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1.
SH波作用下界面任意形状孔洞附近的动应力集中   总被引:1,自引:0,他引:1  
采用Green函数和复变函数法求解了平面SH波在界面任意形状孔洞上的散射问题.首先,取含有任意形状凹陷的弹性半空间,在其水平表面上任意一点承受时间谐和的反平面线源荷载作用时的位移场作为Green函数.然后,按契合方式构造出界面任意形状孔洞对SH波的散射模型,利用所得Green函数按界面位移连续条件建立求解问题的定解积分方程组,求解界面孔附近的动应力集中系数.最后,给出了界面上椭圆孔和方孔边缘动应力集中系数的数值结果,并讨论了不同介质参数和孔洞形状对孔附近动应力集中系数的影响.  相似文献   

2.
位移阶跃SH波对半圆形凹陷地形的散射   总被引:1,自引:0,他引:1  
本文利用积分变换和波函数展开方法求解位移阶跃的平面SH波对半圆形凹陷地形的散射问题,导出了散射位移场的解析表达式,,并给出了在凹陷地形表面上各点位移时程反应的数值结果。本文的结果可做为Duhamel积分的影响系数求解一个随时间任意变化的平面SH波被半圆形凹陷地形散射的问题。  相似文献   

3.
利用波函数展开法求解了二维直角平面角点处圆弧形衬砌对稳态入射平面SH波的散射问题,得到问题的解析解.方法是首先构造出衬砌介质内外的总波场,它们能够预先满足直角平面两直角边界应力自由条件;再利用衬砌边界处的应力和位移连续条件写出确定散射波解中未知系数的方程组并求解.通过算例具体讨论了衬砌内边界处的环向应力集中系数和位移幅度比随无量纲波数、入射角的变化情况,结果表明它们存在不同程度的放大现象.  相似文献   

4.
采用波函数展开法对平面P波入射复杂水域地形的空间变异性地震动场进行研究,该水域地形具有覆水层、饱和双相介质、场地非平坦以及第二类分层(场地跨越分层界面)等属性.首先,依据地震波反射和透射特性推导直角坐标系下的自由波场分布;然后,根据场地属性并引入大圆弧法分析极坐标系下的含有待定系数的散射波场;进而,结合土-水分界面和饱和土层分界面边界条件,求解散射波场中的待定系数;最后,通过自由波场和散射波场得到覆水饱和双相介质圆弧场地波函数理论解.基于理论解,通过算例验证了理论推导的合理性及可靠性,分析了地表位移在不同入射条件下的差异性.结果 表明,相对于均匀介质,饱和双相介质会显著影响地表位移分布.此外,入射波频率和角度对地震地面运动特性也有较大的影响.  相似文献   

5.
圆弧形层状沉积谷地对入射平面SV波散射解析解   总被引:10,自引:0,他引:10  
利用Fourier—Bessel级数展开法给出了圆弧形层状沉积谷地对入射平面SV波散射问题的一个解析解,并分析了谷中层状沉积排列顺序及相对刚度等因素对散射的影响.  相似文献   

6.
利用复变函数法、多极坐标及傅立叶级数展开技术求解了二维直角平面内固定圆形夹杂对稳态入射反平面剪切(shearing horizontal, SH)波的散射问题。首先构造出介质内不存在夹杂时的入射波场和反射波场,然后建立介质内存在夹杂时由夹杂边界产生的能够自动满足直角边应力自由条件的散射波解,从而利用叠加原理写出介质内的总波场。利用夹杂边界处位移条件和傅立叶级数展开方法列出求解散射波中未知系数的无穷代数方程组,在满足计算精度的前提下通过有限项截断,得到相应有限代数方程组的解,最后通过算例具体讨论了二维直角平面水平边界点的位移幅度比和相位随量纲一波数、入射波入射角及夹杂位置的不同而变化的情况,结果表明了算法的有效实用性。  相似文献   

