LDDA动接触力的迭代算法
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摘要
概述了接触非线性问题的各种分析方法,指出了用Lagrange Discontinous Deformation Analysis(LDDA)求解缝面接触问题有较大优点,与DDA方法比较,它对接缝的处理更真实、更自然;又因为LDDA对全部接触力进行平衡迭代,所以接触力的计算精度也较高;同时,推导了LDDA的基本公式,提出了一个新的计算动接触力的迭代求解算法-改进的Uzawa迭代算法,该算法的松驰因子是依据块体接触的物理特性而非按照数学理论选用的,算例表明:LDDA理论和与之相对应的动接触力的迭代求解算法具有较快的收敛速度和较高的计算精度。为接触问题的计算提供了一个有效的方法和工具。
Lagrange Discontinous Deformation Analysis (LDDA) can be used to solve contact nonlinear problem. Compared with other methods, LDDA has many advantages. First, its joint simulation is truer and more natural then DDA; secondly, its contact force can achieve highly accurate solution due to equilibrium iteration. In this paper, LDDA’s primary formulae are derived, a new iterative algorithm for dynamic contact forces is introduced, in which the relax factor is chosen by physical property other than by mathematic theory. The application example indicates that the algorithm has high calculating efficiency. Thusly, an effective measure and implement for contact analysis will be provided.
Lagrange Discontinous Deformation Analysis (LDDA) can be used to solve contact nonlinear problem. Compared with other methods, LDDA has many advantages. First, its joint simulation is truer and more natural then DDA; secondly, its contact force can achieve highly accurate solution due to equilibrium iteration. In this paper, LDDA’s primary formulae are derived, a new iterative algorithm for dynamic contact forces is introduced, in which the relax factor is chosen by physical property other than by mathematic theory. The application example indicates that the algorithm has high calculating efficiency. Thusly, an effective measure and implement for contact analysis will be provided.
引文
[1]朱伯芳,高季章,陈祖煜,厉易生.拱坝设计与研究[M].北京:中国水利水电出版社,2002.Zhu Bofang,Gao Jizhang,Chen Zuyu,Li Yisheng.Design and research for concrete arch dams[M].Beijnig:China Water Power Press,2002.(in Chinese)
[2]刘书,刘晶波,方鄂华.动接触问题及其数值模拟的研究进展[J].工程力学,1999,16(6):14~28.Liu Shu,Liu Jingbo,Fang E’hua.The advances of studies on dynamic contact problem and its numerical methods[J].Engineering Mechanics,1999,16(6):14~28.(in Chinese)
[3]涂劲.有缝界面的混凝土高坝—地基系统非线性地震波动反应分析[D].北京:中国水利水电科学研究院,1999.Tu Jin.Nonlinear seismic response analysis of high concrete dam-foundation systems with joint surface[D].Beijing:China Institute of Water Resources and Hydropower Research,1999.(in Chinese)
[4]Cai Y,He T,Wang R.Numerical simulation of dynamic process of the Tangshan earthquake by a new method LDDA[J].Pure and Applied Geophysics,2000,157(11/12):2083~2104.
[5]Hilbert,LBL,Jr.Y W,Cook N G W,Cai Y,Liang G P.A new discontinuous finite element method for interaction of many deformable bodies in geomechanices[C].In:Proceedings of the8th Int Conf Comp Meth,Adv.Geomech,1994.931~936.
[6]Kolsky H.Stress waves in solids[M].New York:Dover Publications,1963.
[7]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.Zhu Bofang.The finite element method theory and applications[M].Beijing:China Water Power Press,1998.(in Chinese)
[8]李小军,刘爱文.动力方程求解的显式积分格式及其稳定性与适用性[J].世界地震工程,2000,16(2):8~12.Li Xiaojun,Liu Aiwen.Explicit step-by-step integration formulas for dynamic differential equation and their stability and applicability[J].World Information on Earthquake Engineering,2000,16(2):8~12.(in Chinese)
[9]刘金朝,蔡永恩.求解接触问题的一种新的实验误差法[J].力学学报,2002,34(2):286~290.Liu Jinzhao,Cai Yongen.A new test error method to solve the contact problems[J].Acta Mechanica Sinica,2002,34(2):286~290.(in Chinese)
[10]刘金朝,王成国,梁国平.多弹性体接触问题的数值算法[J].中国铁道科学,2003,24(3):69~73.Liu Jinzhao,Wang Chengguo,Liang Guoping.Numerical algorithm to solve elastic multi-body contact problems[J].China Railway Science,2003,24(3):69~73.(in Chinese)
[11]黎勇,栾茂田.非连续变形计算力学模型基本原理及其线性规划解[J].大连理工大学学报,2000,40(3):351~357.Li Yong,Luan Maotian.Fundamentals and formulations of discontinuous deformation mechanics model and its linear programming algorithm[J].Journal of Dalian University of Technology,2000,40(3):351~357.(in Chinese)
[12]杜丽惠,邓良军,陈宏钧,叶建群.直接约束法在水工建筑物接触分析中的应用[J].清华大学学报(自然科学版),2003,43(11):1534~1537.Du Lihui,Deng Liangjun,Chen Hongjun,Ye Jianqun.Direct constraint procedure to solve contact problems in hydrostructures[J].Journal of Tsinghua University(Sci&Tech),2003,43(11):1534~1537.(in Chinese)
[13]Bramble J,Pasciak J,Vassilev A.Analysis of the inexact Uzawa algorithm for saddle point problems[J].Math Comp.,1997,34:1072~1092.
