圆形域多圆孔多裂纹反平面问题研究

本文运用复变函数及积分方程方法，求解了圆形域多圆孔多裂纹反平面问题，建立了两种类型的基本解。复叠加原理和所得的基本解并沿国圆孔和裂纹表面取待定的基本解密度函数，可得到一组以基本解密度函数为未知函数的Ｆｒｅｄｈｏｌｍ积分方程。通过该积分方程组的数值可以得到密度函数的离散值，进而得到了裂纹尖端的应力强度因子。     

半平面多边缘裂纹反平面问题的奇异积分方程

利用复变函数和奇异积分方程方法,求解弹性范围内半平面多边缘裂纹的反平面问题．提出了满足半平面边界自由的由分布位错密度表示的单边缘裂纹的基本解,此基本解由主要部分和辅助部分组成．将半平面多边缘裂纹问题看作是许多单边缘裂纹问题的叠加,建立了一组Cauchy型奇异积分方程．然后,利用半开型积分法则求解该奇异积分方程,得到了裂纹端处的应力强度因子．最后,给出了几个数值算例．     

孔边裂纹对SH波的散射及其 动应力强度因子1)

采用Green函数法研究任意有限长度的孔边裂纹对SH波的散射和裂纹尖端场动应力强度因子的求解.取含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作为Green函数,采用裂纹``切割'方法并根据连接条件建立起问题的定解积分方程,得到动应力强度因子的封闭解答.最后给出了孔边裂纹动应力强度因子的算例和结果,并讨论了圆孔的存在对动应力强度因子的影响.     

孔边裂纹对SH波的散射及其动应力强度因子

采用Ｇｒｅｅｎ函数法研究任意有限长度的孔边裂纹对ＳＨ波的散射和裂纹尖端场动应力强度因子的求解．取含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作为Ｇｒｅｅｎ函数,采用裂纹“切割”方法并根据连接条件建立起问题的定解积分方程,得到动应力强度因子的封闭解答．最后给出了孔边裂纹动应力强度因子的算例和结果,并讨论了圆孔的存在对动应力强度因子的影响     

反平面弹性中边缘内分叉裂纹的奇异积分方程解法

利用复变函数和奇异积分方程方法,求解反平面弹性中半平面边缘内分叉裂纹问题。提出了满足半平面边界自由的由分布位错密度表示的半平面中单裂纹的基本解,此基本解由主要部分和辅助部分组成。将半平面边缘内分叉裂纹问题看作是许多单裂纹问题的叠加,建立了以分布位错密度为未知函数的Cauchy型奇异积分方程组。然后,利用半开型积分法则求解奇异积分方程,得到了裂纹端处的应力强度因子。文中给出两个数值算例的计算结果。     

磁电热弹耦合材料三维多裂纹超奇异积分法

用超奇异积分方程法将多场耦合载荷作用下磁电热弹耦合材料内含任意形状和位置三维多裂纹问题转化为求解一以广义位移间断为未知函数的超奇异积分方程组问题,退化得到内含任意形状平行三维多裂纹问题的超奇异积分方程组;推导出平行三维多裂纹问题的裂纹前沿广义奇异应力场解析表达式、定义了广义(应力、应变能)强度因子和广义能量释放率;应用有限部积分概念及体积力法,为超奇异积分方程组建立了数值求解方法,编制了FORTRAN程序,以平行双裂纹为例,通过典型算例,研究了广义(应力、应变能)强度因子随裂纹位置、裂纹形状及材料参数变化规律,得到裂纹断裂评定准则. 最后,分析了裂纹间干扰、屏蔽作用及其在工程实际中的应用.      

圆孔附近裂纹应力强度因子的一种简便求法

1.前言交替法的基本原理在文[6]中有详细阐述。从原理上讲,线弹性多连域问题都可用交替法求解,但在实际应用中,交替法的应用范围受到二个因素的限制:一是构成多连域的单连域是否可方便地求解,二是收敛速度。交替法在求裂纹问题中也得到应用,如文[5]用交替法求出了圆盘中的径向单裂纹应力强度因子的精确解。本文将利用一种交替法求圆孔附近的裂纹应力强度因子精确解。求解此问题必须首先知道含一裂纹的无限平面的基本解和含一圆孔的无限平面的基本解,这二个基本解都可利用文[1]求得,因此,用交替法求解圆孔附近的裂纹问题是方便的,其应用范围主要受收敛性的限制。     

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     

THE INTERACTION BETWEEN MULTIPLE CURVED RIGID LINE AND ANTIPLANE CIRCULAR INCLUSION

The interaction between multiple curved rigid line and ciruclar inclusion in antiplane loading condition is considered in this paper. By utilizing the point force elementary solutions and taking density function of traction difference along curved rigid lines, a group of weakly singular integral equations with logarithmic kernels can be obtained. After the numerical solution of the integral equations, the discrete values of density functions of traction difference are obtainable. So the stress singularity coefficient at rigid line tips can be calculated, and two numerical examples are given.     

含圆形嵌体弹性平面中径向裂纹问题的超奇异积分方程方法

根据含圆形嵌体平面问题在极坐标下的弹性力学基本解,使用Betti互换定理,在有限部积分意义下将问题归结为两个以裂纹岸位移间断为基本未知量、对于Ⅰ型和Ⅱ型问题相互独立的超奇异积分方程,对含圆形嵌体弹性平面中的径向裂纹问题进行了研究.根据有限部积分原理,建立了问题的数值算法.计算结果表明,嵌体半径、裂纹位置及材料剪切弹性模量等都对裂纹应力强度因子具有较为明显的影响.     

