各向异性介质中SH波引起圆孔周围的能量散射

本文利用复变函数方法求解无限的各向异性介质中入射SH波对圆孔的散射问题.并指出能量的散射与入射波波长和圆孔半径有关.最后给出了圆孔周围能量散射的数值结果.     

各向异性体内含任意孔洞对反平面波散射的边界元方法

本文借助于广义格林公式导出了用位移表示的各向异性介质中SH波入射时的边界积分方程.根据本文作者在文献[8]给出的基本解,求解了各向异性介质中孔洞对SH波的散射问题.边界积分方程的离散基于常数元模式.文中给出了一个圆柱、一个椭圆柱和两个椭圆柱形式的孔洞周围的位移场和应力场的数值结果.最后,对入射波频率较高时的情形作了说明.     

各向异性对半圆形河谷散射影响的数值分析

半圆形河谷场地可构造为包含河谷的广义子结构和具有规则边界的开挖场地两部分,基于土-结构相互作用SSI原理,建立子结构控制方程。利用比例边界有限元SBFEM求解开挖场地动刚度,解析求解各向异性介质自由场qP波波动,将两者代入控制方程,可求得广义结构的动力响应。与文献中各向同性半空间中半圆形河谷在P波入射下的位移结果对比,验证了方法的精度和有效性。进一步分析了椭圆各向异性和非椭圆各向异性对半圆形河谷在qP波入射下位移分布的影响。数值算例显示,介质的各向异性改变了半圆形河谷散射位移的空间分布,增大了水平向位移的峰值;同时,介质的各向异性加剧了入射角对散射波场位移分布的影响。     

各向异性对半圆形河谷散射影响的数值分析

半圆形河谷场地可构造为包含河谷的广义子结构和具有规则边界的开挖场地两部分,基于土-结构相互作用SSI原理,建立子结构控制方程。利用比例边界有限元SBFEM求解开挖场地动刚度,解析求解各向异性介质自由场qP波波动,将两者代入控制方程,可求得广义结构的动力响应。与文献中各向同性半空间中半圆形河谷在P波入射下的位移结果对比,验证了方法的精度和有效性。进一步分析了椭圆各向异性和非椭圆各向异性对半圆形河谷在qP波入射下位移分布的影响。数值算例显示,介质的各向异性改变了半圆形河谷散射位移的空间分布,增大了水平向位移的峰值;同时,介质的各向异性加剧了入射角对散射波场位移分布的影响。     

各向异性介质中SH波与多个半圆形凹陷地形的相互作用

本文利用多极坐标和复变函数方法研究各向异性介质中SH波与多个半圆形凹陷地形的相互作用,各向异性可用来模拟地质条件。本文给出了各向异性介质中多个半圆形凹陷地形的散射波的表达式。并利用移动坐标的方法,来满足给定的多个半圆形凹名地形上的边界条件,将待解的问题归结为对一组无穷代数方程组的求解问题。本文最后给出了两个尺寸相同的半圆形凹陷地形的相互作用问题的解答和数值结果。     

各向异性介质中SH波引起的圆孔附近的动应力集中

本文利用复变函数方法求解无限的各向异性介质中入射的SH波对圆形孔洞的散射问题,指出动应力集中系数与入射波波数K_σ和圆孔半径r有关,最后给出了圆孔附近动应力集中系数的数值结果。     

大延伸非均匀介质中地震波全弹性散射理论Ⅰ--弹性波单次散射理论

所描述的工作聚焦于大延伸非均匀介质中非均匀弹性地震波散射问题的研究.应用Born近似及等效源原理,推出了来自连续横向无界非均匀层的弹性散射波的通解.这一工作是解决大延伸非均匀介质的弹性地震波多次散射问题的基础.在上述通解的基础上,建立了适用于大延伸非均匀介质的全弹性散射理论.该理论可包容小尺度非均匀体、大延伸非均匀介质全弹性波单次弱散射理论及标量波单次弱散射理论,因此可视其为一个更为广义和统一的弱散射理论.     

