结构-地基动力相互作用时域数值分析的显-隐式分区异步长递归算法
摘要
动力相互作用时域数值分析的精度与效率是面向大规模工程问题解决的重要问题。在阻尼溶剂抽取法模拟地基无限域动力性质的基础上,提出并发展了结构–地基动力相互作用时域数值分析的显–隐式分区异步长递归算法,分别在结构、地基分区计算中进行大步长隐式与小步长显式求解,而且采用预报–校正显式积分与Newmark隐式积分,具有相同的运动量数值积分假定,可自然满足分区交界面位移协调性条件。在满足工程精度要求的条件下,分区异步长显–隐式求解算法使动力相互作用时域数值计算效率较传统小步长显式积分算法得到大幅度提高,可明显促进阻尼溶剂抽取法在大规模工程问题分析中的应用。并就积分时间步长、结构–地基交界面异步长内插格式及位移协调性关系对结构动力响应的影响进行数值对比研究,可为具体计算中的参数选择提供依据。
To satisfy the requirement of large engineering problems,evaluation efficiency and accuracy have played important roles in the application of time-domain numerical solution.Based on the damping solvent extraction method(DSEM),a new sub-regional explicit-implicit recursive method with mixed step-size strategy in time domain is proposed to cope with the numerical analysis of dynamic structure-foundation interaction,which can alternatively apply implicit and explicit integral algorithms with different time steps to the computations of structure region and soil region.This method is convenient to combine the numerical advantages of big calculated time steps in implicit numerical integration and wide applicability for explicit integration.According to the same displacement interpolation relations in single time step for the explicit prediction-correction and implicit Newmark-β integral arithmetic,the deformation compatibility on the interface between structure and soil region can also be naturally guaranteed.Finally,key influential factors for the implementation,such as integral time step and various displacement interpolations on the interface,are also numerically discussed in the detailed practical application,which shows that the new proposed method can efficiently improve the evaluation efficiency under the condition of satisfying engineering accuracy well.
To satisfy the requirement of large engineering problems,evaluation efficiency and accuracy have played important roles in the application of time-domain numerical solution.Based on the damping solvent extraction method(DSEM),a new sub-regional explicit-implicit recursive method with mixed step-size strategy in time domain is proposed to cope with the numerical analysis of dynamic structure-foundation interaction,which can alternatively apply implicit and explicit integral algorithms with different time steps to the computations of structure region and soil region.This method is convenient to combine the numerical advantages of big calculated time steps in implicit numerical integration and wide applicability for explicit integration.According to the same displacement interpolation relations in single time step for the explicit prediction-correction and implicit Newmark-β integral arithmetic,the deformation compatibility on the interface between structure and soil region can also be naturally guaranteed.Finally,key influential factors for the implementation,such as integral time step and various displacement interpolations on the interface,are also numerically discussed in the detailed practical application,which shows that the new proposed method can efficiently improve the evaluation efficiency under the condition of satisfying engineering accuracy well.
引文
[1]陈健云,林皋,李建波.无限介质中波动散射问题时域求解的算法研究[J].岩石力学与工程学报,2004,23(19):3330–3336.(CHEN Jianyun,LIN Gao,LI Jianbo.Algorithm research on refined sub-regional reciprocal method in time domain for wave scattering problem in unbounded medium[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(19):3330–3336.(in Chinese))
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[3]李建波,陈健云,林皋.求解非均匀无限地基相互作用力的有限元时域阻尼抽取法[J].岩土工程学报,2004,26(2):263–267.(LI Jianbo,CHEN Jianyun,LIN Gao.Finite element damping-extraction method for dynamic interaction time-domain analysis of non-homogeneous unbounded rock[J].Chinese Journal of Geotechnical Engineering,2004,26(2):263–267.(in Chinese))
[4]杜修力,赵建锋.考虑土–结构相互作用效应的结构地震响应时域子结构分析法[J].北京工业大学学报,2007,33(5):517–523.(DU Xiuli,ZHAO Jianfeng.A time-domain substructure method for seismic response analysis with soil-structure interaction effect[J].Journal of Beijing University of Technology,2007,33(5):517–523.(in Chinese))
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[6]林皋,杜建国.基于SBFEM的坝–库水相互作用分析[J].大连理工大学学报,2005,45(5):723–729.(LIN Gao,DU Jianguo.Analysis of dam-reservoir interaction based on SBFEM[J].Journal of Dalian University of Technology,2005,45(5):723–729.(in Chinese))
[7]林皋,胡志强,陈健云.考虑横缝影响的拱坝动力分析[J].地震工程与工程振动,2004,24(6):45–52.(LIN Gao,HU Zhiqiang,CHEN Jianyun.Dynamic analysis of an arch dam considering the effects of contraction joints[J].Earthquake Engineering and Engineering Vibration,2004,24(6):45–52.(in Chinese))
[8]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(3):51–64.(ZHAO Chongbin,ZHANG Chuhan,ZHANG Guangdou.Simulation of semi-infinite plane elastic foundation using infinite elements[J].Journal of Tsinghua University,1986,26(3):51–64.(in Chinese))
[9]李建波,陈健云,林皋.无限地基–结构动力相互作用分析的分区递归时域算法研究[J].工程力学,2005,22(3):88–96.(LI Jianbo,CHEN Jianyun,LIN Gao.A refined sub-regional reciprocal method in time domain for dynamic soil-structure interaction analysis[J].Engineering Mechanics,2005,22(3):88–96.(in Chinese))
[10]WOLF J P,SONG C M.Finite-element modelling of unbounded media[M].New York:John Wiley and Sons Inc.,1996.
