AN IMPROVED METHOD OF THE CALCULATION OF EQUIVALENT NODAL FORCES IN VISCOUS-ELASTIC ARTIFICIAL BOUNDARY
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摘要: 黏弹性人工边界在场地地震反应和结构-地基动力相互作用等问题的计算中已得到了广泛的应用.地震波在黏弹性人工边界中的输入是通过将地震波转化为作用于人工边界处的等效载荷来实现的.计算等效节点载荷的常规方法默认边界节点对应区域内的应力为均布力，但实际上该节点对应区域内的应力分布通常是不均匀的.本文在有限元方法结合黏弹性局部人工边界的显式时域波动方法的基础上，建立了无限域散射问题地震波等效载荷计算的一种改进方法.该方法采用细化网格与应力积分相结合的方法计算人工边界等效节点力，有效地降低了人工边界上等效节点力的计算误差.以不同角度入射地震波的二维算例为例，算例给出的波场位移云图和节点位移时程曲线验证了本文方法的有效性，其计算精度与网格尺寸和地震波入射角度密切相关，且网格越小、入射角度越小，计算精度越高.对于相同的网格尺寸，本文采用方法的计算精度明显高于常规方法，尤其是对于斜入射问题优势更为明显.Abstract: The viscous-elastic artificial boundary is widely used in the analysis of site seismic response and dynamic structure-soil system interaction problems. Seismic input is usually taken as equivalent nodal forces incorporating in the viscous-elastic artificial boundary, and stress in the control area of any artificial boundary node in the conventional method is considered as uniform distribution. However, its distribution is actually uneven. An improved method is proposed for the seismic input of wave propagation scattering problem in infinite domain. In the proposed method, an viscous-elastic artificial boundary is first introduced; seismic input is considered as the equivalent node forces to be incorporated directly in these local boundaries, and the node force obtained using the mesh refinement process combining stress integration of adjacent node regions is changed along the artificial boundary nodes, and its computation error is effectively reduced; the two-dimensional wave propagation problem in time-domain is then solved using the explicit finite element method. The numerical simulation of two-dimensional finite element site models of wave propagation problem with various mesh sizes and incidence angles are presented to demonstrate the performance of the improved method in this paper. The simulating nephogram of wave propagation and values of response displacement show that the calculating precision of the improved method is closely related to the mesh size and wave incidence angle, and increases with decrease of the mesh size and incidence angle. The simulation result also shows that the calculating precision of the improved method is significantly higher than that of the conventional method in the case of the same mesh size and incidence angle.
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1 刘晶波, 谷音, 杜义欣. 一致黏弹性动力人工边界及黏弹性边界单元. 岩土工程学报,2006,28(9):1070-1075(Liu Jingbo, Gu Yin, Du Yixin. Consistent viscous-spring artificial boundaries and viscous-spring boundary elements. Chinese Jounal of Geotechnical Engineering, 2006,28(9):1070-1075(in Chinese)) 2 刘晶波, 王振宇, 杜修力等. 波动问题中的三维时域黏弹性动力人工边界. 工程力学,2005,22(6):46-51(Liu Jingbo,Wang Zhenyu, Du Xiuli, et al. Three-dimensional visco-elastic artificial boundaries in time domain for wave motion problems. Engineering Mechanics, 2005,22(6):46-51(in Chinese)) 3 廖振鹏,杨柏坡,袁一凡. 暂态弹性波分析中人工边界的研究. 地震工程与工程振动,1982,2(1):1-11(Liao Zhenpeng, Yang Baipo, Yuan Yifan. Artificial boundary in analysis of transient elastic wave propagation. Earthquake Engineering and Engineering Vibration, 1982,2(1):1-11(in Chinese)) 4 Clatton R, Engquist B. Absorbing boundary conditions for acoustic and elastic wave equations. Bulletin of the Seismological Society of America, 1977, 67(6):1529-1540 5 Lysmer J, Kuhlemeyer RL. Finite dynamic model for infinite media. Journal of Engineering Mechanics Division, ASCE, 1969, 95(4):859-878 6 Deeks AJ, Randolph MF. Ax symmetric time-domain transmitting boundaries. Journal of Engineering Mechanics, ASCE, 1994, 120(1):25-42 7 杜修力,赵密,王进廷. 