SH波散射与界面圆孔附近的动应力集中

建立了求解含有界面圆孔的二种不同弹性组合介质中ＳＨ波的散射和界面圆孔附近的动应力集中问题的Ｇｒｅｅｎ函数法给出了一个具有半圆形缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解取基本解作为Ｇｒｅｅｎ函数，建立起问题的定解积分方程最后给出了界面圆孔的动应力集中的算例和结果，并讨论了不同介质参数的组合对动应力集中的影响     

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。     

无限大板开孔弹性波的散射及动应力集中

采用弹性平板理论及复变函数理论，对含孔无限大平板弹性波的散射及动应力集中问题进行了分析研究，建立了求解平板开孔动应力集中问题的复变函数方法。若同时采用映射变换，就为求解平板开任意形状孔的动应力集中问题提供了一种规范而有效的方法。为说明问题，本文给出了平板开圆孔及椭圆孔动应力集中因子的数值结果。     

含孔平板弹性波散射问题的复变函数方法

本文采用平板弯曲波动理论及复变函数方法，对平板开孔弹性波的散射及动应力集中问题进行了分析研究，得到了传播急剧记波时此种平板弯曲波动问题的分析解。若同时采用保角射技术，就为主解平板任意形状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。作为算例，本文给出了平板开圆孔和椭圆孔附近的动应力集中系数的数值结果，并对其进行了讨论。     

弯曲波对含多圆孔薄板的散射与动应力集中

采用复变函数法和多极坐标方法,研究了弯曲波对含有多圆孔薄板的散射问题。通过板的弯曲波动方程和内力方程的推导,求出在入射弯曲波条件下该问题的一般解的函数逼近序列和边界条件的表达式。用展开正交函数的方法将待解的问题归结为对一组无穷代数方程组的求解。最后,给出了含3圆孔薄板的孔边动应力集中系数的结果,并分析了孔间距和波数对动应力分布的影响。     

SH波入射时垂直半空间中双相介质界面附近圆孔的动力分析

利用复变函数和Green函数法研究了垂直半空间中双相介质界面附近圆孔对SH波的散射与动应力集中问题。该问题的解答采用镜像法,首先构造出含有圆孔的直角平面区域出平面问题的Green函数,然后利用契合技术,并根据界面处位移连续性条件将解答归结为具有弱奇异性的第一类Fredholm积分方程组的求解,结合散射波的衰减特性,直接离散该方程组,把积分方程组转化为线性代数方程组可得到该问题的数值结果。最后,通过算例分析了圆孔的动应力集中情况。结果表明,与全空间中界面附近圆孔对SH波的散射相比,由于垂直半空间自由边界的存在,孔边动应力集中系数明显增大;另外,入射波由硬介质(波速大)进入到软介质(波速小)时,与均匀介质相比,孔边动应力集中更显著,最不利的参数组合,孔边动应力集中系数几乎提高了一倍,入射波由软介质进入到硬介质时,情况相反。     

SH波与界面多圆孔的散射及动应力集中

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。     

SH波对直角平面区域内圆形孔洞的散射与地震动

研究了以任意方向入射的平面SH波对直角平面区域内圆形孔洞的散射与地震动问题.首先,利用复变函数法、多极坐标移动技术及叠加原理,构造了一个可以预先满足直角平面区域自由表面上应力自由边界条件的圆孔对SH波散射的波函数;其次,利用镜像法,将直角平面区域内的波场镜像于半无限空间,并得到了满足边界条件的总波场;最后,作为对抗暴抗震问题的研究,通过算例考虑了圆孔的动应力集中和地表的动位移.结果表明,圆孔的动应力集中和地表的位移幅值取决于入射波频率、角度和圆孔的位置.     

SH波对双相介质界面附近圆形孔洞的散射

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．     

弯曲波在含非圆孔洞无限压电薄板中的散射

基于线性压电动力学理论,采用波函数展开法、保角映射以及复变函数,对含非圆孔洞无限大压电薄板弹性波的散射及动应力集中问题进行了分析,给出了其动弯矩集中系数(DMCF)的解析表达式.为说明问题,以PZT-4为例,讨论了外加电场、椭圆孔长短半轴比、椭圆孔倾角以及入射波频率对含圆孔和椭圆孔无限大压电薄板弹性波散射的影响,并分别...     

含孔von Karman板中非线性波散射与边值问题

基于ｖｏｎ Ｋａｒｍａｎ板大挠度弯曲理论,利用小参数摄动法,分析研究了含孔ｖｏｎＫａｒｍａｎ板的非线性波散射与动应力集中问题,其中一类可看成是薄板弯曲波动问题的控制方程。当有单频波入射时,由于弯曲应力与膜应力状态的非线性耦合,孔洞会产生高次谐波散射现象。建立了求解本问题的边界积分方程法,利用积分方程法交替求求这两类问题,最终可获得问题的近似分析解。     

Application of complex path-independent integrals to the solution of the problem of a straight crack in a finite plane isotropic elastic medium

The classical problem of a straight crack in a finite, plane, isotropic, elastic medium of arbitrary shape is reconsidered by the well-known method of Muskhelishvili for such a crack (but in an infinite medium). Both the crack and the boundary of the medium are assumed loaded in an arbitrary way. It is shown that this problem can be completely solved if the numerical values of the first complex potential (z) of Muskhelishvili are known along a closed contour surrounding the crack, probably along the boundary of the medium. To this end, complex path-independent integrals associated with (z) and Chebyshev polynomials have been used. Numerical results for the stress intensity factors are displayed in an application. Generalizations of the method are also proposed and the second fundamental crack problem, the problem of a crack in an anisotropic medium and the problem of an interface crack between two isotropic media are considered in some detail.     

