线源荷载对半圆形凸起圆形夹杂附近浅埋圆孔的动力作用
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摘要
采用复变函数法和Green函数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半圆形凸起的圆柱形弹性夹杂对浅埋圆孔的动力作用。该问题采用"分区"、"契合"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,并就具体算例分析讨论了浅埋圆孔边缘动应力集中系数(DSCF)的数值结果。结果表明:圆柱形弹性夹杂的"软"、"硬"对浅埋圆孔孔边动应力集中系数有不同的影响。
The dynamic effects of a subsurface circular cavity by a cylindrical elastic inclusion with a semi-cylindrical hill above subsurface circular cavity in half space with out-of-plane harmonic line source load on horizontal interface have been considered using the methods of complex function and Green’s function.The solution to dynamic effects is given by the idea of "partitioning"and "conjunction".Firstly,we divide the solution domain into two.The one is an elastic half space with the semi-circular canyon and circular cavity,and the other is a cylindrical elastic inclusion.Secondly,the scattering wave field,which satisfies the free stress boundary conditions of the half space on the horizontal interface and circular cavity boundary could be constructed,moreover,the standing waves in the inclusion and the scattering waves outside it are formulated separately.Finally,we conjoin the two domains to satisfy the continuity condition of displacement and stress around the common boundary and the stress free boundary condition of circular cavity boundary,and a series of infinite algebraic equations could be obtained to solve this problem.In the examples,numerical results for dynamic stress concentration factor(DSCF) around the subsurfacecircular cavity edge are presented and discussed.Numerical results show that the softness and hardness of cylindrical inclusion have different effects on DSCF around the subsurface circular cavity edge.
The dynamic effects of a subsurface circular cavity by a cylindrical elastic inclusion with a semi-cylindrical hill above subsurface circular cavity in half space with out-of-plane harmonic line source load on horizontal interface have been considered using the methods of complex function and Green’s function.The solution to dynamic effects is given by the idea of "partitioning"and "conjunction".Firstly,we divide the solution domain into two.The one is an elastic half space with the semi-circular canyon and circular cavity,and the other is a cylindrical elastic inclusion.Secondly,the scattering wave field,which satisfies the free stress boundary conditions of the half space on the horizontal interface and circular cavity boundary could be constructed,moreover,the standing waves in the inclusion and the scattering waves outside it are formulated separately.Finally,we conjoin the two domains to satisfy the continuity condition of displacement and stress around the common boundary and the stress free boundary condition of circular cavity boundary,and a series of infinite algebraic equations could be obtained to solve this problem.In the examples,numerical results for dynamic stress concentration factor(DSCF) around the subsurfacecircular cavity edge are presented and discussed.Numerical results show that the softness and hardness of cylindrical inclusion have different effects on DSCF around the subsurface circular cavity edge.
引文
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[8]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,2005,14(3):155-161.DU Yongjun,ZHAO Qicheng,LIU Diankui,et al.Scattering of SH-waves by a semi-cylindrical hill above multiple subsurface cavities[J].Jour-nal of Natural Disasters,2005,14(3):155-161.(in Chinese)
[9]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,2005,04:487-492.GAO Xiangbin,LIU Diankui,LUO Yifeng.Scattering of SH-waves by multiple semi-cylindrical hill above subsurface cavity[J].Journal of HarbinEngineering University.2005,04:487-492.(in Chinese)
[10]杨在林,许华南,陈志刚.等腰三角形凸起与半圆形凹陷地形对SH波的散射[J].哈尔滨工业大学学报,2011,S1:6-11.YANG Zailin,XU Huanan,CHEN Chigang.Scattering of SH-waves by two isosceles triangle hills and a semi-cylindrical canyon[J].Journal ofHarbin Institute of Technology,2011,S1:6-11.(in Chinese)
[2]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 Yuxian,ZHOU Xiyuan.Development trend of earthquake engineering toward new century[J].Earthquake Resistant Engineering.1999,1:3-9.(in Chinese)
[3]Liu Diankui,Han Feng.Scattering of plane SH-waves by cylindrical canyon of arbitrary shape in anisotropic media[J].Acta Mechanics Sinica,1990,6(3):256-260.
[4]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,1996,02:1-13.YUAN Xiaoming,LIAO Zhenpeng.Scattering of plane SH waves by a cylindrical hill of circular-Arc cross-section[J].Earthquake Engineeringand Engineering Vibration,1996,02:1-13.(in Chinese)
[5]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[J].工程力学,2012,5:31-36.NAN Jingfu,QI Hui.Green’s function solution of elastic half space including a semi-lining Hill[J].Engineering Mechanics,2012,5:31-36.(in Chinese)
[6]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 Jiaxi,QI Hui,GUO Jing,et al.Scattering of out-plane line source load by a cylindrical elastic inclusion with a semi-cylindrical hill in halfspace[J].Engineering Mechanics,2008,25(5):235-240.(in Chinese)
[7]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 Diankui.Scattering of SH-waves by a semi-cylindrical hill with a hole above a subsurface cavity in half-space[J].Journal of HarbinEngineering University,2005,26(5):608-612.(in Chinese)
[8]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,2005,14(3):155-161.DU Yongjun,ZHAO Qicheng,LIU Diankui,et al.Scattering of SH-waves by a semi-cylindrical hill above multiple subsurface cavities[J].Jour-nal of Natural Disasters,2005,14(3):155-161.(in Chinese)
[9]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,2005,04:487-492.GAO Xiangbin,LIU Diankui,LUO Yifeng.Scattering of SH-waves by multiple semi-cylindrical hill above subsurface cavity[J].Journal of HarbinEngineering University.2005,04:487-492.(in Chinese)
[10]杨在林,许华南,陈志刚.等腰三角形凸起与半圆形凹陷地形对SH波的散射[J].哈尔滨工业大学学报,2011,S1:6-11.YANG Zailin,XU Huanan,CHEN Chigang.Scattering of SH-waves by two isosceles triangle hills and a semi-cylindrical canyon[J].Journal ofHarbin Institute of Technology,2011,S1:6-11.(in Chinese)
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