近场波动模拟的人工应力边界条件. 力学学报,2006,38(1):49-56(Du Xiuli, Zhao Mi, Wang Jinting. A stress artificial boundary in fea for near field wave problem. Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):49-56(in Chinese)) 8 廖振鹏,刘晶波. 波动的有限元模拟-基本问题和基本研究方法. 地震工程与工程振动,1989,9(4):1-14(Liao Zhenpeng, Liu Jingbo. Finite element simulation of wave motion-basic problems and conceptual aspects. Earthquake Engineering and Engineering Vibration, 1989,9(4):1-14(in Chinese)) 9 李小军,廖振鹏. 时域局部透射边界的计算飘移失稳. 力学学报,1996,28(5):627-632(Li Xiaojun, Liao Zhenpeng. The drift instability of local transmitting boundary in time domain. Acta Mechanica Sinica, 1996, 2(5):627-632(in Chinese)) 10 李小军. 非线性场地地震反应分析方法的研究.[博士论文]. 哈尔滨:中国地震局工程力学研究所, 1993(Li Xiaojun. Study on the method of analyzing the earthquake response of nonlinear site.[PhD Thesis]. Harbin:Institute of Engineering Mechanics, China Earthquake Administration, 1993(in Chinese)) 11 范留明,赵钦,刘云贺. 倾斜入射地震波作用下成层场地动力反应的界面子波算法. 岩土工程学报,2015,37(4):601-607(Fan Liuming, Zhao Qin, Liu Yunhe. Interfacial wavelet algorithm for dynamic response of horizontal layered site due to inclined seismic waves. Chinese Journal of Geotechnical Engineering, 2015, 37(4):601-607(in Chinese)) 12 何卫平,何蕴龙. 考虑地震波幅衰减的斜入射二维自由场. 振动与冲击, 2016,35(1):84-88(He Weiping, He Yunlong. Free field motions considering amplitude attenuation of oblique seismic waves. Journal Of Vibration and Shock, 2016,35(1):84-88(in Chinese)) 13 路德春,李云,马超等. 斜入射地震作用下地铁车站结构抗震性能分析. 北京工业大学学报,2016,42(1):87-94(Lu Dechun, Li Yun, Ma Chao, et al. Analysis of the three-dimensional seisic performance of underground. Journal of Beijing University Of Technology, 2016,42(1):87-94(in Chinese)) 14 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. 土木工程学报,1998,31(3):55-64(Liu Jingbo, Lü Yandong. A direct method for analysis of dynamic soil-structure interaction. China Civil Engineering Journal, 1998,31(3):55-64(in Chinese)) 15 Heymsfield E. Two-dimensional scattering of SH waves in a soil layer underlain with a sloping bedrock. Soil Dynamics and Earthquake Engineering, 2000, 19(7):489-500 16 郜新军,赵成刚,刘秦. 地震波斜入射下考虑局部地形影响和土结动力相互作用的多跨桥动力响应分析. 工程力学,2011, 28(11):237-243(Gao Xinjun, Zhao Chenggang, Liu Qin. Seismic response analysis of multi-span viaduct considering topographic effect and soil-structure dynamic interaction based on inclined wave. Engineering Mechanics,2011,28(11):237-243(in Chinese)) 17 杜修力,徐海斌,赵密. SV波斜入射下高拱坝地震反应分析. 水利发电学报, 2015,34(4):139-145(Du Xiuli, Xu Haibin, Zhao Mi. Analysis on seismic response of high arch dam to SV wave of oblique incidence. Journal of Hydroelectric Engineering,2015,34(4):139-145(in Chinese)) 18 杜修力,黄景琦,赵密等. SV波斜入射对岩体隧道洞身段地震响应影响研究. 岩土工程学报, 2014,36(8):1400-1406(Du Xiuli, Huang Jingqi, Zhao Mi, et al. Effect of oblique incidence of SV wave on seismic response of portal section of rock tunnels. Chinese Journal of Geotechnical Engineering, 2014,36(8):1400-1406(in Chinese)) 19 黄景琦,杜修力,田志敏等. 斜入射SV波对地铁车站地震响应的影响. 工程力学,2014,31(9):81-88(Huang Jingqi, Du Xiuli, Tian Zhimin, et al. Effect of the oblique incidence of seismic SV wave on the seismic response of subway station structure. Engineering Mechanics, 2014, 31(9):81-88(in Chinese)) 20 柴少波,李建春,李海波等. 