摘要
本文在线弹性力学范畴内,采用多极坐标方法、Green函数和裂纹切割相结合的方法分别研究了在SH波作用下弹性空间多个圆形夹杂与附近任意位置任意长度直线形裂纹的相互作用问题,和弹性半空间多个圆形孔洞与附近任意位置任意长度单条直线形裂纹的相互作用问题。首先,采用多极坐标方法构造了适合解决本文问题的Green函数,分别为含有多个圆形夹杂的弹性空间任意一点承受时间谐和的出平面线源荷载作用时的位移函数基本解,和含有多个圆形孔洞的弹性半空间任意一点承受时间谐和的出平面线源荷载作用时的位移函数基本解。然后采用裂纹切割方法构造裂纹,即在欲出现裂纹区域加置与缺陷对SH波产生应力相对应的大小相等、方向相反的出平面载荷,从而构造出裂纹,从而得到缺陷和裂纹同时存在时的位移、应力表达式。最后讨论了缺陷周围的动应力集中情况。本文所作的具体工作如下:
1.研究了含多个圆形夹杂的弹性空间对线源载荷散射时圆形夹杂周边的动应力集中问题。利用多极坐标方法求出了多圆夹杂相互作用的位移、应力表达式,研究了圆形夹杂周围的动应力集中情况,并利用具体的算例讨论了剪切模量比、入射波数、夹杂与点源的相对位置等因素对此问题的影响情况。
2.研究了SH波入射情况下弹性空间多圆夹杂与周围直线型裂纹的动应力集中问题。利用适用于此问题的Green函数,采用裂纹切割方法导出了多圆夹杂与裂纹相互作用的位移、应力表达式,研究了圆形夹杂周围的动应力集中情况,并给出具体的算例,讨论了剪切模量比、入射波数、入射角度、夹杂与裂纹相对位置等因素对此问题的影响情况。
3.研究了SH波入射情况下半空间多圆孔洞与周围直裂纹的动应力集中问题。利用适用于此问题的Green函数,采用裂纹切割方法导出多圆孔洞与裂纹相互作用的位移、应力表达式,研究了圆形孔洞周围的动应力集中情况,并利用具体的算例,讨论了入射波数、入射角度、孔洞与裂纹相对位置、埋深等因素对此问题的影响情况。
In this paper, by using Green's Function method, the method of crack-division and the method of multi-polar coordinate system, the interaction problem of multiple circular inclusions with a linear crack in elastic space by SH-wave, and the interaction problem of multiple circular cavities with a linear crack in semi-space by SH-wave is studied. Firstly, the suitable Green's functions are constructed, which are the solution of displacement field for elastic space with multiple inclusions and the solution of displacement field for elastic semi-space with multiple circular shallow-buried cavities while bearing anti-plane harmonic line source force at any point separately. Then applying the method of crack-division, integration for solution is established:while the scattering problems of SH-wave by defects(cavity or inclusion) are studied, reverse stresses are inflicted along the cracks, that is,out-of-plane harmonic line source forces which are equal in the quantity but opposite in the direction to the stresses produced for the reason of SH-wave scattering by defects are loaded at the region where cracks whill appear, so cracks can be made out. So the expression of displacement and stress is established while defects and cracks exist at the same time. Using the expression dynamic stress concentration near the defects is discussed. The works in detail are as follows:
1. Green's Function is studied, which is the solution of displacement field for elastic space with multiple inclusions while bearing anti-plane harmonic line source force at any point. Applying the method of multi-polar coordinate system, the expression of displacement and stress is obtained. Then using the expressions, the dynamic stress concentration factor at the edge of the inclusion is discussed to the case of different parameters(.wave number, the radio of the shear modulus, the geometrical location of the circular inclusions and the line source).
2. The problem of SH-wave scattering by circular inclusions with a crack of any limited lengths near the inclusions in elastic space is investigated. By using Green's function which is suitable to this problem and the method of crack-division, the expression of displacement and stress is established. Then the dynamic stress concentration at the edge of the circular inclusion is discussed to the case of different parameters(the radio of the shear modulus, wave number, incident angles of SH-wave, and the geometrical location of the circular inclusions and the crack).
