地震分析中人工边界处理与地震动输入方法研究
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摘要
基于柱面波波动方程,推导建立了适用于土-结构地震动力相互作用分析的地震动输入和人工边界的处理方法。其中,地震动的输入是通过在人工边界上施加等效节点力来实现的,等效节点力的大小与入射地震波波速成正比;而人工边界的处理方法使得人工边界条件不仅在时间上是局部的,而且在空间上也是局部的。这种处理方法简单、有效,物理意义清晰,且很容易在有限元法中实现,结合Newmark时间积分是无条件稳定的。为了验证方法的有效性和精度,给出了两个算例,分别用于检验人工边界条件的性能以及地震动输入方法的正确性。算例分析结果表明,所提出的方法是十分有效的。
Based on the cylindrical wave equation, a method of earthquake input and artificial boundary for seismic soil–structure interaction analysis is presented. The artificial boundary condition is local in both time and space and the earthquake input is implemented at the base of the finite computational domain through a set of nodal equivalent forces, which is proportional to the velocity of the incident seismic wave. The proposed method is simple but efficient; and it can be implemented in finite element method without difficulty. Moreover, the time-stepping algorithm based on Newmark’s method in conjunction with this method is unconditionally stable. Two Numerical examples were conducted to verify the validity and accuracy of the method.
Based on the cylindrical wave equation, a method of earthquake input and artificial boundary for seismic soil–structure interaction analysis is presented. The artificial boundary condition is local in both time and space and the earthquake input is implemented at the base of the finite computational domain through a set of nodal equivalent forces, which is proportional to the velocity of the incident seismic wave. The proposed method is simple but efficient; and it can be implemented in finite element method without difficulty. Moreover, the time-stepping algorithm based on Newmark’s method in conjunction with this method is unconditionally stable. Two Numerical examples were conducted to verify the validity and accuracy of the method.
引文
[1]栾茂田,武亚军.土与结构间接触面的非线性弹性-理想塑性模型及其应用[J].岩土力学,2004,25(4):508-513.LUAN Mao-tian,WU Ya-jun.A nonlinear elasto-perfectly plastic model of interface element for soil-structure interaction and its applications[J].Rock and Soil Mechanics,2004,25(4):508-513.
[2]Clough R W.Nonlinear mechanisms in the seismic response of arch dams[A].International Conference on Earthquake Engineering[C].Skopje,Yugoslavia[s.n.],1980.
[3]徐艳杰,张楚汉,金峰.非线性拱坝-地基动力相互作用的FE-BE-IBE模型[J].清华大学学报,1998,38(11):99-103.XU Yan-jie,ZHANG Chu-han,JIN Feng.Model of FE-BE-IBE coupling for soil-structure interaction on nonlinear response of arch dams[J].Journal of Tsinghua University(Sci&Tech),1998,38(11):99-103.
[4]Givoli D.Non-reflecting boundary conditions[J].Journal of Computational Physics,1991,94:1-29.
[5]Lysmer J,Kuhlemeyer R L.Finite dynamic model for infinite media[J].Journal of the Engineering Mech-anics Division(ASCE),1969,95:859-877.
[6]邱流潮,金峰.无限介质中波动分析的显式时域辐射边界[J].清华大学学报,2003,43(11):1530-1533.QIU Liu-chao,JIN Feng.Explicit time-domain radiation boundaries for analysis of wave propagation in unbounded media[J].Journal of Tsinghua University(Sci&Tech),2003,43(11):1530-1533.
[7]Kellezi L.Local transmitting boundaries for transient elastic analysis[J].Soil Dynamics and Earthquake Engineering,2000,19:533-547.
[8]Whitham G B.Linear and Nonlinear Waves[M].New York:Wiley,1974.
[9]Guddati M N,Tassoulas J L.Characteristics methods for transient analysis of wave propagation in unbounded media[J].Computer Methods in Applied Mechanics and Engineering,1998,164:187-206.
[10]Kramer S L.Geotechnical Earthquake Engineering[M].New Jersey:Prentice Hall,1996.
[2]Clough R W.Nonlinear mechanisms in the seismic response of arch dams[A].International Conference on Earthquake Engineering[C].Skopje,Yugoslavia[s.n.],1980.
[3]徐艳杰,张楚汉,金峰.非线性拱坝-地基动力相互作用的FE-BE-IBE模型[J].清华大学学报,1998,38(11):99-103.XU Yan-jie,ZHANG Chu-han,JIN Feng.Model of FE-BE-IBE coupling for soil-structure interaction on nonlinear response of arch dams[J].Journal of Tsinghua University(Sci&Tech),1998,38(11):99-103.
[4]Givoli D.Non-reflecting boundary conditions[J].Journal of Computational Physics,1991,94:1-29.
[5]Lysmer J,Kuhlemeyer R L.Finite dynamic model for infinite media[J].Journal of the Engineering Mech-anics Division(ASCE),1969,95:859-877.
[6]邱流潮,金峰.无限介质中波动分析的显式时域辐射边界[J].清华大学学报,2003,43(11):1530-1533.QIU Liu-chao,JIN Feng.Explicit time-domain radiation boundaries for analysis of wave propagation in unbounded media[J].Journal of Tsinghua University(Sci&Tech),2003,43(11):1530-1533.
[7]Kellezi L.Local transmitting boundaries for transient elastic analysis[J].Soil Dynamics and Earthquake Engineering,2000,19:533-547.
[8]Whitham G B.Linear and Nonlinear Waves[M].New York:Wiley,1974.
[9]Guddati M N,Tassoulas J L.Characteristics methods for transient analysis of wave propagation in unbounded media[J].Computer Methods in Applied Mechanics and Engineering,1998,164:187-206.
[10]Kramer S L.Geotechnical Earthquake Engineering[M].New Jersey:Prentice Hall,1996.
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