平面P波入射含结构面岩体并引起地表面的振动研究. 岩石力学与工程学报, 2015, 34(2):3888-3895(Chai Shaobo, Li Jianchun, Li Haibo, et al. Study of P-wave propagation across a natyral atructural plan and its influence on ground motion. Chinese Journal of Rock Mechanics and Engineering, 2015,34(2):3888-3895(in Chinese)) 21 黄景琦,杜修力,赵密等. 近场数值波动分析中地震波输入的一种简化方法. 振动与冲击,2015,34(3):77-82(Huang Jingqi, Du Xiuli, Zhao Mi, et al. A simplified seismic wave input method for near-field wave analysis. Journal of Vibration and Shock, 2015, 34(3):77-82(in Chinese)) 22 梁建文,齐晓原,巴振宁. 基于黏弹性边界的三维凹陷地形地震响应分析. 地震工程与工程振动,2014,34(4):21-28(Liang Jianwen, Qi Xiaoyuan, Ba Zhenning. Seismic respones analysis of 3D canyon based on the viscous-spring boundary. Earthquake Engineering and Engineering Dynamics, 2014,34(4):21-28(in Chinese)) 23 Zhang CH, Pan JW, Wang JT. Infulence of seismic input mechanisms and radiation damping pn arch dam response. Soil Dynamics and Earthquake Engineering, 2009, 29(9):1282-1293 24 郜新军,赵成刚,张延. 多源散射叠加黏弹性人工边界探究及在桥梁工程中的应用. 土木工程学报,2010,43(11):131-138(Gao Xinjun, Zhao Chenggang, Zhang Yan. A study of viscous-spring superposition artifical boundary for multi-sources scattering problem and its applicatio in bridge engineering. China Civil Engineering Jounal, 2010,43(11):131-138(in Chinese)) 25 刘晶波,李彬. 三维黏弹性性静-动力统一人工边界. 中国科学(E辑), 2005,35(9):966-980(Liu Jingbo, Li Bin. Three dimensional static-dynamic unified viscoelastic artificial boundary. Science in China:Series E, 2005,35(9):866-980(in Chinese)) 26 杨勋,王欢欢,余克勤等. 行波激励下防波堤地震动力响应分析. 岩土力学,2014, 35(6):1775-1781(Yang Xun, Wang Hunahuan, Yu Keqin, et al. Seismic dynamic response analysis of breakwater under traveling wave excitations. Rock and Soil Mechanics, 2014, 35(6):1775-1781(in Chinese)) 27 胡豹,金先龙,占昌宝等. 地铁车辆会对单洞双线隧道影响的数值模拟. 振动与冲击,2015,34(24):32-39(Hu Bao, Jin Xianlong, Zhan Changbao, et al. Numerical simulation of the nonstop crossing of opposite subways in a single bore tunnel. Journal of Vibration and Shock, 2015,34(24):32-39(in Chinese)) 28 贾磊,谢咏平,李慎奎. 爆破振动对邻近隧道衬砌安全的数值模拟分析. 振动与冲击, 2015,34(11):173-177(Jia Lei, Xie Yongping, Li Shenkui. Numerical simulation for impact of blasting vibration on nearby tunnel lining saety. Journal of Vibration and Shock, 2015,34(11):173-177(in Chinese)) 29 张燎军,张慧星,王大胜等. 黏弹性人工边界在ADINA中的应用. 世界地震工程,2008,24(1):12-16(Zhang Liaojun, Zhang Huixing, Wang Dasheng, et al. The application of artificial viscous spring boundary in ADINA. Word Earthquake Engineering, 2008, 24(1):12-16(in Chinese)) 30 柳锦春,还毅,李建权. 人工边界及地震动输入在有限元软件中的实现. 地下空间与工程学报,2011,7(增2):1774-1779(Liu Jinchun, Huan Yi, Li Jianquan. Application of artication boundary and seismic input in general finite element software. Chinese Jounral of Underground Space and Engineering, 2011,7(S2):1774-1779(in Chinese)) 31 张海,王雪杰,李雅. 地震波输入方向对软土地区车站结构响应的影响. 世界地震工程,2014,30(2):29-35(Zhang Hai, Wang Xuejie, Li Ya. Influence of input seisic wave's direcion on response of station structure in soft soil area. World Earthquake Engineering, 2014,30(2):29-35(in Chinese)) 32 廖振鹏,刘晶波. 离散网格中的弹性波(I). 地震工程与工程振动,1986,6(2):1-16(Liao Zhenpeng, Liu Jingbo. Elastic wave motion in discrete grids (I). Earthquake Engineering and Engineering Vibration, 1986,6(2):1-16(in Chinese)) -
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