出平面线源荷载作用下半空间内浅埋圆孔对半圆形凸起的圆柱形弹性夹杂的动力影响
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摘要
采用复变函数和多极坐标方法研究了在水平界面承受出平面线源荷载时弹性半空间内浅埋圆孔对半圆形凸起的圆柱形弹性夹杂的动力作用。该问题采用先"分区"再"契合"的思想求解,首先,将整个求解区域分割成两部分,其一为含半圆形凹陷和圆孔的弹性半空间,其二为圆柱形弹性夹杂;其次,构造满足含半圆形凹陷半空间水平界面应力自由和圆孔边界应力自由的散射波,构造满足圆形夹杂上半表面应力自由下半表面应力连续条件的驻波和散射波;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,同时满足圆孔边界应力自由的边界条件,建立起求解该问题的无穷代数方程组,并就具体算例讨论了圆柱形弹性夹杂周边动应力集中系数的数值结果。结果表明:圆孔的存在对"软"、"硬"夹杂周边动应力集中系数有不同的影响。
The dynamic effect of a subsurface circular cavity in half space bearing out-of-plane harmonic line source load along horizontal interface on a cylindrical elastic inclusion with a semi-cylindrical hill was studied using the methods of complex function and multi-polar coordinate.The dynamic effect was solved with an idea of partitioning and conjunction.Firstly,the solving domain was divided into two.The one was an elastic half space with a semi-circular canyon and a circular cavity,and the second one was a cylindrical elastic inclusion.Secondly,the scattering wave field satisfying stress free boundary conditions of the half space along horizontal interface and circular cavity boundary was constructed,moreover,a standing wave in the inclusion and a scattering wave outside the inclusion were constructed separately.Finally,the two sub-domains satisfying the continuous conditions of displacement and stress around the common boundary and the stress free boundary condition of the circular cavity boundary were conjoined,and a group of infinite algebraic equations were built to solve this problem.In examples,numerical results for dynamic stress concentration factor around the cylindrical elastic inclusion edge were presented and discussed.Numerical results showed that the existence of the circular cavity has different effects on the dynamic stress concentration factors around soft and hard edges of the cylindrical inclusion.
The dynamic effect of a subsurface circular cavity in half space bearing out-of-plane harmonic line source load along horizontal interface on a cylindrical elastic inclusion with a semi-cylindrical hill was studied using the methods of complex function and multi-polar coordinate.The dynamic effect was solved with an idea of partitioning and conjunction.Firstly,the solving domain was divided into two.The one was an elastic half space with a semi-circular canyon and a circular cavity,and the second one was a cylindrical elastic inclusion.Secondly,the scattering wave field satisfying stress free boundary conditions of the half space along horizontal interface and circular cavity boundary was constructed,moreover,a standing wave in the inclusion and a scattering wave outside the inclusion were constructed separately.Finally,the two sub-domains satisfying the continuous conditions of displacement and stress around the common boundary and the stress free boundary condition of the circular cavity boundary were conjoined,and a group of infinite algebraic equations were built to solve this problem.In examples,numerical results for dynamic stress concentration factor around the cylindrical elastic inclusion edge were presented and discussed.Numerical results showed that the existence of the circular cavity has different effects on the dynamic stress concentration factors around soft and hard edges of the cylindrical inclusion.
引文
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[4]胡聿贤,周锡元.地震工程跨世纪发展趋势[J].工程抗震,1999,1:3-9.HU Yu-xian,ZHOU Xi-yuan.Development trend of earthquake engineering toward new century[J].Earthquake Resistant Engineering,1999,1:3-9.
[5]徐植信.弹性波传播理论一些问题的研究现状和展望[J].上海力学,1989,10(3):6-10.XU Zhi-xin.The status and prospects of some topics of elastic wave propagation[J].Shanghai Journal of Mechanics,1989,10(3):6-10.
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[10]杜永军,赵启成,刘殿魁,等.半圆形凸起地形对SH波的散射与地震动-有多个浅埋圆孔情形[J].自然灾害学报,2005,3:155-161.DU Yong-jun,ZHAO Qi-cheng,LIU Dian-kui,et al.Scattering of sh-waves by a semi-cylindrical hill above multiple subsurface cavities[J].Journal of Natural Disasters,2005,3:155-161.
[11]刘殿魁,吕晓棠.浅埋圆柱形弹性夹杂附近的半圆形凸起对SH波的散射[J].哈尔滨工程大学学报,2006,27(2):189-194.LIU dian-kui,LXiao-tang.Scattering of sh-wave by a semicylindrical hill above a subsurface elastic cylindrical inclusion[J].Journal of Harbin Engineering University,2006,27(2):189-194.
[12]高相斌,刘殿魁,罗轶锋.SH波对浅埋圆孔附近多个半圆形凸起地形的散射[J].哈尔滨工程大学学报,2005,4:487-492.GAO Xiang-bin,LIU Dian-kui,LUO Yi-feng.Scattering of sh-waves by multiple semi-cylindrical hill above subsurface cavity[J].Journal of Harbin Engineering University,2005,4:487-492.
[13]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(2):209-218.LIU Dian-kui,WANG Guo-qing.Antiplane SH-deformation of a semi-cylindrical hill above a subsurface cavity[J].Acta Mechanica Sinica,2006,2:209-218.
[14]袁晓铭,廖振鹏.任意圆弧形凸起地形对平面SH波的散射[J].地震工程与工程振动,1996,2:1-13.YUAN Xiao-ming,LIAO Zhen-peng.Scattering of plane sh waves by a cylindrical hill of circular-arc cross-section[J].Earthquake Engineering And Engineering Vibration,1996,2:1-13.