3. The problem of SH-wave scattering by circular cavities with a crack of any limited lengths near the inclusions in elastic semi-space is investigated. By using Green's function which is suitable to this problem and the method of crack-division, the expression of displacement and stress is established. Then the dynamic stress concentration at the edge of the circular cavities is discussed to the case of different parameters(wave number, incident angles of SH-wave, and the geometrical location of the circular inclusions and the crack, the embedded depth of the circular inclusions and the crack).
引文
[1]Morgan F.R. Foundations wave theory for seismic exploration. International Human Resources Development Corporatation Boston,1983:1-7P
[2]鲍亦兴,毛昭宙著.刘殿魁,苏先樾译.弹性波的衍射与动应力集中.北京:科学出版社.1993:3-25页,72-202页
[3]Rayleigh Lord. Investigation of the disturbance produced by a spherical obstacle on the waves of sound. Proc. Math. Soc.1872,4:253-304P
[4]Sezawa K. Scattering of Elastic Waves and Some Allied Problems. Bull Earthquake Res Inst Tokyo Imperial Univ,1927,3:19-41P
[5]Nishimura G, Jimbo Y. A dynamic problem of stress concentration stresses in the vicinity of a spherical matter included in an elastic solid under dynamical force. Journal of Faculty of Engineering,University of Tokyo,1955,24:101P
[6]Ying C.F.,Rohn Truell. Scattering of a Plane Longitudinal Wave by a Spherical Obstacle in an Isotropic Elastic Solid. J. Appl. Phys.1956, 27(9):1086-1097P
[7]White R. M.. Elastic Wave Scattering at a Cylindrical Discontinuity in a Solid. J. Acoustical Soc. Amer.1958,30(8):771-785P
[8]Freeman Gilbert, Leon Knopoff. Scattering of Impulsive Elastic Waves by a Rigid Cylinder. J.Acoustical soc. Amer.1959,31(9):1169-1175P
[9]Einspruch N G,Witterholt E J,Truell R. Scattering of a Plane Transverse Wave by a Spherical Obstacle in an Elastic Medium. J. Appl. Phys. 1960,31(5):806-818P
[10]Datta S K, Shah A.H. Scattering Of SH-waves By Embedded Cavities. Wave Motion.1982,4:265-283P
[11]Datta S K, Akily N E. Diffraction of Elastic Waves in a Half Space. J.Acoust.Soc. Am.1978,64:1692-1699P
[12]Datta S K. Scattering of Elastic Waves. Mechanics Today ed. Nemat-Nasser S.1978,4:149-208P
[13]Datta S K, Wong K C, Shah A H. Dynamic Stresses and Displacements Around Cylindrical Cavities of Arbitrary Shapes. ASME J Appl Mech,1984, 51:798-803P
[14]Miklowitz J. Scattering of a plane Elastic Compressional Pulse by a Cylindrical Cavity. Proc 11th Int Cong of Appl Mech,Munich,1964,469P
[15]Norwood F R, Miklowitz J. Diffraction of Transient Elastic Waves by a Spherical Cavity. J Appl Mech,1967,34(3):735P
[16]Pao Y. H., and Mow C. C. Diffraction of Elastic Waves and Dynamic Stress Concentrations. Crane and Russak, New York,1973:114-304
[17]Pao Y H,Mow C C.Dynamic Stress Concentration in an Elastic Plate with Rigid Circular Inclusion. Proc 4th National Cong of Appl Mech.1962.
[18]Mow C C,Mente L J.Dynamic Stresses and Displacements Around Cyindrical Discontinuiti-es due to Plane Harmonic Shear Waves. J Appl Mech. 1963,30(4):598P
[19]Mow C C.Transient Response of a Rigid Spherical Inclusion in an Elastic Medium. J Appl Mech,1965,32(3):637P
[20]Mow C C. On the Transient Motion of a Rigid Spherical Inclusion in an Elastic Medium and its Inverse problem.J Appl Mech,1966,33(4):807P
[21]Pao.Y. H.. Applied mechanics in science and engineering, Applied Mechanics Review,1998,51(2):141-153P
[22]Modile T.B.,Haddow J.B., A. Mioduchowski, and Tait R.J. Plane Elastic Waves Generated by Dynamical Loading Applied to Edge of Circular Hole. ASME.J. Appl.Mech.1981,48:577-581P
[23]M. M. Fredman. A New Way to Calculate Scattering of Elastic Waves. Dokl. Akad. Nauk.1948,60:1145-1178P
[24]Sih,GC. Elastodynamic Crack Problems. Mechanics of Fracture.1977,4: 381-388P
[25]Sih G C. Mechanics of Fracture, Vol.6, Cracks in Composite Material. Leyden:Noordhoff.1981.
