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。     

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。     

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。     

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,并分别给出了无限压电薄板开圆孔和椭圆孔动弯矩集中系数的数值结果。     

含双圆孔平板弹性波散射与动应力分析

利用复变量及局部坐标系方法，对平板中含双圆孔弹性波的衍射与动应力集中问题进行了研究，给出了不同方向入射弯曲波条件下该问题一般解的函数逼近序列和边界条件的表达式用正交函数展开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给出了双圆孔附近的动应力集中系数的数值结果，分析了孔间距对动应力分布的影响     

论弹性波绕射与动应力集中问题

本文综述了弹性波绕射与动应力集中问题的复变函数解法,给出了单连通问题、多连通问题及多裂纹问题的具体求解过程及算式.      

采用精确化理论求解厚板任意形开孔动应力集中

摘要：本文基于复变函数与保角映射法,采用平板弯曲振动精确化方程[9],对含任意形开孔平板中弹性波散射与动应力集中问题进行了研究。利用正交函数展开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。作为算例,计算了自由边界条件下圆孔和椭圆孔的动弯矩集中系数的数值结果,并对板厚与孔径比对动弯矩分布的影响做了分析研究。结果表明：入射波数、平板厚度和椭圆偏心率等参数对动弯矩的分布都有很大的影响。在较低频率和平板较薄的情况下,基于文献[9]的方程与基于Mindlin板的动弯矩结果在数值分布上是基本一致的;在较高频率和平板较厚的情况下,基于文献[9]的方程与基于Mindlin板的动弯矩结果在数值分布计算结果相差较大。由于文献[9]给出的平板振动精确化方程是在没有任何工程假设条件下得到的,因此本文的分析计算结果更精确一些。     

SH波作用下界面任意形状孔洞附近的动应力集中

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.     

小内力平板弹性波散射问题的摄动方法

基于平板小挠度弯曲波动方程,采用摄动方法具有纵向内力作用下的平板开孔弹性波的散射问题进行了研究,得么了传播稳态波时此种平板弯曲波动问题的分析解,分析了均匀纵向内力对弹性波散射结果的影响,作为算例,本文给出了平板圆形开孔的动应力集中系数的数值结果,并对计算结果进行了讨论。     

圆柱壳大开孔问题——单圆孔的理论解

从Ｄｏｎｎｅｌｌ圆柱壳方程出发，利用复变函数与保角映射的方法，将圆柱壳展开面上的开孔边界线保角晨射成单位圆，并在映射平面上给出了逼近大开孔圆柱壳方程解答的完备函数逼近序列，进而利用边界条件和正交函数展开的方法得到了自由孔边应力集中系数的表达式，最后，对具有开孔率的圆柱壳在不同荷载条件下的自由孔口边界上的应力集中的系数进行了计算，此种方法，同时研究圆柱壳开非圆大孔和接管等问题提供了可能性。     

带边框承重墙板的应力分析

本文讨论周界用边框加固的承重墙板局部应力集中现象和整个应力分布情况.所用方法是以满足板的双调和方程为基础,运用最小余能原理,达到板与框架的位移协调一致.     

The concentration of stress and strain in finite thickness elastic plate containing a circular hole

The elastic stress and strain fields of finite thickness large plate containing a hole are systematically investigated using 3D finite element method. It is found that the stress and strain concentration factors of the finite thickness plate are different even if the plate is in elasticity state except at notch root of plate surface. The maximum stress and strain do not always occur on the mid plane of plate. They occur on the mid plane only in thin plate. The maximum stress and strain concentration factors are not on mid plane and the locations of maximum stress and strain concentration factors are different in thick plate. The maximum stress and strain concentration factors of notch root increase from their plane stress value to their peak values, then decrease gradually with increasing thickness and tend to each constant related to Poisson’s ratio of plate, respectively. The stress and strain concentration factors at notch root of plate surface are the same and are the monotonic descent functions of thickness. Their values decrease rapidly and tend to each constant related to Poisson’s ratio with plate thickness increasing. The difference between maximum and surface value of stress concentration factor is a monotonic ascent function of thickness. The thicker the plate is or the larger the Poisson’s ratio is, the larger the difference is. The corresponding difference of strain concentration factor is similar to the one of stress concentration factor. But the difference magnitude of stress concentration factor is larger than that of strain concentration factor in same plate.     

