研究了应用Ansys 有限元软件进行地震波场数值模拟的边界条件问题,提出一种基于波动方程的Ansys 模型黏弹性边界条件构建方法。由波动方程推导并建立了黏弹性边界条件的理论基础,在Ansys 模型中选用带阻尼的Combin14 单元作为加载有限元,采用APDL 代码成功地将黏弹性边界条件施加于Ansys 模型中。对模型进行实例计算,在模型边界设置虚拟检波器,加载Ricker 子波震源,提取计算后的波场快照和时间记录进行对比,结果显示,所施加的黏弹性边界条件可以很好地吸收边界反射波,表明了该方法所构建的Ansys 模型黏弹性边界条件的有效性。
This paper researched boundary conditions of numerical simulation of seismic wave field in the application of finite element software Ansys. We propose a viscoelastic boundary conditions based on wave equation. Deduced from the wave equation and a viscoelastic boundary conditions theoretical foundation established, we selected damping Combin 14 unit as load finite element method, adopted APDL code successfully to apply viscoelastic boundary conditions in Ansys. The examples set up a virtual detector in the model boundaries, loaded Ricker wavelet source, extract wave field snapshot and time recording. Compared results demonstrate that viscoelastic boundary conditions imposed can well absorb boundary reflection, it shows the effectiveness of the viscoelastic model boundary conditions.
[1] Clayton R, Engquist B. Absorbing boundary conditions for waveequation migration[J]. Geophysics, 1980, 45(5): 895-904.
[2] Reynolds A C. Boundary conditions for the numerical solution of wave propagation problems[J]. Geophysics, 1978, 43(6): 1099-1110.
[3] Liao Z P. Extrapolation non-reflecting boundary conditions[J]. Wave Motion, 1996, 24(2): 117-138.
[4] Higdon R L. Absorbing boundary-conditions for elastic-waves[J]. Geophysics, 1991, 56(2): 231-241.
[5] Scandrett C L, Kriegsmann G A, Achenbach J D. Scattering of a pulse by a cavity in an elastic half-space[J]. Journal of Computational Physics, 1986, 65(2): 410-431.
[6] Cerjan C, Kosloff D, Kosloff R, et al. A nonreflecting boundary condition for discrete acoustic and elastic wave equations[J]. Geophysics, 1985, 50(4): 705-708.
[7] Sochacki J, Kubichek R, George J, et al. Absorbing boundary conditions and surface waves[J]. Geophysics, 1987, 52(1): 60-71.
[8] Randall C J. Absorbing boundary-condition for the elastic wave-equation velocity-stress formulation[J]. Geophysics, 1989, 54(9): 1141-1152.
[9] Lindman E L. Free-space boundary conditions for the time dependent wave equation[J]. Journal of Computational Physics, 1975, 18(1): 66-78.
[10] Randall C J. Absorbing boundary condition for the elastic wave equation[J]. Geophysics, 1988, 53(5): 611-624.
[11] Long L T, Liow J S. A transparent boundary for finite-difference wave simulation[J]. Geophysics, 1990, 55(2): 201-208.
[12] Lysmer J, Kuhlemeyer R L. Finite dynamic model for infinite media[J]. Journal of engineering mechanics, 1969, 95(4): 859-877.
[13] Novak M, Hindy A. Seismic analysis of underground tubular structures. Proceedings of the 7th World Conference on Earthquake Engineering. (1980)[C]. Istanbul, Turk: Turk Ankara Natl Common Earthquake Eng, 1980, 287-294.
[14] Deeks A J, Randolph M F. Axisymmetrical time-domain transmitting boundaries[J]. Journal of Engineering Mechanics-Asce, 1994, 120(1): 25-42.
[15] Wolf J P. A comparison of time-domain transmitting boundaries[J]. Earthquake Engineering & Structural Dynamics, 1986, 14(4): 655-673.
[16] 刘晶波, 谷音, 杜义欣. 一致粘弹性人工边界及粘弹性边界单元[J]. 岩土工程学报, 2006, 28(9): 1070-1076. Liu Jingbo, GuYin, Du Yixin. Consistent viscous-spring artificial boundaries and viscous-spring boundary elements[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(9): 1070-1075.