有限元-无限元法在重力坝应力分析中的应用
|
摘要
为考虑坝体-地基共同作用,建立了有限元-无限元耦合分析模型.首先介绍了二维问题中常用的单向无限单元的坐标变换式和位移函数,然后运用ABAQUS程序对一具有精确解的平面问题分别进行了有限元、有限元-无限元耦合分析,验证了引入无限元模拟无限域或半无限域问题的正确性和精确性.然后对KOYNA重力坝进行了静力计算分析,对有限元、有限元-无限元计算结果进行了比较.结果表明,基于ABAQUS的有限元-无限元法计算量小、精度高,为求解类似的无限域或半无限域问题提供了简洁、合理、精确的计算方法.
The finite-infinite elements coupling analysis models are built in order to consider dam-foundation combined action problems.The coordinate transformation format and displacement function of single direction infinite elements which are in common use in the numerical analysis of 2-D problems is firstly introduced.Then a plane problem which has an exact solution is analyzed based on ABAQUS program with the general finite element method and the finite-infinite element coupling method.It is derived that the finite-infinite element coupling method for the infinite or half infinite region problem has the advantage of more satisfactory precision and reliability.Then the static stress of Koyna gravity dam is analyzed;and the results of the general finite element method and the finite-infinite element coupling method are compared.The results show that the coupling method which is based on ABAQUS has low computational complexity and high accuracy;and offers a simple,logical,accurate calculation method for the analogous infinite or half infinite region problem.
The finite-infinite elements coupling analysis models are built in order to consider dam-foundation combined action problems.The coordinate transformation format and displacement function of single direction infinite elements which are in common use in the numerical analysis of 2-D problems is firstly introduced.Then a plane problem which has an exact solution is analyzed based on ABAQUS program with the general finite element method and the finite-infinite element coupling method.It is derived that the finite-infinite element coupling method for the infinite or half infinite region problem has the advantage of more satisfactory precision and reliability.Then the static stress of Koyna gravity dam is analyzed;and the results of the general finite element method and the finite-infinite element coupling method are compared.The results show that the coupling method which is based on ABAQUS has low computational complexity and high accuracy;and offers a simple,logical,accurate calculation method for the analogous infinite or half infinite region problem.
引文
[1]Ungless R F.An infinite finite element[D].M.A.Sc:University of British Columbia,1973:1-10.
[2]Bettess P,Zienkiewicz O C.Diffraction and refractionof surface waves using finite and infinite elements[J].International Journal for Numerical Methods in Engi-neering,1977,13:1271-1290.
[3]Bettess P.More on infinite element[J].InternationalJournal for Numerical Methods in Engineering,1980,16:1613-1626.
[4]Beer G,Meek J L.Infinite domain element[J].Inter-national Journal for Numerical Methods in Engineer-ing,1981,17:43-52.
[5]Zienkiewicz O C.A novel boundary infinite element[J].International Journal for Numerical Methods inEngineering,1983,19:393-404.
[6]Zhang Chuhan,Zhao Chongbin.Coupling method offinite and infinite elements for strip foundation waveproblems[J].Earthquake Engineering and StructuralDynamics,1987,15:839-851.
[7]赵崇斌,张楚汉,张光斗.用无穷元模拟半无限平面弹性地基[J].清华大学学报,1986,26(1):51-64.
[8]赵崇斌.拱坝地基无限域模拟与地震波输入研究[D].北京:清华大学,1987:14-42.
[9]葛修润,谷先荣,丰定祥.三维无限元和节理无界元[J].岩土工程学报,1986,8(5):9-20.
[10]燕柳斌.用三维映射无限元模拟重力坝地基[J].水利学报,1991,22(10):7-12.
[11]燕柳斌.结构分析的有限元及无限元法[M].武汉:武汉工业大学出版社,1998:1-10.
[12]燕柳斌.结构与岩土介质相互作用分析方法及其应用[D].广西:广西大学,2004:2-62.
[13]向前.无限元参与地基基础-坝体动力相互作用分析[D].广西:广西大学,2004:28-35.
[14]孙萍.映射无限元在无限域问题中的模拟应用[J].广西水利水电,2007,(2):10-13.
[15]王后裕,朱可善,言志信.三维双向及三向映射无限元[J].工程力学,2002,19(3):95-98.
[16]朱以文.ABAQUS与岩土工程分析[M].香港:中国图书出版社,2005:135-150.
[17]徐芝纶.弹性力学[M].北京:高等教育出版社,2005:116-117.
[18]王金昌,陈业开.ABAQUS在土木工程中的应用[M].杭州:浙江大学出版社,2006:261-267.
[2]Bettess P,Zienkiewicz O C.Diffraction and refractionof surface waves using finite and infinite elements[J].International Journal for Numerical Methods in Engi-neering,1977,13:1271-1290.
[3]Bettess P.More on infinite element[J].InternationalJournal for Numerical Methods in Engineering,1980,16:1613-1626.
[4]Beer G,Meek J L.Infinite domain element[J].Inter-national Journal for Numerical Methods in Engineer-ing,1981,17:43-52.
[5]Zienkiewicz O C.A novel boundary infinite element[J].International Journal for Numerical Methods inEngineering,1983,19:393-404.
[6]Zhang Chuhan,Zhao Chongbin.Coupling method offinite and infinite elements for strip foundation waveproblems[J].Earthquake Engineering and StructuralDynamics,1987,15:839-851.
[7]赵崇斌,张楚汉,张光斗.用无穷元模拟半无限平面弹性地基[J].清华大学学报,1986,26(1):51-64.
[8]赵崇斌.拱坝地基无限域模拟与地震波输入研究[D].北京:清华大学,1987:14-42.
[9]葛修润,谷先荣,丰定祥.三维无限元和节理无界元[J].岩土工程学报,1986,8(5):9-20.
[10]燕柳斌.用三维映射无限元模拟重力坝地基[J].水利学报,1991,22(10):7-12.
[11]燕柳斌.结构分析的有限元及无限元法[M].武汉:武汉工业大学出版社,1998:1-10.
[12]燕柳斌.结构与岩土介质相互作用分析方法及其应用[D].广西:广西大学,2004:2-62.
[13]向前.无限元参与地基基础-坝体动力相互作用分析[D].广西:广西大学,2004:28-35.
[14]孙萍.映射无限元在无限域问题中的模拟应用[J].广西水利水电,2007,(2):10-13.
[15]王后裕,朱可善,言志信.三维双向及三向映射无限元[J].工程力学,2002,19(3):95-98.
[16]朱以文.ABAQUS与岩土工程分析[M].香港:中国图书出版社,2005:135-150.
[17]徐芝纶.弹性力学[M].北京:高等教育出版社,2005:116-117.
[18]王金昌,陈业开.ABAQUS在土木工程中的应用[M].杭州:浙江大学出版社,2006:261-267.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心