Due to the advantages of effectively eliminating soil boundary reflections and being easy to combine with finite elements, viscoelastic boundaries have become commonly used artificial boundaries in the analysis of structure-soil dynamic interaction. The viscoelastic boundary is proposed based on single source and solid source. However, the environmental vibration caused by the vibration of railway infrastructure such as sleepers, subgrade and bridge piers under traffic loads is a multi-source and movement source problem. Using the existing viscoelastic boundary will produce certain error. Based on the characteristics of multi-source and moving sources, the paper used the wave equation to modify the existing viscoelastic boundary, and proposed the moving multiple sources viscoelastic boundary equation. At the same time, in order to reduce the pre-processing workload, the uniform viscoelastic boundary element and the viscoelastic constitutive equation were further used to construct the moving multiple sources viscoelastic boundary element combined with the UMAT subroutine, which realized the automatic update of the material properties of the boundary element, and then example verification were carried out. The research results show that multiple sources and moving source, the difference between the calculation results of the moving multiple source viscoelastic boundary and the free boundary is basically kept within 5%, while the maximum difference between results of viscoelastic boundary before correction and the free boundary can reach 35%. It can be seen that compared with the uncorrected viscoelastic boundary, the modified viscoelastic boundary has higher accuracy in dealing with multiple source and moving source problems.
Key words
railway traffic loads /
viscoelastic boundary /
moving source /
multiple sources /
soil vibration
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References
[1] Ochiai Y. Calculation of singular integrals on elements of three-dimensional problems by triple-reciprocity boundary element method[J]. Engineering analysis with boundary elements,2022(137-):137.
[2] Azevedo, Alvaro, Kausel, et al. Formulation of the boundary element method in the wavenumber-frequency domain based on the thin layer method[J]. Computers & structures, 2015.
[3] 廖振鹏. 工程波动理论导论[M].北京:科学出版社,2002.
Liao Zhenpeng. Introduction to wave motion theories in engineering[M]. Beijing: Science Press, 2002.
[4] Lysmer J, Drake L A. A Finite element method for seismology[J]. Methods in Computational Physics: Advances in Research and Applications,1972,11:181-216.
[5] Smith W D. A nonreflecting boundary for wave propagation problems[J]. Journal of Computational Physics,1974,15(4):492-503.
[6] Deeks A J, Randolph M F. Axisymmetric Time-Domain Transmitting Boundaries[J]. Journal of Engineering Mechanics,1994,120(1):25-42.
[7] Jingbo L, Yixin D , Xiuli D ,et al.3D viscous-spring artificial boundary in time domain[J].Earthquake Engineering and Engineering Vibration, 2006.
[8] 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.
Liu Jinbo, Wang Zhenyu, Du Xiuli, et al. THREE-dimensional visco-elastic artificial boundaries in time domain for wave motion problems[J]. Engineering Mechanics,2005,22(6):46-51.
[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,2007,2 4(12):31-37.
Gu Yin, Liu Jinbo, Du Yixin. 3D consistent viscous-spring artificial boundary and viscous-spring boundary element[J]. Engineering Mechanics,2007,2 4(12):31-37.
[10] 刘晶波,宝鑫,李述涛等.采用粘弹性人工边界时显式算法稳定性的改善研究[J].工程力学,2023,40(05):20-31.
Liu Jinbo, Bao Xin, Li Shutao, et.al. Engineering Mechanics, 2023,40(05):20-31.
[11] 陈震,徐远杰.基于波动理论的粘弹性人工边界内源波动有限元分析[J].武汉大学学报(工学版),2011,44(06):735-739.
Chen Zhen, Xu Yuanjie. Stability improvement of explicit algorithm when using viscoelastic artificial boundary[J]. Engineering Journal of Wuhan University, 2011, 44(06): 735-739.
[12] 郜新军,赵成刚,张延.多源散射黏弹性叠加人工边界探究及在桥梁工程中的应用[J].土木工程学报,2010,43(11):130-138.
Gao Xinjun, Zhao Chenggang, Zhang Yan. A study of viscous-spring superposition artificial boundary for multi-source scattering problems and its application in bridge engineering[J]. China Civil Engineering Journal, 2010,43(11): 130-138.
[13] 王笃国,赵成刚.地震波斜入射下考虑场地非线性、地形效应和土结动力相互作用的大跨连续刚构桥地震响应分析[J].工程力学,2017,34(04):32-41.
Wang Duguo, Zhao Chenggang. Seismic analysis of long-span continuous rigid frame bridge considering site nonlinearity, topography effect and soil-structure dynamic interaction under oblique incidence[J]. Engineering Mechanics, 2017,34(04):32-41.
[14] 夏晨.基于活动断层的地下结构地震反应分析研究[D].北京交通大学,2016.
Xia Chen. Study of seismic response analysis of underground structures in active fault area[D]. Beijing jiaotong university, 2016.
[15] 董亮. 高速铁路路基动力特性及列车循环荷载作用下变形性质研究[D]. 北京:北京交通大学,2008.
Dong Liang. Research on dynamic characteristics of high-speed railway subgrade and deformation properties under cyclic train load[D]. Beijing: Beijingjiaotong university, .2008.
[16] 崔仁浩.数学物理方程[M].哈尔滨: 哈尔滨工业大学出版社,2016.
Cui Renhao. Mathematical Physics Equations[M]. Harbin: Harbin Institute of Technology Press, 2016.
[17] 阚前华,康国政,徐祥.非线性本构关系在ABAQUS中的实现[M].北京: 科学出版社, 2019.
Kan Qianhua, Kang Guozheng, Xu Xiang. Implementations of nolinear constitutive relations in ABAQUS[M]. Beijing: Science Press, 2019.
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