各向异性平面问题的复应力函数基本解

应用复变函数Ｃａｕｃｈｙ积分的方法，对于各向异性半平面边界为自由或固定两种情形，分别导出了其在任意集中力或集中力偶作用下的复应力函数基本解，其特例与前人结果一致。     

用振动法检测特殊桩基的质量

对于一些特殊桩基，可用振动法对其质量进行检测，如码头的桩基，可根据相干函数的数值来确定桩基质量的好坏，实测表明，用码头面与被测桩基的相干函数或用质量完好桩基与被测桩基的相干函数都能检测这类特殊桩基的质量。     

正交异性平面内的椭圆孔或裂纹系问题

应用Ｆａｂｅｒ级数展开和各向异性体平面问题复应力函数的方法，对于含有任意个椭圆或裂纹的正异性平面，给出了孔周应力场解或孔附近裂纹应力强度因子解，其特例与前人结果一致。     

滑动最小二乘插值函数在板弯曲问题上的应用

 利用滑动最小二乘插值函数作为加权残值法的试函数，分析了 该试函数的拟合特性，对试函数中的基函数以及权函数的选取提出了 建议；采用最小二乘配点法求出试函数中的系数，进而可得到定解问 题的近似解；利用该试函数对薄板的挠曲、中厚板的弯曲两个例子进 行了数值计算，并与理论结果或其它数值结果进行对比，结果表明， 该试函数适用于多种边值问题，且精度高. 该法简化了选择试函数的 过程，尤其适用于工程中的各种数值计算.     

正交异性平面内的椭圆孔或裂纹系问题

应用Ｆａｂｅｒ级数展开和各向异性体平面问题复应力函数的方法，对于含有任意个椭圆孔或裂纹的正交异性平面，给出了孔周应力场解或孔附近裂纹应力强度因子解，其特例与前人结果一致．     

以互信息为基础的广义相关系数及其应用

以往分析变量间相关性时，大多局限于仅反映线性相关程度的互相关函数或自相关函数上，但我们所研究的问题，却常常是非线性，因而对这种非线性结构上的广义相关程度进行度量显得更为重要。本文着重讨论了描述变量间这种广义相关程度的一种以互信息为基础的广义相关系数的概念、算法及操作中的技术问题，并实例其应用。     

参数激励的刚体混沌运动

讨论定点运动或圆轨道上运动的自由刚体，由于其内部或外部附件转动或振动引起转动惯量的周期变化，使系统受到周期的激励，而成为一受周期扰动的近Ｅｕｌｅｒ情形的运动刚体。通过计算动力学方程宿轨道的Ｍｅｌｎｉｋｏｖ函数，以及Ｐｏｉｎｃａｒｅ截面的数值计算，证明系统具有Ｓｍａｌｅ马蹄意义下的混沌。     

双材料应力分析中的镜像点方法

提出一种分析各类双材料中任一点受集中力作用问题的方法.通过将结合界面或其自由表面看作镜面,将应力函数或位移函数设定成固定于受载点及其镜像点上的局部坐标系下的形式,利用界面连续条件和Dirichlet的单值性原理,所有应力函数或位移函数就可由无限体中集中力的解或半无限体表面集中力的解的应力函数求得.这种方法不仅可适用于单一界面的情况,也可使用于多个界面并存的情况,并且也可适用于具有自由表面的结合材料.这一方法可应用于各类结合材料、涂层薄膜材料、板材等.     

集中载荷作用下各向异性平面内的椭圆孔或裂纹问题

应用复变函数Cauchy积分的方法,对含有椭圆孔或裂纹的各向异性平面,系统地导出了当其在面内受任意集中载荷作用时的复应力函数解或裂纹应力强度因子解析解,即基本解;并通过基本解的迭加,得到了在椭圆孔周或裂纹表面作用一般外载时的解,其特例证实了上述解的正确性。     

复合材料层合板挠曲变形的梁函数分析

本文利用克雷洛夫函数的组合，构造了一个适应于固支边界条件的梁函数。首先将它应用于均质各向同性、受任意载荷二端固主梁．由计算结果发现，该梁函数具有很高的收敛速度，仅取前两项，其结果和材料力学结论相比，其相对误差可控制在1％左右。而后将此梁函数用于求解四边固支复合材料短形板的挠曲变形。通过一系列的参数变化对最大挠度的影响分析，得到一些有益的结果，可供工程应用参考。     

Two-dimensional Eshelby’s problem for piezoelectric materials with a parabolic boundary

We use complex variable techniques to obtain analytic solutions of Eshelby’s problem consisting of an inclusion of arbitrary shape in an anisotropic piezoelectric plane with a parabolic boundary. The region of the physical plane below the parabola is mapped onto the lower half of the image plane. The problem is then more conveniently studied in the image plane rather than in the physical plane. The critical step in our approach lies in the construction of certain auxiliary functions in the image plane which allow for the technique of analytic continuation to be applied to an inclusion of arbitrary shape.     