各向异性体内多个夹杂对反平面波的散射

本文导出了各向异性介质反平面剪切运动的基本解。在此基础上引用等效体力及二维亥维赛函数建立了内含多个任意形状夹杂(空洞)时散射位移场的积分方程。针对两个异质物情形运用Born近似理论讨论了散射远场。同时定义和推导了微分横截线,并给出了计算实例。     

各向异性平板开孔动应力集中问题的研究

采用各向异性平板弯曲波动理论及摄动方法，对正交各向异性平板开孔弯曲波的散射及动应力集中问题进行了分析研究，得到了此种平板稳态弯曲波动问题的渐近形式的分析解。同时采用保角映射技术，为求解正交各向异性平板开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。     

SH波对内含裂纹衬砌结构的散射及动应力集中

当衬砌结构内含裂纹时 ,采用Green函数的方法 ,研究了SH波对裂纹的散射及其动应力集中 ,构造了在含有半圆形衬砌的弹性半空间上 ,在水平面上任一点承受时间谐和出平面线源载荷作用时的位移函数作为Green函数 ;推导了SH波对衬砌内有裂纹的散射定解积分方程组 ,进而求得裂纹尖端的动应力因子 ,重点讨论了衬砌及周围介质对裂纹尖端动应力因子的影响 ,给出了介质参数变化对裂纹尖端动应力因子的影响曲线 ,为工程设计提供了依据。     

A boundary element solution to scattering of elastic SH wave by arbitrarily shaped inclusions embedded in an infinite anisotropic medium

Scattering problems for inhomogeneous bodies are investigated by the integral equation method. The boundary integral equation (BIE) for the scattered displacement field associated with finite inhomogeneities in an anisotropic medium are derived with the help of the generalized Green's identity. The discretization of BIE is based upon the constant element, linear element and quadratic element. Several numerical examples for calculating the scattering displacement, stress and scattering cross section from a cylinder, an interface crack, and two elliptic cylinders are given. Results show that the present method can be advantageously applied to a wide range of scattering problems of elastic waves.     

各向异性体对瞬态SH波散射问题的边界元方法

本文利用Fourier变换和加权残数法建立了正交各向异性体反平面瞬态波散射问题的边界积分方程,构造了在边界上能满足波动方程的边界元函数,它比常用的二次元和高次元具有较好的适应性。数值结果表明利用该形函数计算高频情形下的散射问题具有很高的精度。     

Weakly-singular,weak-form integral equations for cracks in three-dimensional anisotropic media

Singularity-reduced integral relations are developed for displacement discontinuities in three-dimensional, anisotropic linearly elastic media. An isolated displacement discontinuity is considered first, and a systematic procedure is followed to develop relations for the displacement and stress fields induced by the discontinuity. The singularity-reduced relation for the stress is particularly important since it is in a form which allows a weakly-singular, weak-form traction integral equation to be readily established. The integral relations obtained for a general displacement discontinuity are then specialized to an isolated crack and to dislocations; the relations for dislocations are introduced to emphasize their direct connection to corresponding results for cracks and to allow earlier independent findings for these two types of discontinuities to be put into proper context. Next, the singularity-reduced integral equations obtained for an isolated crack are extended to allow treatment of cracks in a finite domain, and a pair of weakly-singular, weak-form displacement and traction integral equations is established. These integral equations can be combined to obtain a final formulation which is in a symmetric form, and in this way they serve as the basis for a weakly-singular, symmetric Galerkin boundary element method suitable for analysis of cracks in anisotropic media.     

