弹性水平成层场地稳态波动的谱单元模拟
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摘要
采用谱单元法模拟弹性水平成层场地的一维稳态波动反应。在空间域采用谱单元离散,在时间域采用逐步微分求积法(DQ法),形成整体的空间域-时域计算格式,导出了计算表达式,并进行了数值实验。数值实验表明,采用谱单元法模拟弹性水平成层场地的一维稳态波动反应问题具有较高的计算精度。在控制精度的前提下,可以通过适当放宽空间以及时间网格的尺度来达到提高计算效率的目的。谱单元法提供了有限元方法以外的另一条解决问题途径,可望满足工程场地地震动模拟对于计算精度和计算效率的需求。
One-dimensional steady-state wave motion in the horizontal layer site was numerically simulated using spectral element method(SEM).The site was discreted in space domain by spectral elements,and the time-strepping procedure established on the basis of differential quadrature(DQ) rule was employed for the solution of dynamic equation.The corresponding formula were deduced.The results from numerical tests showed that the suggested procedure could gain higher accuraey for analysis of the wave propagation in the horizontal layer site.So the computational effects would be decreased by properly enlarging the element scales in space or time domain.
One-dimensional steady-state wave motion in the horizontal layer site was numerically simulated using spectral element method(SEM).The site was discreted in space domain by spectral elements,and the time-strepping procedure established on the basis of differential quadrature(DQ) rule was employed for the solution of dynamic equation.The corresponding formula were deduced.The results from numerical tests showed that the suggested procedure could gain higher accuraey for analysis of the wave propagation in the horizontal layer site.So the computational effects would be decreased by properly enlarging the element scales in space or time domain.
引文
[1]白建方.场地地震反应分析导论[M].北京:中国铁道出版社,2010.
[2]Funaro D.Domain decomposition methods for pseudospectral ap-proximations-part I,second order equations in one dimension[J].Numerische Mathematic,1988,52(3):329-344.
[3]Bernadi C,Girault V,Maday Y.Mixed spectral element approxi-mation of the Navier-Stokes equations in the stream-function andvorticity formulation[J].IMA Journal of Numerical Analysis,1992,12:565-608.
[4]Guo B Y.Spectral methods and their applications[M].Singa-pore:World Scientific,1998.
[5]Zampieri E,Pavarino L F.Approximation of acoustic waves by explic-it Newmark's schemes and spectral element methods[J].Journal ofComputational and Applied Mathematics,2006,185:308-325.
[6]王秀明,Seriani G,林伟军.利用谱元法计算弹性波场的若干理论问题[J].中国科学:G辑,2007,37(1):41-59.
[7]Bert C W,Malik M.Differential quadrature method in computa-tional mechanics:a review[J].Applied Mechanics Reviews,1996,49(1):1-28.
[8]Kang K,Bert C W,Striz A G.Vibration analysis of horizontallycurved beams with warping using DQM[J].Journal of StructureEngineering,1996,122(6):657-662.
[9]de Rose M A,Franciosi C.Exact and approximate dynamic analy-sis of circular arches using DQM[J].International Journal of Sol-ids and Structures,2000,37:1103-1117.
[10]Nie G J,Zhong Z.Elastio-plastic analysis of beams by differentialquadrature method[J].Journal of Engineering Mechanics,2005,22(1):59-62.
[11]Fung T C.Solving initial value problems by differential quadraturemethod:part 1:first-order equations[J].International Journal forNumerical Methods in Engineering,2001,50:1411-1427.
[12]Fung T C.Solving initial value problems by differential quadraturemethod:part 2:second-and higher-order equations[J].InternationalJournal for Numerical Methods in Engineering,2001,50:1429-1454.
[13]李鸿晶,王通.结构地震反应分析的逐步微分积分方法[J].力学学报,2011,43(2):430-435.
[14]李鸿晶,廖旭,王通.结构地震反应DQ解法的两种数值格式[J].应用基础与工程科学学报,2011,19(5):758-766.
[2]Funaro D.Domain decomposition methods for pseudospectral ap-proximations-part I,second order equations in one dimension[J].Numerische Mathematic,1988,52(3):329-344.
[3]Bernadi C,Girault V,Maday Y.Mixed spectral element approxi-mation of the Navier-Stokes equations in the stream-function andvorticity formulation[J].IMA Journal of Numerical Analysis,1992,12:565-608.
[4]Guo B Y.Spectral methods and their applications[M].Singa-pore:World Scientific,1998.
[5]Zampieri E,Pavarino L F.Approximation of acoustic waves by explic-it Newmark's schemes and spectral element methods[J].Journal ofComputational and Applied Mathematics,2006,185:308-325.
[6]王秀明,Seriani G,林伟军.利用谱元法计算弹性波场的若干理论问题[J].中国科学:G辑,2007,37(1):41-59.
[7]Bert C W,Malik M.Differential quadrature method in computa-tional mechanics:a review[J].Applied Mechanics Reviews,1996,49(1):1-28.
[8]Kang K,Bert C W,Striz A G.Vibration analysis of horizontallycurved beams with warping using DQM[J].Journal of StructureEngineering,1996,122(6):657-662.
[9]de Rose M A,Franciosi C.Exact and approximate dynamic analy-sis of circular arches using DQM[J].International Journal of Sol-ids and Structures,2000,37:1103-1117.
[10]Nie G J,Zhong Z.Elastio-plastic analysis of beams by differentialquadrature method[J].Journal of Engineering Mechanics,2005,22(1):59-62.
[11]Fung T C.Solving initial value problems by differential quadraturemethod:part 1:first-order equations[J].International Journal forNumerical Methods in Engineering,2001,50:1411-1427.
[12]Fung T C.Solving initial value problems by differential quadraturemethod:part 2:second-and higher-order equations[J].InternationalJournal for Numerical Methods in Engineering,2001,50:1429-1454.
[13]李鸿晶,王通.结构地震反应分析的逐步微分积分方法[J].力学学报,2011,43(2):430-435.
[14]李鸿晶,廖旭,王通.结构地震反应DQ解法的两种数值格式[J].应用基础与工程科学学报,2011,19(5):758-766.
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