An exact solutin for incompressible flow through a two-dimensional Laval nozzle

A careful examination of the variation of the velocity along the centerline and the contour of a Laval nozzle in the physical plane shows that either the upper or the lower half of the Laval nozzle assumes the same form of a slitted thick airfoil with tandem trailing edges. These two airfoils lie on different Riemann sheets in the hodograph plane. The interior of the airfoil is then mapped onto an infinite strip in the complex potential plane. Making use of these results, we obtained an exact solution for the incompressible potential flow through a two-dimensional Laval nozzle. The solution is applicable for nozzles with any given contraction ratio mexpansion rations, and throat wall radius R^*. As examples of the method, various nozzle contours, the velocity distribution of the flow, and the locations of the fluid particles at different time intervals are presented.     

一类半平面焊接的界面裂纹问题

利用复变方法和解析函数边值问题的基本理论，研究一类带孔洞的两个半平面焊接的界面裂纹问题。通过适当的函数分解和消元方法，将问题转化为一类简单的Riemann边值问题，从而得到弹性体应力函数的封闭解，给出了裂纹尖端应力强度因子的一般表达式。     

Elastic equilibrium of a half plane containing a finite array of elliptic inclusions

An accurate analytical method has been proposed to solve for stress in a half plane containing a finite array of elliptic inclusions, the last being a model of near-surface zone of the fibrous composite part. The method combines the Muskhelishvili’s method of complex potentials with the Fourier integral transform technique. By accurate satisfaction of all the boundary conditions, a primary boundary-value elastostatics problem for a piece-homogeneous domain has been reduced to an ordinary well-posed set of linear algebraic equations. A properly chosen form of potentials provides a remarkably simple form of equations and thus an efficient computational algorithm. The theory developed is rather general and can be applied to solve a variety of elastostatics problems. Up to several hundred interacting inclusions can be considered in this way in practical simulations which makes the model of composite half plane realistic and flexible enough to account for the microstructure statistics. The stress concentration factors and effective thermoelastic properties of random structure composites with dilute concentration of fibers are estimated in the vicinity of a free edge. The numerical examples are given showing accuracy and numerical efficiency of the developed method and disclosing the way and extent to which the nearby free or loaded boundary influences the local and mean stress concentration in the fibrous composite.     

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。     

On estimating the complex growth rates in ferromagnetic convection with magnetic-field-dependent viscosity in a rotating sparsely distributed porous medium

It is proved analytically that the complex growth rate of an arbitrary oscillatory motion of growing amplitude in ferromagnetic convection with magnetic-field-dependent viscosity in a rotating sparsely distributed porous medium for the case of free boundaries is located inside a semicircle in the right half of the plane whose centre is at the origin of the coordinate system and whose radius depends on the Rayleigh number, Prandtl number, Taylor number, and magnetic number. Bounds for the case of rigid boundaries are also derived.     

The effect of initial stresses on harmonic stress fields within the stratified half plane

The effect of initial stresses on dynamic (harmonic) stress fields within an elastic stratified half plane is investigated. It is assumed that the point-located harmonic force acting on the free plane of the layer by which the half plane is stratified causes this stress field. By employing displacement potentials and the exponential Fourier transform the governing system of partial differential equations of motion is solved. The necessary inverse transformations including rigorous mathematical complexity is performed numerically. The analysis of the numerical results, which shows the influence of the homogeneous initial stresses on the distribution of the stresses on the inter-medium plane, is made. These analyses are examined for various problem parameters and it is assumed that the material of both the layer and the half plane is homogeneous, isotropic, compressible and linearly elastic. It has been observed that the initial stresses may change significantly the values of the superimposed harmonic stresses.     

The problem of the simple smooth crack in an infinite anisotropic elastic medium

The problem of the simple smooth curvilinear crack in an infinite anisotropic elastic medium under conditions of generalized plane stress or plane strain and under the supposition that the plane of the problem is a plane of elastic symmetry of the anisotropic medium is reduced to a complex Cauchy-type singular integral equation along the crack together with a condition of single-valuedness of displacements around the crack by using the complex potentials technique. Application to the case of a straight crack is also given.     

压电介质平面问题的基本解

应用复变函数的方法,对于压电介质平面问题,分析导出了无限介质或半无限介质受任意 集中载荷作用时的复势函数基本解;这些结果可作为边界元法的基本解,以求解具有复杂边界压电体的平面问题。     

Exact solution of a flat smooth punch on a piezoelectric half plane

This paper derives an exact solution for a flat smooth punch applied on a piezoelectric half plane. The piezoelectric solid occupies the lower half plane, and a flat rigid punch is applied on it. As the permittivity of the air (environment) is far less than that of the piezoelectric material, the electric induction of air may be neglected. The permittivity of the punch is also far less than that of the piezoelectric material and consequently the normal component of the electric displacement vanishes at the contact boundary. The exact solution is obtained by eigen-function representation and analytic continuation. The distribution of pressure under the punch has been found. The electric field along the surface of the lower half plane is extracted in a closed form.