空间结构-地基动力相互作用数值分析时域算法研究
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摘要
对于大型结构地震响应分析,结构-无限地基耦合系统动力分析的数值实现,往往由于有限元网格过多,以及地基无限域时域计算模型中存在的复杂卷积运算,严重限制了求解规模.为解决此问题,提出了基于阻尼溶剂抽取法的三维结构-地基相互作用分析的分区时域逐步求解模型.并针对三维大规模工程问题的数值求解,在积分算法及矩阵存储格式等方面,结合阻尼溶剂抽取法的特点进行了详细的探讨,以推进动力相互作用时域数值分析的实用化.以三维全空间球形空腔动力变形及大岗山拱坝的地震响应分析为例,针对上述数值实现算法进行了具体验证,并就不同的地基弹模及地震波输入方式对坝体响应的影响进行了探讨.计算结果表明,地基辐射阻尼以及河谷散射效应对结构的动力响应有很大影响,而该模型表现出了良好的精度和计算效率.
The dynamic analysis of structure-unbounded foundation system in the time domain often involves excessive finite elements and convolution integrals,and they severely limit the application to large 3-D engineering problems.A sub-regional progressive algorithm for 3-D problems is presented on the basis of the damping solvent extraction method.What′s more,some research work was done on the integral arithmetic and storage style of matrices such that convolutional integrals can be fully avoided,the discretization of the system′s equations of motion can be simplified and the computation capacity can be expanded.A spherical cavity embedded in full-space under radial even load and the Dagangshan Arch Dam under seismic load were analyzed as verification.In addition,the influence of elastic modulus and input mode of the seismic wave on the response of the dam was discussed.It′s shown that the radiation damping of unbounded foundation and scattering effect of the river valley have great influence on the response of structure.In the meantime,the algorithm proposed exhibits good accuracy and efficiency.
The dynamic analysis of structure-unbounded foundation system in the time domain often involves excessive finite elements and convolution integrals,and they severely limit the application to large 3-D engineering problems.A sub-regional progressive algorithm for 3-D problems is presented on the basis of the damping solvent extraction method.What′s more,some research work was done on the integral arithmetic and storage style of matrices such that convolutional integrals can be fully avoided,the discretization of the system′s equations of motion can be simplified and the computation capacity can be expanded.A spherical cavity embedded in full-space under radial even load and the Dagangshan Arch Dam under seismic load were analyzed as verification.In addition,the influence of elastic modulus and input mode of the seismic wave on the response of the dam was discussed.It′s shown that the radiation damping of unbounded foundation and scattering effect of the river valley have great influence on the response of structure.In the meantime,the algorithm proposed exhibits good accuracy and efficiency.
引文
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[9]PROULX J,DARBRE G R,KAM ILER IS N.A na lytica l and experim en ta l investigation of dam p ingin arch dam s based on recorded earthquakes[C]∥P roceed ings of 13th W CEE.V ancouver:B a lkem a,2004
[10]CHOPRA A K,TAN H.M ode ling ofdam-foundation in teraction in ana lys is of arch dam s[C]∥P roceed ings of the 10th W CEE.R otterdam:B a lkem a,1992
[11]吴健,金峰,张楚汉,等.无限地基辐射阻尼对溪洛渡拱坝地震响应的影响[J].岩土工程学报,2002,24(6):717-719
[12]阎俊义,张楚汉.结构-地基相互作用的FE-SBFE时域耦合方法及工程应用[D].北京:清华大学,2003
[2]廖振鹏,黄孔亮,杨柏坡,等.暂态波透射边界[J].中国科学(A辑),1984,27(6):556-564
[3]杜修力,陈厚群,侯顺载.拱坝系统三维非线性地震波动分析[J].地震工程与工程振动,1996,16(3):39-47
[4]宋崇民,张楚汉.水坝抗震分析的动力边界元方法[J].地震工程与工程振动,1988,8(4):14-25
[5]金峰,张楚汉,王光纶.结构地基相互作用的有限元-边界元-无限边界元耦合模型[J].清华大学学报,1993,33(2):17-25
[6]W OLF J P,SONG C.F in ite-E lem en t M odeling ofUnbounded M ed ia[M].N ew Y ork:John W iley&Sons,1997
[7]HUGHES T J R,L IU W K.Im p lic it-exp lic it fin itee lem en ts in trans ien t ana lys is:stab ility theory[J].JApp lM ech,1978,45(6):371-374
[8]HUGHES T J R,L IU W K.Im p lic it-exp lic it fin itee lem en ts in trans ien t ana lys is:im p lem en tation andnum erica l exam p les[J].J App lM ech,1978,45(6):375-378
[9]PROULX J,DARBRE G R,KAM ILER IS N.A na lytica l and experim en ta l investigation of dam p ingin arch dam s based on recorded earthquakes[C]∥P roceed ings of 13th W CEE.V ancouver:B a lkem a,2004
[10]CHOPRA A K,TAN H.M ode ling ofdam-foundation in teraction in ana lys is of arch dam s[C]∥P roceed ings of the 10th W CEE.R otterdam:B a lkem a,1992
[11]吴健,金峰,张楚汉,等.无限地基辐射阻尼对溪洛渡拱坝地震响应的影响[J].岩土工程学报,2002,24(6):717-719
[12]阎俊义,张楚汉.结构-地基相互作用的FE-SBFE时域耦合方法及工程应用[D].北京:清华大学,2003
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