Fredholm integral equation for the multiple circular arc crack problem in plane elasticity

Summary An elementary solution for the multiple circular arc problem is obtained in this paper. The elementary solution is defined as a particular case of the single circular arc crack problem, in which remote stresses are equal to zero, and two pairs of concentrated forces are applied at a prescribed point of crack face. By using the principle of superposition, Fredholm integral equation for the multiple circular arc problem in plane elasticity is obtained. The suggested approach is illustrated by several numerical examples. If a smaller arc crack is surrounded by a larger arc crack, the stress intensity factors for the former become rather small. The phenomenon of shielding is illustrated by examples. Accepted for publication 17 September 1996     

On the solutions in the linear theory of micropolar viscoelasticity

In the present paper the linear theory of micropolar viscoelasticity is considered. The explicit expression of fundamental solution of the system of equations of steady vibrations is constructed by means of elementary functions and its basic properties are established. The Green's formulas in the considered theory are obtained. The formulas of integral representations of Somigliana-type of regular vector and regular (classical) solution are presented. The representation formulas of Galerkin-type solution of the system of nonhomogeneous equations and of the general solution of the system of homogeneous equations by means of eight metaharmonic functions are presented. The completeness of these solutions is proved.     

Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground

The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground was studied.First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soils were transformed into a group of governing differential equations with 1-order by the technique of Fourier ex- panding with respect to azimuth,and the state equation is established by Hankel integral transform method,furthermore the transfer matrixes within layered media are derived based on the solutions of the state equation.Secondly,by the transfer matrixes,the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions, drainage conditions on the surface of.ground as well as the contact conditions.Thirdly, the problem was led to a pair of dual integral equations describing the mixed boundary- value problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily.At the end of this paper,a numerical result concerning vertical and radical displacements both the surface of saturated ground and plate is evaluated.     

Well-posedness of two-phase local/nonlocal integral polar models for consistent axisymmetric bending of circular microplates

Previous studies have shown that Eringen's differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates. Based on the nonlocal integral models along the radial and circumferential directions, we propose nonlocal integral polar models in this work. The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates. The governing differential equations and boundary conditions (BCs) as well as constitutive constraints are deduced. It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected. Meanwhile, the purely strain-and stress-driven nonlocal integral polar models are ill-posed, because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints. Several nominal variables are introduced to simplify the mathematical expression, and the general differential quadrature method (GDQM) is applied to obtain the numerical solutions. The results from the current models (CMs) are compared with the data in the literature. It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models, respectively. The proposed two-phase local/nonlocal integral polar models (TPNIPMs) may provide an e-cient method to design and optimize the plate-like structures for microelectro-mechanical systems.     

Thermoelectroelastic Green's function and its application for bimaterial of piezoelectric materials

Summary For a two-dimensional piezoelectric plate, the thermoelectroelastic Green's functions for bimaterials subjected to a temperature discontinuity are presented by way of Stroh formalism. The study shows that the thermoelectroelastic Green's functions for bimaterials are composed of a particular solution and a corrective solution. All the solutions have their singularities, located at the point applied by the dislocation, as well as some image singularities, located at both the lower and the upper half-plane. Using the proposed thermoelectroelastic Green's functions, the problem of a crack of arbitrary orientation near a bimaterial interface between dissimilar thermopiezoelectric material is analysed, and a system of singular integral equations for the unknown temperature discontinuity, defined on the crack faces, is obtained. The stress and electric displacement (SED) intensity factors and strain energy density factor can be, then, evaluated by a numerical solution at the singular integral equations. As a consequence, the direction of crack growth can be estimated by way of strain energy density theory. Numerical results for the fracture angle are obtained to illustrate the application of the proposed formulation. Received 10 November 1997; accepted for publication 3 February 1998     

Axially symmetric thermal stress of an external circular crack under general thermal conditions

Summary The paper presents a solution for the linear thermoelastic problem of determining axisymmetric stress and displacement fields in an isotropic elastic solid of infinite extent weakened by an external circular crack under general mechanical loadings and general thermal conditions. The mechanical loadings and thermal conditions applied on the crack faces are axisymmetric, being non-symmetric about the crack plane. In similar lines of [7], equations of equilibrium of an elastic solid conducting heat have been solved using Hankel transforms and Abel operators of the first kind. Expressions for stress, displacement, temperature and heat flux functions are obtained in terms of Abel transforms of the first kind of the jumps of stress, displacement, temperature and heat flux at the crack plane. Two types of thermal conditions, that is, general surface temperatures and general heat flux on faces of the crack are considered. In both the cases, closed form solutions have been obtained for the unknown functions solving Abel type of integral equations. Explicit expressions for stresses, displacements, temperature fields, stress intensity factors have been obtained. Two special cases of thermal conditions in which: (i) crack faces are subjected to constant non-symmetric temperatures over a circular ring area, (ii) crack faces are subjected to constant non-symmetric heat flux over a circular ring area, have been considered. In some special cases, results have been compared with those from the literature.     

THE MESHLESS VIRTUAL BOUNDARY METHOD AND ITS APPLICATIONS TO 2D ELASTICITY PROBLEMS

A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network (IRBFN) constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations (BIE) can be established while the fundamental solutions to the problems are introduced. The singular value decomposition (SVD) method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.