结构-地基系统高阶时域模型的动输入方法
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摘要
近场有限域采用有限元法,远场无限域采用基于比例边界有限元法(the scaled boundary finite element method,SBFEM)的高阶边界条件,在时域里构建了一种结构-地基动力相互作用的高阶模型及相适配的动输入方法.借鉴黏弹性人工边界中等效力的动输入法,将截断边界上的总波场分解为散射场和自由场,其中局部场地效应引起的散射场可由高阶边界条件自动满足,无局部场地效应影响的自由场则由弹性理论求出.通过两个数值算例验证了建立的高阶时域模型及相应的动输入机制的正确性、精确性.
A high-order time-domain model and its dynamic input mechanism,which is based on finite element method(FEM)and the scaled boundary finite element method(SBFEM)for transient dynamic response of structure-foundation systems,are presented.Employing the idea of dynamic input method of equivalent force of the viscous-spring boundary,the total wave field at the truncated boundary is separated into the scattering field induced by local topography effect and the free field without local topography effect,in which the scattering field is satisfied exactly by the high-order time-domain model and the free field is solved by the elastic theory.The correctness,accuracy of the high-order time-domain model and its dynamic input mechanism are validated by two numerical examples.
A high-order time-domain model and its dynamic input mechanism,which is based on finite element method(FEM)and the scaled boundary finite element method(SBFEM)for transient dynamic response of structure-foundation systems,are presented.Employing the idea of dynamic input method of equivalent force of the viscous-spring boundary,the total wave field at the truncated boundary is separated into the scattering field induced by local topography effect and the free field without local topography effect,in which the scattering field is satisfied exactly by the high-order time-domain model and the free field is solved by the elastic theory.The correctness,accuracy of the high-order time-domain model and its dynamic input mechanism are validated by two numerical examples.
引文
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[12]Birk C,Prempramote S,Song C.An Improved Continued-fraction-based High-order Transmitting Boundary for Time-domain Analyses in Unbounded Domains[J].International Journal for Numerical Methods in Engineering,2012,89:269-298.
[13]陈灯红,戴上秋,彭刚.坝-基动力相互作用的高阶时域模型[J].水利学报,2014,45(5):547-556.
[14]杜修力,赵密.基于黏弹性边界的拱坝地震反应分析方法[J].水利学报,2006,37(9):1063-1069.
[15]马怀发,王立涛,陈厚群.粘弹性人工边界的虚位移原理[J].工程力学,2013,30(1):168-173.
[16]Chen D,Wang M,Dai S Q,et al.A High-order Doubly Asymptotic Continued-fraction Solution for Frequencydomain Analysis of Vector Wave Propagation in Unbounded Domains[J].Soil Dynamics and Earthquake Engineering,2018,113:230-240.
[17]Chen D,Birk C,Song C,et al.A high-order Approach for Modelling Transient Wave Propagation Problems U-sing the Scaled Boundary Finite Element Method[J].International Journal for Numerical Methods in Engineering,2014,97:937-959.
[18]陈灯红,杜成斌.结构-地基动力相互作用的时域模型[J].岩土力学,2014,35(4):1164-1172.
[2]Deeks A J,Randolph M F.Axisymmetric Time-domain Transmitting Boundaries[J].Journal of Engineering Mechanics,1994,120:25-42.
[3]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.
[4]Liao Z P,Wong H L.A Transmitting Boundary for the Numerical Simulation of Elastic Wave Propagation[J].Soil Dynamics and Earthquake Engineering,1984,3:174-183.
[5]Bettess P.Infinite Elements[J].International Journal for Numerical Methods in Engineering,1977,11:53-64.
[6]Beskos D E.Boundary Element Methods in Dynamic A-nalysis[J].Applied Mechanics Reviews,1987,40:1-23.
[7]Wolf J.P.,Song C.Finite element modelling of unbounded media[M].Chichester:John Wiley&Sons,1996.
[8]Song C.The Scaled Boundary Finite Element Method:Introduction to Theory and Implementation[M].New Jersey:John Wiley&Sons,2018.
[9]陈厚群.坝址地震动输入机制探讨[J].水利学报,2006,37(12):1417-1423.
[10]Song C,Bazyar M H.Development of a Fundamentalsolution-less Boundary Element Method for Exterior Wave Problems[J].Communications in Numerical Methods in Engineering,2008,24:257-27.
[11]Bazyar M H,Song C.A Continued-fraction-based Highorder Transmitting Boundary for Wave Propagation in Unbounded Domains of Arbitrary Geometry[J].International Journal for Numerical Methods in Engineering,2008,74:209-237.
[12]Birk C,Prempramote S,Song C.An Improved Continued-fraction-based High-order Transmitting Boundary for Time-domain Analyses in Unbounded Domains[J].International Journal for Numerical Methods in Engineering,2012,89:269-298.
[13]陈灯红,戴上秋,彭刚.坝-基动力相互作用的高阶时域模型[J].水利学报,2014,45(5):547-556.
[14]杜修力,赵密.基于黏弹性边界的拱坝地震反应分析方法[J].水利学报,2006,37(9):1063-1069.
[15]马怀发,王立涛,陈厚群.粘弹性人工边界的虚位移原理[J].工程力学,2013,30(1):168-173.
[16]Chen D,Wang M,Dai S Q,et al.A High-order Doubly Asymptotic Continued-fraction Solution for Frequencydomain Analysis of Vector Wave Propagation in Unbounded Domains[J].Soil Dynamics and Earthquake Engineering,2018,113:230-240.
[17]Chen D,Birk C,Song C,et al.A high-order Approach for Modelling Transient Wave Propagation Problems U-sing the Scaled Boundary Finite Element Method[J].International Journal for Numerical Methods in Engineering,2014,97:937-959.
[18]陈灯红,杜成斌.结构-地基动力相互作用的时域模型[J].岩土力学,2014,35(4):1164-1172.