[11]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131–136.(ZHONG Wanxie.On precise time-integration method for structural dynamics[J].Journal of Dalian University of Technology,1994,34(2):131–136.(in Chinese))
[12]HUGHES T J R,LIU W K.Implicit-explicit finite elements in transient analysis:stability theory[J].Journal of Applied Mechanics,1978,45(6):371–374.
[13]朱伯芳.有限单元法原理与应用[M].2版.北京:中国水利水电出版社,1998.(ZHU Bofang.Principle and application of finite element method[M].2nd Edition.Beijng:China Water Power Press,1998.(in Chinese))
[14]唐学军,王建华,寇新建.自适应有限元不同网格间力学结果传递方法及程序实现[J].岩石力学与工程学报,2007,26(1):66–74.(TANG Xuejun,WANG Jianhua,KOU Xinjian.Method and procedure for transferring mechanical fields between different meshes of adaptive finite elements[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(1):66–74.(in Chinese))
[15]BYCROFT G N.Forced vibration of rigid circular plate on a semi-infinite elastic space and on elastic stratum[J].Philosophical Trans.Royal Soc.,1956,248:327–368.
[16]BASU U,CHOPRA A K.Numerical evaluation of the damping-solvent extraction method in the frequency domain[J].Earthquake Engineering and Structural Dynamics,2002,31(6):1231–1250.
[2]钟红,林皋,李建波.空间结构–地基动力相互作用数值分析时域算法研究[J].大连理工大学学报,2007,47(1):78–84.(ZHONG Hong,LIN Gao,LI Jianbo.Numerical analysis of soil-structure dynamic interaction for3D problems in time domain[J].Journal of Dalian University of Technology,2007,47(1):78–84.(in Chinese))
[3]李建波,陈健云,林皋.求解非均匀无限地基相互作用力的有限元时域阻尼抽取法[J].岩土工程学报,2004,26(2):263–267.(LI Jianbo,CHEN Jianyun,LIN Gao.Finite element damping-extraction method for dynamic interaction time-domain analysis of non-homogeneous unbounded rock[J].Chinese Journal of Geotechnical Engineering,2004,26(2):263–267.(in Chinese))
[4]杜修力,赵建锋.考虑土–结构相互作用效应的结构地震响应时域子结构分析法[J].北京工业大学学报,2007,33(5):517–523.(DU Xiuli,ZHAO Jianfeng.A time-domain substructure method for seismic response analysis with soil-structure interaction effect[J].Journal of Beijing University of Technology,2007,33(5):517–523.(in Chinese))
[5]邱流潮,金峰.地震分析中人工边界处理与地震动输入方法研究[J].岩土力学,2006,27(9):1501–1504.(QIU Liuchao,JIN Feng.Study on method of earthquake input and artificial boundary conditions for seismic soil-structure interaction analysis[J].Rock and Soil Mechanics,2006,27(9):1501–1504.(in Chinese))
[6]林皋,杜建国.基于SBFEM的坝–库水相互作用分析[J].大连理工大学学报,2005,45(5):723–729.(LIN Gao,DU Jianguo.Analysis of dam-reservoir interaction based on SBFEM[J].Journal of Dalian University of Technology,2005,45(5):723–729.(in Chinese))
[7]林皋,胡志强,陈健云.考虑横缝影响的拱坝动力分析[J].地震工程与工程振动,2004,24(6):45–52.(LIN Gao,HU Zhiqiang,CHEN Jianyun.Dynamic analysis of an arch dam considering the effects of contraction joints[J].Earthquake Engineering and Engineering Vibration,2004,24(6):45–52.(in Chinese))
[8]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(3):51–64.(ZHAO Chongbin,ZHANG Chuhan,ZHANG Guangdou.Simulation of semi-infinite plane elastic foundation using infinite elements[J].Journal of Tsinghua University,1986,26(3):51–64.(in Chinese))
[9]李建波,陈健云,林皋.无限地基–结构动力相互作用分析的分区递归时域算法研究[J].工程力学,2005,22(3):88–96.(LI Jianbo,CHEN Jianyun,LIN Gao.A refined sub-regional reciprocal method in time domain for dynamic soil-structure interaction analysis[J].Engineering Mechanics,2005,22(3):88–96.(in Chinese))
[10]WOLF J P,SONG C M.Finite-element modelling of unbounded media[M].New York:John Wiley and Sons Inc.,1996.
[11]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131–136.(ZHONG Wanxie.On precise time-integration method for structural dynamics[J].Journal of Dalian University of Technology,1994,34(2):131–136.(in Chinese))
[12]HUGHES T J R,LIU W K.Implicit-explicit finite elements in transient analysis:stability theory[J].Journal of Applied Mechanics,1978,45(6):371–374.
[13]朱伯芳.有限单元法原理与应用[M].2版.北京:中国水利水电出版社,1998.(ZHU Bofang.Principle and application of finite element method[M].2nd Edition.Beijng:China Water Power Press,1998.(in Chinese))
[14]唐学军,王建华,寇新建.自适应有限元不同网格间力学结果传递方法及程序实现[J].岩石力学与工程学报,2007,26(1):66–74.(TANG Xuejun,WANG Jianhua,KOU Xinjian.Method and procedure for transferring mechanical fields between different meshes of adaptive finite elements[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(1):66–74.(in Chinese))
[15]BYCROFT G N.Forced vibration of rigid circular plate on a semi-infinite elastic space and on elastic stratum[J].Philosophical Trans.Royal Soc.,1956,248:327–368.
[16]BASU U,CHOPRA A K.Numerical evaluation of the damping-solvent extraction method in the frequency domain[J].Earthquake Engineering and Structural Dynamics,2002,31(6):1231–1250.
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