An Improved Viscous-Spring Artificial Boundary Model

Abstract:

A new artificial boundary model is proposed based on conventional viscous-spring artificial boundary model. Firstly, the stress formula on artificial boundary are derived based on the wave propagation theory and the new artificial boundary model is constructed by adding the nodal force to conventional viscous-spring on the boundary of finite field, which could include the effect of lateral boundary displacement. And then the values of the stiffness, the damp and nodal force are deduced based on stress wave theory. Finally, a numerical example is given to verify the proposed model. Compared with viscous-spring artificial boundary, this proposed artificial boundary model possesses the merits of same efficiency and conciseness, but higher precision than conventional viscous-spring artificial model.

• Periodical: Applied Mechanics and Materials (Volumes 29-32)
• Pages: 2627-2632
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.29-32.2627
• Online since: August 2010
• Authors: Jian Yun Chen, Qiang Xu, Jing Li
• Keywords: Dynamic Analysis, Lateral Boundary Displacement, Seismic Analysis, Viscous-Spring Artificial Boundary

References

[1] GU Yin, LIU Jing-bo, DU Yi-xin. 3D consistent viscous-spring artificial boundary and viscous-spring boundary element[J] Engineering Mechanics, 2007, 24(12): 31-38(in chinese).

[2] Lysmer J, Kuhlemeyer RL. Finite dynamic model for infinite media[J]. J Engng Mech Div ASCE, 1969, 95: 759-877.

DOI: 10.1061/jmcea3.0001144

[3] Y.Y. Jiao, X.L. Zhang, J. Zhao, Q.S. Liu. Viscous boundary of DDA for modeling stress wave propagation in jointed rock[J] International Journal of Rock Mechanics & Mining Sciences, 2007, 44: 1070-1076.

DOI: 10.1016/j.ijrmms.2007.03.001

[4] LIU Jingbo, WANG Zhen-yu, DU Xiu-li. Three-dimensional visco-elastic artificial boundaries in time domain for wave motion problems[J] Engineering Mechanics, 2005, 22(6): 46-51(in chinese).

[5] Deeks A J, Randolph M F. Axisymmetric time-domain transmitting boundaries[J]. Journal of Engineering Mechanics, ASCE, 1994, 120(1): 25-42.

DOI: 10.1061/(asce)0733-9399(1994)120:1(25)

[6] WANG Zhen-yu , Computational theory of dynamic response of large structure-soil systems and its application[D]. Beijing: Tsinghua University; 2002: 24-28. (in chinese).

[7] Zhang Chuhan, PanJianwen, WangJinting. Influence of seismic input mechanisms and radiation damping on arch dam response[J] Soil Dynamics and Earthquake Engineering 2009, 29: 1282-1293.

DOI: 10.1016/j.soildyn.2009.03.003

[8] LIU Jing-bo, GU Yin, DU Yi-xin. Consistent viscous-spring artificial boundaries and viscous-spring boundary elements[J] Chinese Journal of Geotechnical Engineering, 2006, 28(9): 1070-1075(in chinese).

[9] Clayton R, B Engquist. Absorbing boundary condition for wave-equation migration[J] Geophysics, 1980, 45: 895-904.

DOI: 10.1190/1.1441094

[10] Clayton R, B Engquist. Absorbing boundary condition for acoustic and elastic wave equations[J] Bull. Seism. Soc. Am, 1977, 67: 1529-1540.

DOI: 10.1785/bssa0670061529

[11] Higdon R L. Absorbing Boundary Condition for Acoustic and elastic waves in stratified media[J] Comp. Phys., 1992, 101: 386-418.

DOI: 10.1016/0021-9991(92)90016-r

[12] S.V. Tsynkov. Artificial boundary conditions for the numerical simulation of unsteady acoustic waves[J]. Journal of Computational Physics , 2003, 189: 626-650.

DOI: 10.1016/s0021-9991(03)00249-3

[13] Chongbin Zhao, Tianyun Liu. Non-reflecting artificial boundaries for modeling scalar wave propagation problems in two-dimensional half space[J]. Comput. Methods Appl. Mech. Engrg. 2002, 191: 4569-4585.

DOI: 10.1016/s0045-7825(02)00370-5

[14] Smith W.A. Non-reflecting plane boundary for wave propagation problems[J]. J Comp Phys, 1973, 15: 492-503.

[15] GadiFibich, Semyon Tsynkov. High-order two-way artificial boundary conditions for nonlinear wave propagation with backscattering[J] Journal of Computational Physics, 2001, 171, 632-677.

DOI: 10.1006/jcph.2001.6800

[16] Song C, Wolf JP. The scaled boundary finite element method alias consistent infinitesimal finite element cell method for elasto-dynamics[J]. Computer methods in applied mechanics and engineering, 1997, 147(3-4): 329-355.

DOI: 10.1016/s0045-7825(97)00021-2

[17] Z.P. Liao, H.L. Wong, B. Yang, Y. Yuan, A transmitting boundary for transient wave analysis[J] Sci. Sinica, 1984, 27: 1063-1073.

[18] Liao Z P, Liu J B. Numerical instabilities of a local transmitting boundary[J]. Earthq Eng Struct Dyn, 1992, 21: 65-77.

DOI: 10.1002/eqe.4290210105