[26]Achenbach J.D., Brind R.J. Elastodynamic Stress-Intensity Factors for a Crack near a Free Surface. J. Appl. Mech.1981,48:539-552P
[27]A. K. Gautensen,J. D. Achenbach, and H. Mcmaken. Surface-Wave Rays in Elastodynamic Diffaction by Cracks. Acoust. Soc. Am.1978,63:1824-1831P
[28]J.D. Achenbach, L.M. Keer, D.A. Mendelsohn.Elastodynamic Analysis of an Edge Crack. ASME J. Appl. Mech.1980,47:551-556P
[29]J.D. Achenbach, L. Adler, D.K. Lewis and H.McMaken. Diffaction of Ultrasonic Waves by Penny-Shaped Cracks in Metals:Theory and Experiment. J.Acoust.Soc.Am.1979,64:1848-1856P
[30]J.D. Achenbach, L.Z. Li.Propagation of Horizontally Polarized Transverse Waves in a Solid with a Periodic Distribution of Cracks. Wave Motion.1986,8:371-382P
[31]Wickham GR. The Diffraction of Stress Waves by a Plane Finite Crack in Two Dimensions:Uniqueness and Existence. Proc.R.Soc. 1981,378(1773):241-261P
[32]A.K. Mal. Interaction of Elastic Waves with a Penny-shaped Crack. International Journal of Engineering Science.1970,8(5):381-388P
[33]A.K. Mal. Interaction of Elastic Waves with a Griffith Crack. International Journal of Engineering Science.1970,8(9):763-776P
[34]R.L.Ryan,S. Mall. Scattering of Antiplane Shear Waves by a Submerged Crack. International Journal of Solids and Structures.1982,18(12):1145-1152P
[35]F.L. Neerhoff, J.H.M.T. Van Der Hijden. Scattering of Elastic Waves by a Plane Crack of Finite Width. ASME J. Appl. Mech..1984,51(3):646-651P
[36]S.M. Gracewski and D.B. Bogy. Elastic Wave Scattering from an Interface Crack in a Layered Half Space Submerged in Water:Part Ⅰ:Applied Tractions at The Liquid-Solid Interface. ASME J. Appl. Mech.1986,53:326-332P
[37]S.M. Gracewski and D.B. Bogy. Elastic Wave Scattering from an Interface Crack in a Layered Half Space Submerged in Water:Part II:Incident Plane Waves and Bounded Beams. ASME J. Appl. Mech.1986,53:333-338P
[38]S. Itou. Diffraction of an Antiplane Shear Wave by Two Coplanar Griffith Cracks in an Infinite Elasic Medium. International Journal of Solids and Structures.1980,16:1147-1153P
[39]Srivastava K. N, Gupta O. P and Palaiya R. M. Interaction of Elastic Waves in Two Bonded Dissimilar Elastic Half-planes Having Griffith Crack at Interface. Int. J. Fract.1978,14:143-154P
[40]Srivastava K. N Palaiya R. M and Gupta O. P. Interaction of Longitudinal Wave with a Penny-shaped Crack at the Interface of Two Bonded Dissimilar Elastic Solids-II. Int. J. Fract.1979,15:591-599P
