed.Beijing:China Water Power Press,1998.(in Chinese))
[10]陆述远.水工建筑物专题(复杂坝基和地下结构)[M].武汉:水利电力出版社,1994.(LU Shuyuan.Special topic on hydraulic structures(complicated foundations and underground structures)[M].Wuhan:Water Resource and Hydropower Press,1994.(in Chinese))
[11]BATHE K J.Finite element procedures in engineering analysis[M].Englewood Cliffs,New Jersey:Pretice-Hall,Inc.,1982.
[12]方义琳,卓家寿,章青.具有任意形状单元离散模型的界面元法[J].工程力学,1998,15(2):27-37.(FANG Yilin,ZHUO Jiashou,ZHANG Qing.Interface stress element method for distinct model with elements of arbitrary shape[J].Engineering Mechanics,1998,15(2):27-37.(in Chinese))
[13]鲁祖统,郭乙木.岩土材料动态特性参数的内在机制及相互关系的探讨[J].振动与冲击,1994,(1):31-40.(LU Zutong,GUO Yimu.A probe of internal mechanisms and mutual relations of dynamic characteristic parameters of geotechnical materials[J].Journal of Vibration and Shock,1994,(1):31-40.(in Chinese))
[14]肖诗云,林皋,王哲,等.应变率对混凝土抗拉特性影响[J].大连理工大学学报,2001,41(6):721-725.(XIAO Shiyun,LIN Gao,WANG Zhe,et al.Effects of strain rate on dynamic behavior of concrete in tension[J].Journal of Dalian University of Technology,2001,41(6):721-725.(in Chinese))
[15]王文亮.结构动力学[M].上海:复旦大学出版社,1993.(WANG Wenliang.Structural dynamics[M].Shanghai:Fudan University Press,1993.(in Chinese))
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