地下结构静-动力分析中的人工边界转换方法研究
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摘要
对同时考虑静力效应和动力效应的地下结构静-动力分析问题,静力分析与动力分析的人工边界转换对动力分析结果有较大的影响。通过对人工边界转换方法边界转换原理的分析,表明以静力分析结果中的应力场为初始条件进行动力分析时,在输入静应力场的同时输入引起此应力场的荷载和边界条件,以及去掉边界约束条件的同时施加以相应的约束反力,均可保证模型在动力计算初始时刻为静力平衡状态。提出了一种在动力分析中施加零动力荷载的方法来检验静、动力人工边界转换的误差。算例表明采用粘弹性静-动力统一人工边界及其相应计算方法时,该边界在某些地下结构静力计算中存在较大误差。通过分析,推荐了较为合理的地下结构静-动力分析人工边界转换方法。该方法在人工边界转换时先去掉静力分析的约束,并在施加动力人工边界进入动力分析前将静力分析的荷载、静力场和约束反力一并输入模型。通过算例分析,验证了该方法的合理性。
For the problem of static-dynamic analysis of underground structure considering both static and dynamic effect,the transformation of artificial boundaries from static analysis to dynamic analysis has great effect on dynamic calculation results.Through analysis on boundaries transformation principles in transformation methods,it is indicated that if the stress field resulted in static analysis as well as the corresponding loads and boundary conditions are input simultanuously and used as the initial state of dynamic analysis,and the constraint reaction forces are taken to replace the constraint boundary conditions,the model can be ensured in static equilibrum state at the starting moment of dynamic analysis.The error of the artificial boundaries transformation methods in static-dynamic analysis was checked by imposing zero dynamic load in the dynamic analysis.The calculation results of some examples indicate that,when the unified visco-elastic boundary conditions and its corresponding calculating methods are applied in static-dynamic analysis of underground structure,big error will be resulted in the static calculation.On this basis,a more rational transformation method of artificial boundaries for static-dynamic analysis of underground structure was recommended.In the method,the static constraints were relieved first in the transformation of artificial boundaries;and the loads,the static fields and the constraint reactions were all together brought into the model while applying the dynamic artificial boundaries in dynamic analysis.The accuracy of the method was checked through the analysis of calculation results of an engineering case.
For the problem of static-dynamic analysis of underground structure considering both static and dynamic effect,the transformation of artificial boundaries from static analysis to dynamic analysis has great effect on dynamic calculation results.Through analysis on boundaries transformation principles in transformation methods,it is indicated that if the stress field resulted in static analysis as well as the corresponding loads and boundary conditions are input simultanuously and used as the initial state of dynamic analysis,and the constraint reaction forces are taken to replace the constraint boundary conditions,the model can be ensured in static equilibrum state at the starting moment of dynamic analysis.The error of the artificial boundaries transformation methods in static-dynamic analysis was checked by imposing zero dynamic load in the dynamic analysis.The calculation results of some examples indicate that,when the unified visco-elastic boundary conditions and its corresponding calculating methods are applied in static-dynamic analysis of underground structure,big error will be resulted in the static calculation.On this basis,a more rational transformation method of artificial boundaries for static-dynamic analysis of underground structure was recommended.In the method,the static constraints were relieved first in the transformation of artificial boundaries;and the loads,the static fields and the constraint reactions were all together brought into the model while applying the dynamic artificial boundaries in dynamic analysis.The accuracy of the method was checked through the analysis of calculation results of an engineering case.
引文
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[2]王后裕,陈上明,言志信,等.考虑动力相互作用的地下平面钢框架地震反应分析[J].振动与冲击,2005,24(1):99-103.
[3]陈万祥,郭志昆.粘弹性边界梁在低速冲击下的动力响应分析[J].振动与冲击,2008,27(12):69-72,78,108.
[4]Deeks A J.Randolph M F.Axisymmetric time-domaintransmitting boundaries[J].Journal of EngineeringMechanics,1994,120(1):25-42.
[5]刘晶波,吕彦东.结构-地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998,31(3):55-64.
[6]刘晶波,王振宇,杜修力,等.波动问题中的三维时域粘弹性人工边界[J].工程力学,2005,22(6):46-51.
[7]卢华喜,梁平英,尚守平.地基非线性波动问题中黏-弹性人工边界研究[J].岩土力学,2005,29(7):1911-1916.
[8]刘晶波,谷音,杜义欣.一致粘弹性人工边界及粘弹性边界单元[J].岩土工程学报,2006,28(9):1070-1075.
[9]谷音,刘晶波,杜义欣.三维一致粘弹性人工边界及等效粘弹性边界单元[J].工程力学,2007,24(12):31-37.
[10]高峰,关宝树.深圳地铁地震反应分析[J].西南交通大学学报,2001,36(4):355-359.
[11]关宝树.隧道力学概论[M].成都:西南交通大学出版社,1993.
[12]徐芝纶.弹性力学(上册)[M].北京:高等教育出版社,2006.
[13]潘昌实.隧道力学数值方法[M].北京:中国铁道出版社,1995.
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