7.
利用复变函数法、多极坐标移动技术及傅立叶级数展开求解二维直角平面内圆形弹性夹杂对稳态入射平面SH波的散射问题。首先写出直角平面内不含夹杂时的入射波场和反射波场;其次建立直角平面内含夹杂时夹杂外的散射波解和夹杂内的驻波解,并利用叠加原理写出问题的总波场,借助夹杂边界处应力和位移的连续条件建立求解散射波解和驻波解中未知系数的无穷代数方程组并求解,通过算例具体讨论了直角平面水平边界点的位移幅度比和夹杂边界处径向应力集中系数随不同无量纲波数、入射角及圆孔位置的变化情况,结果表明了算法的有效实用性。  相似文献   

8.
本文引用加权残数法建立了各向异性介质内含任意形式异质夹杂时的散射问题的边界积分方程式,导出了相应的辐射条件,计算了内含圆柱体,椭圆柱体、界面裂纹情形下对SH 波的散射位移场、应力场以及散射横截面.数值结果表明本方法用于解答各向异性介质的弹性波散射问题具有良好的精度和应用前景.  相似文献   

9.
弹性波绕任意形状界面孔的散射   总被引:2,自引:1,他引:1  
求解了弹性波绕任意形状界面孔的散射问题.通过入射波、反射波或折射波及孔的散射波场的叠加,得到了界面孔在SH波绕射下的总波场.总波场波函数的级数项待定系数可采用边界配点法来确定,该法不受边界正交性的限制,能够适用于任意形状的边界.最后,对界面椭圆孔进行了实例计算,得到了椭圆孔边的动应力集中系数.  相似文献   

10.
SH波与界面多圆孔的散射及动应力集中   总被引:14,自引:0,他引:14  
研究了平面SH波对相邻多个界面圆孔的散射及其动应力集中,为了求解,首先利用复变函数和多极坐标方法构造了在含有多个半圆形缺口的弹性半空间,水平面上任一点随时间谐和出平面线源载荷作用时失主移,邓Green函数,且采用“契合”模型,推导了SH波对相邻多个界面圆孔散射的定解积分方程组,进而求得圆孔附近的动应力系数,作为算例,讨论了具有两个界面圆孔对SH波的散射及其相互影响,给出了孔附近的动应力分布曲线。  相似文献   

11.
SCATTERING OF CIRCULAR CAVITY IN RIGHT-ANGLE PLANAR SPACE TO STEADY SH-WAVE   总被引:1,自引:0,他引:1  
Complex function method and multi-polar coordinate transformation technology are used here to study scattering of circular cavity in right-angle planar space to SH-wave with out-of-plane loading on the horizontal straight boundary. At first, Green function of right-angle planar space which has no circular cavity is constructed; then the scattering solution which satisfies the free stress conditions of the two right-angle boundaries with the circular cavity existing in the space is formulated. Therefore, the total displacement field can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering solution field can be gained using multi-polar coordinate and the free stress condition at the boundary of the circular cavity. It can be solved by using limit items in the infinite series which can give a high computation precision. An example is given to illustrate the variations of the tangential stress at the boundary of the circular cavity due to different dimensionless wave numbers, the location of the circular cavity, the loading center and the distributing range of the out-of-plane loading. The results show the efficiency and effectiveness of the method introduced here.  相似文献   

12.
In this paper, based on a variational formalism which originally proposed by Mei [1] for infinite elastic medium and extended by Yeh, et al. [2,3] for elastic half-plane, a hybrid method which combines the finite element and series expansion method is implemented to solve the diffraction of plane waves by a cavity buried in an elastic half-plane. The finite domain which encloses all inhomogeneities including the cavity can be easily formulated by finite element methods. The unknown boundary data obtained by subtracting the known free fields from the total fields which include the boundary nodal displacements and tractions at the interface between the finite domain and the surrounding elastic half-plane are not independent of each other and can be correlated through aseries repre sentation. Due to the continuity condition at the interface, the same series representation is still valid for the exterior elastic half-plane to represents the scattered wave. The unknown coefficients of this series are treated as generalized coordinates and can be easily formulated by the same variational principle. The expansion function of the series is composed of basis function. Each basis function is constructed from the basis function for an infinite plane by superimposing an additional homogeneous reflective term to satisfy both traction free conditions at ground surface and radiation conditions at infinity. The numerical results are made against those obtained by boundary element methods, and good agreements are found.  相似文献   