Doubly-periodic array of cracks in an infinite isotropic medium

The problem of a doubly-periodle array of curvilinear cracks in an infinite isotropic medium under conditions of generalized plane stress or plane strain is reduced, by using the method of complex potentials of Muskhelishvili [1], to a complex Cauchy-type singular integral equation on one of the cracks, which can be further numerically solved by reduction to a system of two real Cauchy-type singular integral equations and application of the Gauss or Lobatto-Chebyshev method of numerical solution of such equations.

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Zusammenfassung Das Problem einer zwei-periodischer Anordung gekrümmten Rissen in einem unendlichem isotropem Medium im allgemeinen ebener Spannung-bzw Dehnung-Zustand, unter Anwendung der Methode von komplexen Potentialen von Muskhelishvili [1], ist in einer Cauchyscher komplexer singulärer Integral-Gleichung auf einem der Rissen reduziert. Diese Gleichung kann weiter numerisch gelöst werden bei Transformation in einem System von zwei reelen Cauchyschen singulären Integral-Gleichungen und bei Anwendung der Methoden von Gauss oder Lobatto-Chebyshev für die numerische Resolution solcher Gleichungen.

     

含孔曲板弹性波散射与动应力分析

基于敞口浅柱壳弹性波动方程及摄动方法，对无限大含孔曲板弹性波散射及动应力问题进行了分析研究，将经典薄板弯曲波动问题的分析解作为本问题的主项，给出了在稳态波下孔洞附近散射波的零阶渐近解。建立了求解含孔曲板弹性波散射与动应力问题的边界积分方程法，利用积分方程法可获得问题的近似分析解。并给出了无限大曲板圆孔附近动应力集中系数的数值结果，且对计算结果进行了分析与讨论。     

正交各向异性平板开孔弹性波的衍射与动应力集中

采用各向异性平板弯曲波动方程及摄动方法，对正交各向异性无限平板开孔弹性波的衍射及动应力集中的问题进行了分析研究，得到了在稳态波作用下此种忆边界条件波动问题的渐近形式分析解。同时采用复变函数方法及保角映射技术，为求解正交各向异性无限平板开孔弹性波的衍射及动力集中问题提供了一种统一规范的分析方法。     

The use of complex valued functions for the solution of three-dimensional elasticity problems

For the treatment of plane elasticity problems the use of complex functions has turned out to be an elegant and effective method. The complex formulation of stresses and displacements resulted from the introduction of a real stress function which has to satisfy the 2-dimensional biharmonic equation. It can be expressed therefore with the aid of complex functions. In this paper the fundamental idea of characterizing the elasticity problem in the case of zero body forces by a biharmonic stress function represented by complex valued functions is extended to 3-dimensional problems. The complex formulas are derived in such a way that the Muskhelishvili formulation for plane strain is included as a special case. As in the plane case, arbitrary complex valued functions can be used to ensure the satisfaction of the governing equations. Within the solution of an analytical example some advantages of the presented method are illustrated.     

Scattering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout

Using the complex variable method and conformal mapping, scattering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied. The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique, the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations. As examples, numerical results for the dynamic stress concentration factor in Mindlin's plates with a circular, elliptic cutout are graphically presented in sequence. The project supported by the National Natural Science Foundation of China     

A semi-analytical elastic solution for stress field of lined non-circular tunnels at great depth using complex variable method

In this paper, a semi-analytical elastic plane strain solution was provided for stress field around a lined non-circular tunnel subjected to uniform ground load. Concrete lining and the surrounding rock mass were assumed as linearly elastic materials. Due to complexity of the problem for non-circular geometric configurations, complex variable method introduced by Muskhelishvili and conformal mapping functions were used to determine stress components within concrete lining and the surrounding rock mass. Finally, the solution was validated by ABAQUS finite element software through an example. Very good agreement was demonstrated between semi-analytical and numerical solution although some discrepancies were found at tunnel corners where large curvature existed. It was demonstrated that the solution predicted stress components more accurately around the tunnels, especially the corners with large stress concentration. Practical significance of the solution was placed in the fact that it could be used as a quick-solver with high accuracy.     

Collinear periodical cracks with surface separation and frictional sliding

Using the method of Muskhelishvili, an exact solution is obtained for the problem of collinear, periodical cracks whose surface undergo separation and frictional sliding.     

Dynamics stress concentrations in Ambartsumian's plate with a cutout

Based on the motion equations of flexural wave in Ambartsumian's plates including the effects of transverse shear deformations, by using perturbation method of small parameter, the scattering of flexural waves and dynamic stress concentrations in the plate with a cutout have been studied. The asymptotic solution of the dynamic stress problem is obtained. Numerical results for the dynamic stress concentration factor in Ambartsumian's plates with a circular cutour are graphically presented and discussed. The project supported by the National Natural Science Foundation of China.