双相介质椭圆形孔洞及界面裂纹对SH波的散射
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摘要
采用复变函数法、格林法和保角映射法研究了双相介质半空间界面裂纹及其附近椭圆形孔洞对水平剪切(SH)波的散射,给出了椭圆形孔洞的动应力集中系数和界面裂纹尖端动应力强度因子的分布情况.首先,将理论模型沿垂直界面剖分为两个直角平面模型,利用保角映射法和镜像叠加原理构造直角平面中平面波场及椭圆形孔洞产生的散射波场;其次,根据界面上的应力和位移连续性条件,利用界面契合技术和裂纹切割技术将两个直角平面契合成含有界面裂纹的双相介质半空间;最后,通过具体算例给出了不同参数条件下椭圆形孔洞的动应力集中系数及界面裂纹尖端的动应力强度因子的分布情况.结果表明:入射角度、入射波数、材料参数、裂纹长度等因素会对动应力集中系数及动应力强度因子的分布产生影响.
Based on Green′s function method and complex function method with conformal mapping method,the scattering problem of shear horizontal(SH)waves by elliptic cavity and interfacial crack in a bi-material half space were investigated.And the distributions of the dynamic stress concentration factor(DSCF)around elliptic cavity and dynamic stress intensity factor(DSIF)at the tip of interfacial crack were presented.Firstly,the theoretical model was divided into two right planes along the interface to study respectively.The plane wave field and scattering wave field of the elliptic cavity in right angle planes were constructed by using image method and conformal mapping method.Secondly,through the continuity conditions of stress and displacement on the vertical interface,the two right planes were combined into bi-material half space with interfacial crack by using conjunction method and crack dividing method.Finally,some examples were given to present the distributions of DSCF and DSIF under different conditions.Numerical results show that incident angel,incident wave number,materials parameters,crack length and some other factors are capable of effecting the distributions of DSCF and DSIF.
Based on Green′s function method and complex function method with conformal mapping method,the scattering problem of shear horizontal(SH)waves by elliptic cavity and interfacial crack in a bi-material half space were investigated.And the distributions of the dynamic stress concentration factor(DSCF)around elliptic cavity and dynamic stress intensity factor(DSIF)at the tip of interfacial crack were presented.Firstly,the theoretical model was divided into two right planes along the interface to study respectively.The plane wave field and scattering wave field of the elliptic cavity in right angle planes were constructed by using image method and conformal mapping method.Secondly,through the continuity conditions of stress and displacement on the vertical interface,the two right planes were combined into bi-material half space with interfacial crack by using conjunction method and crack dividing method.Finally,some examples were given to present the distributions of DSCF and DSIF under different conditions.Numerical results show that incident angel,incident wave number,materials parameters,crack length and some other factors are capable of effecting the distributions of DSCF and DSIF.
引文
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[7]陈志刚.SH波在界面孔上散射的远场解[J].振动与冲击,2014,33(12):138-144.
[8]杨在林,许华南,黑宝平.双相介质中椭圆孔洞与裂纹对SH波的散射[J].工程力学,2014,31(10):33-39.
[9]齐辉,丁晓浩,赵元博.双相介质弹性半空间垂直界面附近椭圆形夹杂对SH波的散射[J].振动与冲击,2015,34(24):76-81.
[10]史文谱,杨洪兰,张春萍,等.四分之一空间内椭圆孔对SH(shearing horizontal反平面剪切)波的散射[J].机械强度,2010,32(5):774-780.
[11]杨杰.半空间垂直界面裂纹及圆夹杂对SH波的散射[D].哈尔滨:哈尔滨工程大学图书馆,2012.
[12]宋天舒,李冬.压电体中孔边III型界面裂纹的动应力强度因子[J].力学学报,2010,42(6):1219-1224.
[2]Luo Hao,Lee V W,Liang Jianwen.Anti-plane(SH)waves diffraction by an underground semi-circular cavity:analytical solution[J].Earthquake Engineering and Engineering Vibration,2010,9(3):385-396.
[3]杨在林,闫培雷,刘殿魁.SH波对浅埋弹性圆柱及裂纹的散射与地震动[J].力学学报,2009,41(2):229-235.
[4]刘殿魁,陈志刚.椭圆孔边裂纹对SH波的散射及其动应力强度因子[J].应用数学和力学,2004,25(9):958-965.
[5]刘殿魁,刘宏伟.孔边裂纹对SH波的散射及其动应力强度因子[J].力学学报,1999,31(3):292-299.
[6]Qi Hui,Yang Jie.Dynamic analysis for circular inclusion of arbitrary positions near interfacial crack impacted by SH-wave in half-space[J].European Journal of Mechanics A:Solids,2012,36:18-24.
[7]陈志刚.SH波在界面孔上散射的远场解[J].振动与冲击,2014,33(12):138-144.
[8]杨在林,许华南,黑宝平.双相介质中椭圆孔洞与裂纹对SH波的散射[J].工程力学,2014,31(10):33-39.
[9]齐辉,丁晓浩,赵元博.双相介质弹性半空间垂直界面附近椭圆形夹杂对SH波的散射[J].振动与冲击,2015,34(24):76-81.
[10]史文谱,杨洪兰,张春萍,等.四分之一空间内椭圆孔对SH(shearing horizontal反平面剪切)波的散射[J].机械强度,2010,32(5):774-780.
[11]杨杰.半空间垂直界面裂纹及圆夹杂对SH波的散射[D].哈尔滨:哈尔滨工程大学图书馆,2012.
[12]宋天舒,李冬.压电体中孔边III型界面裂纹的动应力强度因子[J].力学学报,2010,42(6):1219-1224.