13.
The complex function method used in the solution of static stress concentration around an irregularly shaped cavity in an infinite elastic plane is generalized to the case of dynamic loading. This paper presents the solutions of two dimensional elastic wave equations in terms of complex wave functions, and general expressions for boundary conditions for steady state incident waves. Dynamic stresses around a cavity of arbitrary shape are then expressed in series of complex ‘domain functions’, the coefficient of the series can be determined by truncating a set of infinite algebraic equations. Results of dynamic stress concentration factors for circular and elliptical cavities are given in this paper.  相似文献   

14.
A 2D time domain boundary element method (BEM) is developed to solve the transient scattering of plane waves by a unilaterally frictionally constrained inclusion. Coulomb friction is assumed along the contact interface. The incident wave is assumed strong enough so that localized slip and separation take place along the interface. The present problem is in effect a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (slip, separation and stick regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embeddedin an infinite solid.  相似文献   

15.
采用复变函数法,结合"保角映射"技术及Green函数法,研究SH波作用下半空间内含有部分脱胶的椭圆夹杂以及圆形孔洞的散射问题。首先,利用"保角映射"技术将椭圆夹杂映射为圆夹杂,求出散射波位移场,同时,利用Green函数法与"虚设点源"的方法,求出半空间内椭圆夹杂以及圆孔的位移及应力场;然后,根据椭圆夹杂周围位移、应力连续、圆孔周围应力自由的边界条件,建立无穷线性代数方程组,求解出波函数中的未知系数;最后,在脱胶部分施加大小相等、方向相反的应力,构造出"脱胶模型",得到半空间内含有部分脱胶的椭圆夹杂以及圆形孔洞的总位移场。数值算例表明,入射角度、入射波频率、缺陷之间的距离、夹杂埋深及脱胶角度等对动应力集中因子有较大影响。  相似文献   

16.
研究了平面SH波在半空间双相弹性介质中的传播。通过Green函数和积分方程方法,按照复变函数描述,对透射波被圆孔散射的情况进行稳态分析。将双相介质半空间沿界面剖分为1/4空间介质Ⅰ和含圆孔的1/4空间介质Ⅱ,分别构造了介质Ⅰ和介质Ⅱ中反平面点源荷载的Green函数,按双相介质中平面SH波的处理方法,给出介质Ⅰ和介质Ⅱ中的平面位移波,两种介质之间的相互作用力与对应Green函数的乘积沿界面的积分与平面位移波叠加得到介质Ⅰ和介质Ⅱ中的全部位移场。按照界面的位移连续条件,定解积分方程组,得到问题的稳态解,并给出圆孔位置和介质参数对散射的影响。  相似文献   

17.
SH波对双相介质界面附近圆形孔洞的散射   总被引:11,自引:1,他引:10  
建立了求解平面SH波对双相介质界面附近圆形孔洞散射与动应力集中的一种分析方法.利用复变函数与多极坐标的方法构造了一个Green函数,它是在含有圆形孔洞的弹性半空间的水平面上任一点上作用时间谐和的出平面线源荷载的位移解.利用“契合”模型,并根据界面上位移连续性条件,建立了求解SH波对双相介质界面附近圆形孔洞散射的具有弱奇异性的第一类Fredholm型积分方程.给出了圆孔周边上动应力集中系数的表达式.作为算例,分析了在界面一侧或界面两侧附近具有圆形孔洞时SH波的散射,并讨论了入射波波数、不同的材料组合以及孔心至界面的距离对动应力集中的影响.  相似文献   

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