[41]G.F. Loeber,GC.Sih. Transmission of anti-plane shear waves past an interface crack in dissimilar media. Enging Fract. Mech..1973,5:699-725P
[42]陆建飞,王建华,沈为平.曲线裂纹和反平面圆形夹杂相交问题.固体力学学报.2000,21(3):205-210页
[43]陆建飞,王建华,沈为平.反平面圆形夹杂和多圆孔多裂纹相互作用问题.计算力学学报.2000,17(2):229-234页
[44]Liu D.K., Gai B.Z. and Tao G. Y. Applications of the Method of Complex Functions to Dynamic Stress Concentrations. Wave Motion.1982,4: 293-304P
[45]刘殿魁,刘宏伟.SH波散射与界面圆孔附近的动应力集中.力学学报.1998,30(5):597-604页
[46]刘殿魁,刘宏伟.孔边裂纹对SH波散射及动应力强度因子.力学学报. 1999,31(3):292-299页
[47]刘宏伟,刘殿魁.界面圆孔对SH波的散射远场解.固体力学学报.1999,20(4):349-355页
[48]史守峡,刘殿魁.SH波与界面多圆孔的散射及动应力集中.力学学报.2001(1):60-70页
[49]林宏,史文谱,刘殿魁.SH波入射时浅埋结构的动力分析.哈尔滨工程大学学报.2001,22(6):83-87页
[50]胡超,刘殿魁.无限大板开孔弹性波的散射及动应力集中.力学学报.1995,27:125-134页
[51]刘殿魁,王宁伟.相邻多圆孔各向异性介质中SH波的散射.地震工程与工程振动,1989,9(4):15-28页
[52]史守峡,杨庆山,刘殿魁,齐辉.SH波对圆形夹杂与裂纹的散射及其动应力集中.复合材料学报.2000,17(3):109-112页
[53]韩峰.复变函数方法在弹性波散射及动应力集中问题研究中的应用.哈尔滨建筑大学博士学位论文.1991:8-18页
[54]Yang Zailin, Liu Dankui. Scattering far field solution of SH-wave by movable rigid cylindrical interface. Acta Mechanica Solida Sinica,2002,15(3): 214-220P
[55]Chen Zhigang, Liu Diankui and Yang Zailin. Dynamic stress concentration and scattering of SH-wave by interface elliptic cylindrical cavity. Earthquake engineering and engineering vibration.2003,2(2):299-306P
[56]Liu Diankui, Lin Hong. Scattering of SH-waves by an Interface Linear Crack and a Circular Cavity near Bimaterial Interface. ACTA Mechanica Sinica. 2004,20(3):317-326P
[57]Liu D.K. and Han F. Scattering of Plane SH-waves by Cylindrical Canyon of Arbitrary Shapes in Anisotropic Media. Acta Mechanica Sinica.1990,6(3): 256-266P
[58]Liu Diankui, Han Feng. Scattering of plane SH-wave by Cylindrical Canyon of Arbitrary Shapes. Soil Dynamics and Earthquake Engineering.1991,10(5): 249-255P
[59]Shi S. X. Han F. Wang Z. Q., and Liu. D. K. The Interaction of Plane SH-wave and Non-circular Cavity Surfaced with Lining in Anisotropic Media, Applied Mathematics and Mechanics.1996,17(9):809-820P
[60]Liu D. K. and Hu C. Scattering of Flexural Wave and Dynamic Stress Concentration in Mindlin's Thick Plates With a Cutout. Acta Mechanica Sinica.1996,12(2):169-185P
[61]Liu D. K. and Song T. S. Stress Concentrations of Cylinder with Large Opening. Acta Mechanica Sinica.1997,10(3):214-230P
[62]刘殿魁,盖秉政,陶贵源.论孔附近的动应力集中.力学学报,1981:65-77页
[63]王国庆,刘殿魁.SH波对浅埋相邻多个圆孔作用的动力分析.哈尔滨工程大学学报,2003,24(1):108-113页
[64]崔志刚,曹欣荣,刘殿魁.SH波对半圆型凸起地形的散射.地震工程与工程振动.1998,18(1):140-146页
