稳态SH波动的有限元模拟
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摘要: 将离散的局部透射边界与集中质量有限元方法相结合, 以模拟无限介质中的稳态波动。这种结合使有限元模型中的任一节点与其它节点(除邻近节点外)解耦, 从而使高效率的高斯消去法得以实施, 大大减少了计算机内存和计算时间。首先, 针对成层弹性介质中的稳态SH波动, 详细讨论该方法的列式及其计算精度;然后, 介绍如何减少计算机内存和计算时间的具体算法;接着以若干简单例子说明该方法的具体实施过程;最后, 简要讨论了需要进一步研究的若干问题。
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[1] 廖振鹏、杨柏坡、袁一凡, 1982.暂态波人工透射边界.地展工程与工程振动, 2, 1, 1——11.
[2] 廖振鹏, 1989.近场波动问题的有限元解.地展工程与工程振动, ‘, 2, 1——14.
[3] 廖振鹏、刘晶波, 1986.离散网格中的弹性波动(Ⅰ).地展工程与工程振动, 8, 2, 1——16.
[4] 刘晶波、廖振鹏, 1989.离散网格中的弹性波动(Ⅱ).地展工程与工程振动, 9, 2, 1——16.
[5] 刘晶波、廖振鹏, 1990.离散网格中的弹性波动(Ⅲ).地展工程与工程振动.10, 2, 1——10.
[6] 刘晶波、廖振鹅. 1992.有限元模型中的出平面波动.力学学报, 21, 2, 207——215.
[7] Engquist, B. and Majda, A., 1977. Absorbing boundary conditions for the numerical simulation of waves. Math. Comp., 91, 139, 629——651.
[8] Kausel, E. and Roesset, J. M., 1977. Semianalytic hyperelement for layerod strata. J. Eag. Mech. Dav., ASCE, 103 (EM4), 569——588.
[9] Kausel, E. and Peek, R., 1982. Boundary integral method for stratified soils. Res. Kept. R82——50, Dept. of Civil Eng. Order No. 796, Mass. Inst. of Tech.
[10] Kausel, E., 1988. Local transmitting boundaries. J. Eng. Mech. lhv., ASCE, 111 (EM6), 1011——1027.
[11] Lawrence Flax, Cuillermo C. Gaunaurd and Herbert Uberall, 1981. Theory of resonance scattering. Physics Acoustics, 15, 191——292.
[12] Liao, Z. P., Wong, H. L., Yang, B. P. and Yuan, Y. F., 1984. A Transmitting boundary for transient wave analyses. Scierdia Siaica (Series A), 27, 10, 1063——1067.
[13] Liao, Z. P. and Wong, H, L., 1989. A Transmitting boundary for the numerical simulation of elastic wave propagation. Soil Dyn. and Earthq. Eng., 3, 4, 174——183.
[14] Liao, Z. P. and Liu, J. B., 1992. Numerical instabilities of a local transmitting boundary. Earllyquake Engineering and Stractare Dynamics, 21, 65——77.
[15] Luco, J. P., 1968. Dynamic interaction of a shear waL with the soil. J. Eng. Mech. Div., ASCE, 94, (EM2), 333——396.
[16] Luco, J. P., Hadjian, A. H. and Bos. H. D. 1974. The dynamic modeling of the half plane by finite elements. Nuclear Engiveering and Design, S1, 189——194.
[17] Lysmer, J. and Waas, G., 1972. Shear waves in plane infinite structures. J. Eng. Mech, Div., ASCE, 98 (EM1), 85——105.
[18] Moenn——vaari, N. and Trifunac, M. D. 1985. Scattering of SH wave by cylindrical canyon fo arbitrary shape. Soil Dyn.and Earthq. Eng., 4, 1, 18——31.
[19] Wolf, J. P., 1986. A comparison of time——domain transmitting boundaries, Earlhqaale Engineering and Slrucdne Dyrwmics, 14, 9, 655——673.[1] 廖振鹏、杨柏坡、袁一凡, 1982.暂态波人工透射边界.地展工程与工程振动, 2, 1, 1——11.
[2] 廖振鹏, 1989.近场波动问题的有限元解.地展工程与工程振动, ‘, 2, 1——14.
[3] 廖振鹏、刘晶波, 1986.离散网格中的弹性波动(Ⅰ).地展工程与工程振动, 8, 2, 1——16.
[4] 刘晶波、廖振鹏, 1989.离散网格中的弹性波动(Ⅱ).地展工程与工程振动, 9, 2, 1——16.
[5] 刘晶波、廖振鹏, 1990.离散网格中的弹性波动(Ⅲ).地展工程与工程振动.10, 2, 1——10.
[6] 刘晶波、廖振鹅. 1992.有限元模型中的出平面波动.力学学报, 21, 2, 207——215.
[7] Engquist, B. and Majda, A., 1977. Absorbing boundary conditions for the numerical simulation of waves. Math. Comp., 91, 139, 629——651.
[8] Kausel, E. and Roesset, J. M., 1977. Semianalytic hyperelement for layerod strata. J. Eag. Mech. Dav., ASCE, 103 (EM4), 569——588.
[9] Kausel, E. and Peek, R., 1982. Boundary integral method for stratified soils. Res. Kept. R82——50, Dept. of Civil Eng. Order No. 796, Mass. Inst. of Tech.
[10] Kausel, E., 1988. Local transmitting boundaries. J. Eng. Mech. lhv., ASCE, 111 (EM6), 1011——1027.
[11] Lawrence Flax, Cuillermo C. Gaunaurd and Herbert Uberall, 1981. Theory of resonance scattering. Physics Acoustics, 15, 191——292.
[12] Liao, Z. P., Wong, H. L., Yang, B. P. and Yuan, Y. F., 1984. A Transmitting boundary for transient wave analyses. Scierdia Siaica (Series A), 27, 10, 1063——1067.
[13] Liao, Z. P. and Wong, H, L., 1989. A Transmitting boundary for the numerical simulation of elastic wave propagation. Soil Dyn. and Earthq. Eng., 3, 4, 174——183.
[14] Liao, Z. P. and Liu, J. B., 1992. Numerical instabilities of a local transmitting boundary. Earllyquake Engineering and Stractare Dynamics, 21, 65——77.
[15] Luco, J. P., 1968. Dynamic interaction of a shear waL with the soil. J. Eng. Mech. Div., ASCE, 94, (EM2), 333——396.
[16] Luco, J. P., Hadjian, A. H. and Bos. H. D. 1974. The dynamic modeling of the half plane by finite elements. Nuclear Engiveering and Design, S1, 189——194.
[17] Lysmer, J. and Waas, G., 1972. Shear waves in plane infinite structures. J. Eng. Mech, Div., ASCE, 98 (EM1), 85——105.
[18] Moenn——vaari, N. and Trifunac, M. D. 1985. Scattering of SH wave by cylindrical canyon fo arbitrary shape. Soil Dyn.and Earthq. Eng., 4, 1, 18——31.
[19] Wolf, J. P., 1986. A comparison of time——domain transmitting boundaries, Earlhqaale Engineering and Slrucdne Dyrwmics, 14, 9, 655——673.
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