Elastodynamic analysis of inhomogeneous anisotropic bodies

The integral equation method is presented for elastodynamic problems of inhomogeneous anisotropic bodies. Since fundamental solutions are not available for general inhomogeneous anisotropic media, we employ the fundamental solution for homogeneous elastostatics. The terms induced by material inhomogeneity and inertia force are regarded as body forces in elastostatics, and evaluated in the form of volume integrals. The scattering problems of elastic waves by inhomogeneous anisotropic inclusions are investigated for some test cases. Numerical results show the significant effects of inhomogeneity and anisotropy of materials on wave propagations.     

A boundary element method for calculating the SH waves scattering from arbitrarily shaped holes in an anisotropic medium

The scattering problem of elastic wave by arbitrarily shaped cavities in an infinite anisotropic medium is investigated by the boundary integral equation (BIE) method. The formulations of BIE are derived with the help of generalized Green's formula. The discretization of BIE is based upon constant elements. After confirmation of the accuracy of the present method, some numerical examples are given for various cavities in a full space, in which an isotropic body with a circular cylinder hole is used for comparison and good agreement is observed. It has been proved that the method developed in this paper is effective.     

Singular loadings in elasticity problems and singular solutions of the corresponding integral equations

The method of singular integral equations is an efficient method for the formulation and numerical solution of plane and antiplane, static and dynamic, isotropic and anisotropic elasticity problems. Here we consider three cases of singular loadings of the elastic medium: by a force, by a moment and by a loading distribution with a simple pole. These loadings cause corresponding singularities in the right-hand side function and in the unknown function of the integral equation. A method for the numerical solution of the singular integral equation under the above singular loadings is proposed and the validity of this equation at the singular points is investigated.     

Scattering of elastic waves by elastically transparent obstacles (integral-equation method)

A formulation of elastodynamic diffraction problems for sinusoidally in time varying disturbances in a linearly elastic medium is presented. Starting with the elastodynamic reciprocity relation, an integral representation for the particle displacement is derived. In it, the particle displacement and the traction at the boundary of the obstacle occur. From the integral representation, an associated integral equation is obtained by letting the point of observation approach the boundary of the obstacle. The “obstacle” may be either a rigid body, a void, or a body with elastic properties differing from those of its environment, or a combination of these. The integral equation thus obtained is well-suited for numerical treatment, when obstacles up to a few wavelengths in maximum diameter are considered.     

双相介质半空间中圆孔对透射SH波的稳态分析

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。     

应用边界积分法求圆形夹杂问题的解析解

边界元方法作为一种数值方法, 在各种科学工程问题中得到了广泛的应用.本文参考了边界元法的求解思路, 从Somigliana等式出发, 利用格林函数性质,得到了一种边界积分法, 使之可以用来寻求弹性问题的解析解.此边界积分法也可以从Betti互易定理得到. 应用此新方法, 求解了圆形夹杂问题.首先设定夹杂与基体之间完美连接, 将界面处的位移与应力按照傅里叶级数展开,根据问题的对称性与三角函数的正交性来简化假设, 减少待定系数的个数.其次选择合适的试函数(试函数满足位移单值条件以及无体力的线弹性力学问题的控制方程),应用边界积分法, 求得界面处的位移与应力的值. 然后再求解域内位移与应力.得到了问题的精确解析解, 当夹杂弹性模量为零或趋向于无穷大时,退化为圆孔或刚性夹杂问题的解析解. 求解过程表明,若问题的求解区域包含无穷远处时, 所取的试函数应满足无穷远处的边界条件.若求解区域包含坐标原点, 试函数在原点处位移与应力应是有限的.结果表明了此方法的有效性.      

非均匀介质散射问题的体积分方程数值解法

将非均匀介质视为某一均匀背景介质中的扰动，可建立用均匀背景介质格林函数作基本解的体积分方程．给出了配置法求解体积分方程的数值方法，首先解得扰动域内各点以速度扰动为权的波场函数，然后回代计算得到观测面上各接收点的散射波场．与边界元法和Ｂｏｒｎ近似法计算结果比较表明该方法具有很高的精度，可得到穿过非