含半圆形衬砌凸起弹性半空间问题的Green函数解

南景富; 齐辉

含半圆形衬砌凸起弹性半空间问题的Green函数解

南景富,
齐辉

1.
哈尔滨工程大学航天与建筑工程学院, 哈尔滨 150001;
2.
黑龙江科技学院数力系, 哈尔滨 150001

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中图分类号: O343.1
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- 收稿日期: 2012-05-08
- 修回日期: 2012-05-08
- 刊出日期: 2012-05-24

GREEN’S FUNCTION SOLUTION OF ELASTIC HALF SPACE INCLUDING A SEMI-LINING HILL

NAN Jing-fu,
QI Hui

1.
Civil Engineering College, Harbin Engineering University, Harbin 150001, China;
2.
Heilongjiang Institute of Science and Technology, Harbin 150001, China

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Corresponding author:
NAN Jing-fu: 南景富

摘要

摘要: 采用复变函数法研究了含半圆形衬砌凸起的弹性半空间中水平界面承受出平面线源荷载时的Green 函数解。该问题采用“契合”的思想求解,首先,将整个求解区域分割成两部分来处理,其一为含半圆形凹陷的弹性半空间,其二为圆形衬砌区域;其次,构造满足含半圆形凹陷半空间水平界面应力自由的散射波,构造满足圆形衬砌半圆形凸起应力自由的驻波;最后,在两个区域的“公共边界”上实施“契合”,满足公共边界处位移和应力的连续性条件,同时满足圆形衬砌内边界应力自由边界条件,建立起求解该问题的无穷代数方程组,并给出了水平表面位移幅值的具体算例和数值结果,并对其进行了讨论。
- 弹性半空间 /
- 半圆形衬砌凸起 /
- 出平面线源荷载 /
- Green 函数 /
- 地表位移幅值
Abstract: The Green’s function of an elastic half space including a semi-circular lining hill while a bearing out-of-plane harmonic line source load on a horizontal interface has been considered, using the method of complex functions. The solution of Green’s function is given by the idea of ‘conjunction’. Firstly, we divide the solution domain into two domains. The one is a cylindrical lining, and the second one is an elastic half space with the semi-circular canyon. Secondly, we construct the scattering wave of semi-circular canyon satisfying the stress free boundary condition on the horizontal interface and the standing wave of cylindrical lining satisfying the stress free boundary condition on the semi-circular hill. Finally, we conjoin the two domains to satisfy the continuous condition of displacement and stress around the common ‘conjunction’ boundary and the stress free boundary condition of a circular lining inside boundary, and a series of infinite algebraic equations can be obtained to settle this problem. In the end, the computing expressions of the ground motion in the horizontal surface near elastic lining are given and discussed.
- elastic half space /
- semi-lining hill /
- out-of-plane line source load /
- Green’s function /
- the ground motion in the horizontal surface

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参考文献(10)

[1]	王铎, 汪越胜. 界面动力学研究近况[J]. 上海力学, 1993, 14(4): 1-l5. Wang Duo, Wang Yuesheng. Recent progress in dynamics of interface [J]. Shanghai Journal of Mechanics, 1993, 14(4): 1-15. (in Chinese)
[2]	Williams M L. The stresses around a fault or crack in dissimilar media [J]. Bulletin of the Seismological Society of America, 1959, 49(2): 199-204.
[3]	刘殿魁, 王国庆. 浅埋圆形孔洞附近的半圆形凸起对 SH 波的散射[J]. 力学学报, 2006, 38(2): 209-218. Liu Diankui, Wang Guoqing. Antiplane SH-deformation of a semi-cylindrical hill above a subsurface cavity [J]. Acta Mechanics Sinica, 2006, 38(2): 209-218. (in Chinese)
[4]	崔志刚, 曹欣荣, 刘殿魁. SH 波对半圆形凸起地形的散射[J]. 地震工程与工程振动, 1998, 18(1): 140-146. Cui Zhigang, Cao Xinrong, Liu Diankui. SH wave scattering on the semi-circular protruding topography [J]. Earthquake Engineering and Engineering Vibration, 1998, 18(1): 140-146. (in Chinese)
[5]	梁建文, 严林隽, Vincent W Lee. 圆弧形凹陷地形表面覆盖层对入射平面SV波的影响[J]. 地震学报, 2001, 23(6): 622-636. Liang Jianwen, Yan Linjuan, Vincent W Lee. Arc canyon covering layer on the impact of incident plane SV waves [J]. Earthquake Engineering, 2001, 23(6): 622- 636. (in Chinese)
[6]	Norris A, Yang Y. Dynamic stress on a partially bonded fiber [J]. Journal of Basic Engineering, Transactions of the ASME, 1991, 58: 404-409.
[7]	Wang Y S, Wang D. Shear wave scattering from a partially debonded elastic elliptic inclusion [J]. Mechanics Research Communications, 1995, 22(1): 79- 86.
[8]	Wang Y S, Wang D. Dynamic analysis of a buried rigid elliptic cylinder partially debonded from surrounding matrix under shear waves [J]. Acta Mechanica Solida Sinica, 1995, 8(1): 51-63.
[9]	汪越胜, 王铎. SH 波对有部分脱胶衬砌的圆形孔洞的散射[J]. 力学学报, 1994, 26(4): 462-469. Wang Yuesheng, Wang Duo. SH wave by a circular lining some of degumming cavities [J]. Acta Mechanics Sinica, 1994, 26(4): 462-469. (in Chinese)
[10]	齐辉, 赵嘉喜, 刘殿魁, 王慧文. SH 波对脱胶圆夹杂及其边缘直裂纹的散射[J]. 哈尔滨工程大学学报, 2007, 28(12): 1321-1325. Qi Hui, Zhao Jiaxi, Liu Diankui, Wang Huiwen. SH waves by cylindrical inclusion and the edge of the horizontal cracks scattering [J]. Journal of Harbin Engineering University, 2007, 28(12): 1321-1325. (in Chinese)

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文章访问数: 1120
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含半圆形衬砌凸起弹性半空间问题的Green函数解

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GREEN’S FUNCTION SOLUTION OF ELASTIC HALF SPACE INCLUDING A SEMI-LINING HILL

Corresponding author: NAN Jing-fu: 南景富

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Corresponding author:
NAN Jing-fu: 南景富