P-FEMOL ANALYSIS OF PLATE BENDING PROBLEMS

In this paper,the p-version of the finite element method of lines(FEMOL) for the analysis of the Mindlin-Reissner plate bending problems is presentedand a class of p-FEMOL elements with polynomial degrees as high as nine isdeveloped.Numerical examples given in this paper show tremendous performance ofthe present method;namely,rapid convergence rate,high accuracy for bothdisplacements and stress resultants,removal of shear-locking trouble,capability ofdealing with difficult problems such as the boundary layer behavior near a free edgeand stress concentration around a hole.     

Fatigue of fillet welded joints

The Albrecht method was used to compute stress intensity factors in non-load carrying fillet welds subjected to tension and cantilever bending for cracks growing from the tip of the weld toe through the plate thickness. The stresses were obtained using a two dimensional finite element programme with eight node isoparametric elements with two degrees of freedom in each node. A detailed study of the influence of weld and plate geometry on both the stress concentration and stress intensity factor values was carried out.The results in bending showed stress intensity values 20 to 30% lower than in tension. The weld affected the stress intensity and stress concentration results only for small crack length values less than 0.1 to 0.12 of the thickness of the main plate. The results also indicated that neither the lack of penetration nor the plate length affected the stress intensity values significantly. Weld angle and plate thickness were the main parameters influencing the stress intensity values. The results in tension were compared with similar results published in the literature and good agreement was found.     

Geometric elasticity problem of stress concentration in a plate with a circular hole

We use the geometric elasticity equations [1], which permit relating the medium stress state to the geometry of the Riemannian space generated by the stresses, to consider the plane problem of stress concentration near a circular hole in a thin unbounded plate loaded by normal and tangential stresses. The Riemannian space metric coefficient corresponding to the coordinate normal to the plate plane is treated as the variable thickness of the plate in three-dimensional Euclidean space, which determines the optimal law for the plate material distribution. We consider plates in uniaxial tension, biaxial tension, and shear. For the plate with thickness variation laws thus obtained, we construct direct numerical solutions of the corresponding classical elasticity problems and determine the stress concentration factors.     

Stress concentration around a hole in a radially inhomogeneous plate

The stress concentration factor around a circular hole in an infinite plate subjected to uniform biaxial tension and pure shear is considered. The plate is made of a functionally graded material where both Young’s modulus and Poisson’s ratio vary in the radial direction. For plane stress conditions, the governing differential equation for the stress function is derived and solved. A general form for the stress concentration factor in case of biaxial tension is presented. Using a Frobenius series solution, the stress concentration factor is calculated for pure shear case. The stress concentration factor for uniaxial tension is then obtained by superposition of these two modes. The effect of nonhomogeneous stiffness and varying Poisson’s ratio upon the stress concentration factors are analyzed. A reasonable approximation in the practical range of Young’s modulus is obtained for the stress concentration factor in pure shear loading.     

AN ANALYSIS FOR DIFFRACTION OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN THICK PLATES WITH A CAVITY

By using the complex variable method and conformal mapping,the diffraction of flexu-ral waves and dynamic stress concentrations in thick plates with a cavity have been studied.A generalsolution of the stress problem of the thick plate satisfying the boundary conditions on the contour of anarbitrary cavity is obtained.By employing the orthogonal function expansion technique,the dynamicstress problem can be reduced to the solution of an infinite algebraic equation series.As an example,the numerical results for the dynamic stress concentration factor in thick plates with a circular,ellipticcavity are graphically presented.The numerical results are discussed.     

机匣模拟疲劳试验的相似条件研究

理论分析和试验结果表明，受内压的机匣与其相应的平板模型在开孔附近的等效应力分布非常相似；机匣模拟疲劳试验的应力相似条件下可表为，机匣与其模型在控制疲劳寿命的关键部位的等效应力水平和分布相同。