[14]张伯艳.高拱坝坝肩抗震稳定研究[D].西安:西安理工大学,2005.Zhang Boyan.High arch dam abutment aseismatic stability study[D].Xi’an:Xi’an University of Technology,2005.(in Chinese)
[15]周正华,周扣华.有阻尼振动方程常用显式积分格式稳定性分析[J].地震工程与工程振动,2001,21(3):22~28.Zhou Zhenghua,Zhou Kouhua.Stability analysis of explicit integral methods for damped vibration equation[J].Earthquake Engineering and Engineering Vibration,2001,21(3):22~28.(in Chinese)
[16]陈学良,袁一凡.求解振动方程的一种显式积分格式及其精度与稳定性[J].地震工程与工程振动,2002,22(3):9~14.Chen Xueliang,Yuan Yifan.Explicit integration formula for vibration equation and its accuracy and stability[J].Earthquake Engineering and Engineering Vibration,2002,22(3):9~14.(in Chinese)
[2]刘书,刘晶波,方鄂华.动接触问题及其数值模拟的研究进展[J].工程力学,1999,16(6):14~28.Liu Shu,Liu Jingbo,Fang E’hua.The advances of studies on dynamic contact problem and its numerical methods[J].Engineering Mechanics,1999,16(6):14~28.(in Chinese)
[3]涂劲.有缝界面的混凝土高坝—地基系统非线性地震波动反应分析[D].北京:中国水利水电科学研究院,1999.Tu Jin.Nonlinear seismic response analysis of high concrete dam-foundation systems with joint surface[D].Beijing:China Institute of Water Resources and Hydropower Research,1999.(in Chinese)
[4]Cai Y,He T,Wang R.Numerical simulation of dynamic process of the Tangshan earthquake by a new method LDDA[J].Pure and Applied Geophysics,2000,157(11/12):2083~2104.
[5]Hilbert,LBL,Jr.Y W,Cook N G W,Cai Y,Liang G P.A new discontinuous finite element method for interaction of many deformable bodies in geomechanices[C].In:Proceedings of the8th Int Conf Comp Meth,Adv.Geomech,1994.931~936.
[6]Kolsky H.Stress waves in solids[M].New York:Dover Publications,1963.
[7]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.Zhu Bofang.The finite element method theory and applications[M].Beijing:China Water Power Press,1998.(in Chinese)
[8]李小军,刘爱文.动力方程求解的显式积分格式及其稳定性与适用性[J].世界地震工程,2000,16(2):8~12.Li Xiaojun,Liu Aiwen.Explicit step-by-step integration formulas for dynamic differential equation and their stability and applicability[J].World Information on Earthquake Engineering,2000,16(2):8~12.(in Chinese)
[9]刘金朝,蔡永恩.求解接触问题的一种新的实验误差法[J].力学学报,2002,34(2):286~290.Liu Jinzhao,Cai Yongen.A new test error method to solve the contact problems[J].Acta Mechanica Sinica,2002,34(2):286~290.(in Chinese)
[10]刘金朝,王成国,梁国平.多弹性体接触问题的数值算法[J].中国铁道科学,2003,24(3):69~73.Liu Jinzhao,Wang Chengguo,Liang Guoping.Numerical algorithm to solve elastic multi-body contact problems[J].China Railway Science,2003,24(3):69~73.(in Chinese)
[11]黎勇,栾茂田.非连续变形计算力学模型基本原理及其线性规划解[J].大连理工大学学报,2000,40(3):351~357.Li Yong,Luan Maotian.Fundamentals and formulations of discontinuous deformation mechanics model and its linear programming algorithm[J].Journal of Dalian University of Technology,2000,40(3):351~357.(in Chinese)
[12]杜丽惠,邓良军,陈宏钧,叶建群.直接约束法在水工建筑物接触分析中的应用[J].清华大学学报(自然科学版),2003,43(11):1534~1537.Du Lihui,Deng Liangjun,Chen Hongjun,Ye Jianqun.Direct constraint procedure to solve contact problems in hydrostructures[J].Journal of Tsinghua University(Sci&Tech),2003,43(11):1534~1537.(in Chinese)
[13]Bramble J,Pasciak J,Vassilev A.Analysis of the inexact Uzawa algorithm for saddle point problems[J].Math Comp.,1997,34:1072~1092.
[14]张伯艳.高拱坝坝肩抗震稳定研究[D].西安:西安理工大学,2005.Zhang Boyan.High arch dam abutment aseismatic stability study[D].Xi’an:Xi’an University of Technology,2005.(in Chinese)
[15]周正华,周扣华.有阻尼振动方程常用显式积分格式稳定性分析[J].地震工程与工程振动,2001,21(3):22~28.Zhou Zhenghua,Zhou Kouhua.Stability analysis of explicit integral methods for damped vibration equation[J].Earthquake Engineering and Engineering Vibration,2001,21(3):22~28.(in Chinese)
[16]陈学良,袁一凡.求解振动方程的一种显式积分格式及其精度与稳定性[J].地震工程与工程振动,2002,22(3):9~14.Chen Xueliang,Yuan Yifan.Explicit integration formula for vibration equation and its accuracy and stability[J].Earthquake Engineering and Engineering Vibration,2002,22(3):9~14.(in Chinese)
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