[65]崔志刚,邹永超,刘殿魁.SH波对圆弧形凸起地形的散射.地震工程与工程振动.1998,18(4):8-14页
[66]田家勇.界面圆形弹性夹杂对SH波散射及动应力集中.哈尔滨工程大学硕士学位论文,1998:20-25页
[67]李宏亮.SH波作用下孔洞、夹杂与直线形裂纹的相互作用.哈尔滨工程大学博士学位论文.2004:25-83页
[68]王国庆.界面附近相邻多个圆形孔洞对SH波的散射.哈尔滨工程大学硕士学位论文.2002:15-44页
[69]刘宏伟.界面圆孔和孔边裂纹对SH波散射问题的研究.哈尔滨工程大学博士学位论文.1997:67-79页
[70]李宏亮,刘殿魁,杨勇.SH波作用下弧形裂纹对圆形衬砌动应力集中系数的影响.哈尔滨工程大学学报.2007,28(08):856-860页
[71]李宏亮,刘殿魁.SH波作用下裂纹对圆夹杂散射动应力集中问题的影响.哈尔滨工程大学学报.2005,26(03):359-363页
[72]张学义,刘殿魁,李宏亮.SH波作用下圆形衬砌与直线形裂纹的相互作用.哈尔滨工程大学学报.2006,27(04):514-518页
[73]李宏亮,刘殿魁.SH波作用下圆形夹杂与裂纹的相互作用.哈尔滨工程大学学报.2004,25(5):618-622页
[74]齐辉.界面圆环形衬砌对SH波散射及动应力集中.哈尔滨工程大学博士学位论文.2000:33-47页
[75]王艳,刘殿魁.SH波入射时浅埋衬砌结构动力分析.哈尔滨工程大学学报.2002,23(6):43-47页
[76]林宏,刘殿魁.半无限空间中圆形孔洞周围SH波的散射.地震工程与工程振动.2002,22(2):9-16页
[77]齐辉,王艳,刘殿魁.半无限空间界面附近SH波对圆形衬砌的散射.地震工程与工程振动.2003,23(3):41-46页
[78]刘殿魁,林宏.浅埋的圆形孔洞对SH波散射与地震动.爆炸与冲击.2003,23(1):6-12页
[79]杨在林.SH波作用下半空间中夹杂与裂纹的相互作用.哈尔滨工程大学博士学位论文.2005:85-96页
[80]何钟怡,樊洪明,刘有军.SH波绕界面孔的散射.力学学报.2002,34(1):68-75页
[81]梁建文,李艳恒,Vincent W Lee.地下洞室群对地面运动影响问题的级数解答:SH波入射.岩土力学.2006,27(10):1663-1672页
[82]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.地震工程与工程振动.2008,28(01):1-10页
[83]杨彩红,梁建文,张郁山.多层沉积凹陷地形对平面SH波散射问题的解 析解.岩土力学.2006,27(12):2191-2196页
[84]梁建文,罗昊,W.L.Vincent.任意圆弧形凸起地形中隧洞对入射平面SH波的影响.地震学报.2004,26(05):495-508页
[85]梁建文,张郁山,顾晓鲁,Vincent W Lee.圆弧形层状凹陷地形对平面SH波的散射.振动工程学报.2003,16(2):158-165页
[86]梁建文,张郁山,顾晓鲁,Vincent W Lee.圆弧形层状沉积河谷场地在平面SH波入射下动力响应分析.岩土工程学报.2000,22(4):396-401页
[87]COUSSY O. Scattering of Elastic waves by an inclusion with an interface crack. Wave Motion,1984 (6):223-229P
[88]YANG Y, NORRIS A. Shear wave scattering from a debonded fiber. J Mech Phys Solids,1991,39:273-280P
[89]A. Norris and Y. Yang.Dynamic Stress on a Partially Bonded Fiber.J. Appl Mech.1991,58:404-411P
[90]Karim M.R.,Awal M.A.,Kundu T..Elastic Wave Scattering by Cracks and Inclusions in Plates:In-Plane Case.International Journal of Solids and Structures.1992,29(19):2355-2367P
[91]林皋.地下结构抗震分析综述(上).世界地震工程.1990,5(2):1-10页
[92]王竹溪,郭敦仁.特殊函数概论.北京:北京大学出版社,2000:337-417页,601-620页
[93]黎在良,刘殿魁著:固体中的波.北京:科学出版社,1995:286-319页,377-431页
[94]王铎,马兴瑞,刘殿魁.弹性动力学最新进展.北京:科学出版社,1995:13-15页
[95]马兴瑞,邹振祝,邵成勋,黄文虎.层状介质交界裂纹的弹性波(P波和SV波)散射研究.航空学报.1989,10:434-447页
[96]阿肯巴赫.J.D著.徐植信译.弹性固体中波的传播.上海:同济大学出版 社.1992:279-284页
[97]王铎,汪越胜.界面动力学研究近况.上海力学.1993(4):1-15页
[98]汪越胜,王铎.剪切波作用下圆弧形界面裂纹的动应力强度因子.固体力学学报.1993,14(4):362-367页
[99]汪越胜,王铎.SH波对有部分脱胶衬砌的圆形孔洞的散射.力学学报.1994,26(4):462-468页
[100]廖振鹏著.工程波动理论导论.第二版.北京:科学出版社,2002:141-187页
[101]徐植信.弹性波传播理论一些问题的研究现状和展望.上海力学.1989,10(3):6-10页