[15]梁建文,巴振宁.弹性层状半空间中凸起地形对入射平面SH波的放大作用[J].地震工程与工程振动,2008,28(1):1-10.[15]LIANG Jian-wen,BA Zhen-ning.Surface motion of a hill in layered half-space subjected to incident plane sh waves[J].Earthquake Engineering and Engineering Vibration,2008,28(1):1-10.
[16]赵嘉喜,齐辉,郭晶,等.出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射[J].工程力学,2008,25(5):235-240.ZHAO Jia-xi,QI Hui,GUO Jing,et al.Scattering of outplane line source load by cylindrical elastic inclusion with a semi-cylindrical hill in half space[J].Engineering Mechanics,2008,25(5):235-240.
[17]杨在林,闫培雷,刘殿魁.浅埋圆柱形弹性夹杂及裂纹对SH波的散射与地震动[J].力学学报,2009,41(2):229-235.YANG Zai-lin,YAN Pei-lei,LIU Dian-kui.Scattering of SH-waves and ground motion by an elastic cylindrical inclusion and a crack in half space[J].Acta Mechanica Sinica,2009,41(2):229-235.
[2]Pao Y H,Mow C C.Diffraction of elastic waves and dynamic stress concentrations[M].New York,Crane and Russak,1973:114-304.
[3]洪善桃.关于弹性波近代发展的概述[J].上海力学,1986,3:66-77.HONG Shan-tao.A summary of recent developments of the elastic wave propagation[J].Shanghai Journal of Mechanics.1986,3:66-77.
[4]胡聿贤,周锡元.地震工程跨世纪发展趋势[J].工程抗震,1999,1:3-9.HU Yu-xian,ZHOU Xi-yuan.Development trend of earthquake engineering toward new century[J].Earthquake Resistant Engineering,1999,1:3-9.
[5]徐植信.弹性波传播理论一些问题的研究现状和展望[J].上海力学,1989,10(3):6-10.XU Zhi-xin.The status and prospects of some topics of elastic wave propagation[J].Shanghai Journal of Mechanics,1989,10(3):6-10.
[6]Wolf A.Motion of a rigid sphere in an acoustic wave field[J].Geophysics,1945,10:1-91.
[7]Nagase M.Diffraction of elastic wave by a spherical surface[J].Phys.Soc,Japan,1957,11(3):279-301.
[8]Knopoff L.Scattering of compressional waves by spherical obstacles[J].Geophysics,1959,24(1):30-39.
[9]李敏,刘殿魁.SH波入射时含圆形孔洞的半圆形凸起地形与其附近的圆形孔洞的相互作用[J].哈尔滨工程大学学报,2005,26(5):608-612.LI Min,LIU Dian-kui.Scattering of sh-waves by a semicylindrical hill with A Hole above a subsurface cavity in halfspace[J].Journal of Harbin Engineering University.2005,3:155-161.
[10]杜永军,赵启成,刘殿魁,等.半圆形凸起地形对SH波的散射与地震动-有多个浅埋圆孔情形[J].自然灾害学报,2005,3:155-161.DU Yong-jun,ZHAO Qi-cheng,LIU Dian-kui,et al.Scattering of sh-waves by a semi-cylindrical hill above multiple subsurface cavities[J].Journal of Natural Disasters,2005,3:155-161.
[11]刘殿魁,吕晓棠.浅埋圆柱形弹性夹杂附近的半圆形凸起对SH波的散射[J].哈尔滨工程大学学报,2006,27(2):189-194.LIU dian-kui,LXiao-tang.Scattering of sh-wave by a semicylindrical hill above a subsurface elastic cylindrical inclusion[J].Journal of Harbin Engineering University,2006,27(2):189-194.
[12]高相斌,刘殿魁,罗轶锋.SH波对浅埋圆孔附近多个半圆形凸起地形的散射[J].哈尔滨工程大学学报,2005,4:487-492.GAO Xiang-bin,LIU Dian-kui,LUO Yi-feng.Scattering of sh-waves by multiple semi-cylindrical hill above subsurface cavity[J].Journal of Harbin Engineering University,2005,4:487-492.
[13]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(2):209-218.LIU Dian-kui,WANG Guo-qing.Antiplane SH-deformation of a semi-cylindrical hill above a subsurface cavity[J].Acta Mechanica Sinica,2006,2:209-218.
[14]袁晓铭,廖振鹏.任意圆弧形凸起地形对平面SH波的散射[J].地震工程与工程振动,1996,2:1-13.YUAN Xiao-ming,LIAO Zhen-peng.Scattering of plane sh waves by a cylindrical hill of circular-arc cross-section[J].Earthquake Engineering And Engineering Vibration,1996,2:1-13.
[15]梁建文,巴振宁.弹性层状半空间中凸起地形对入射平面SH波的放大作用[J].地震工程与工程振动,2008,28(1):1-10.[15]LIANG Jian-wen,BA Zhen-ning.Surface motion of a hill in layered half-space subjected to incident plane sh waves[J].Earthquake Engineering and Engineering Vibration,2008,28(1):1-10.
[16]赵嘉喜,齐辉,郭晶,等.出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射[J].工程力学,2008,25(5):235-240.ZHAO Jia-xi,QI Hui,GUO Jing,et al.Scattering of outplane line source load by cylindrical elastic inclusion with a semi-cylindrical hill in half space[J].Engineering Mechanics,2008,25(5):235-240.
[17]杨在林,闫培雷,刘殿魁.浅埋圆柱形弹性夹杂及裂纹对SH波的散射与地震动[J].力学学报,2009,41(2):229-235.YANG Zai-lin,YAN Pei-lei,LIU Dian-kui.Scattering of SH-waves and ground motion by an elastic cylindrical inclusion and a crack in half space[J].Acta Mechanica Sinica,2009,41(2):229-235.
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