On integral equation approaches to the mechanics of fibre-crack interaction

The paper examines the problem of a penny-shaped crack which is formed by the development of a crack in both the fibre and the matrix of a composite consisting of an isolated elastic fibre located in an elastic matrix of infinite extent. The composite region is subjected to a uniform strain field in the direction of the fibre. The paper presents two integral-equation based approaches for the analysis of the problem. The first approach considers the formulation of the complete integral equations governing the associated elasticity problem for a two material region. The second approach considers the boundary integral equation formulation of the problem. Both methods entail the numerical solution of the governing integral equations. The solutions to these integral equations are used to evaluate the stress intensity factor at the boundary of the penny-shaped crack.     

A BOUNDARY INTEGRAL EQUATION AND ITS NUMERICAL SOLUTION OF POTENTIAL FLOW AROUND SURFACE-IRREGULA-RITIES

In this paper,using complex functional theory,the authors turn the potentialflow around the surface irregularities in a pressure conduit and semi-infinite platforms intoDirichlet problem.Based on Schwarz formula and by the application of Plemelj's formula,theauthors change the problem into the integration of a Cauchy boundary integral equation in theflow plane through the substitution of variables.Using numerical integration,the authors obtainthe velocity distribution and pressure coefficient along surface irregularities and platforms.Thephysical concept of this method is clear,the convergent speed is rapid and the computative effi-ciency is high.The calculated values agree well with the measured results.It is an effective andsimple method in solving potential flow.     

二维金属凹槽填充各向异性介质时散射的边界元方法:TE情形

由各向异性介质无界空间Green函数和Green恒等式出发，推导了TE波入射时二维任意截面金属凹槽填充各向异性介质时所满足的边界积分方程，并用边界元法和广义网络原理计算了金属凹槽填充各向异性介质时的散射。用文中方法退化计算了凹槽填充各向同性介质时的散射，计算结果与解析结果一致。并给出了凹槽填充各向异性介质时的散射算例。     

用改进的逐次逼近解法计算二维井间电磁场

提出了一种计算积分方程的新方法——改进的逐次逼近解法 (MSAM) ,并用该方法计算了轴对称二维井间电磁场。与传统的逐次逼近解法 (SAM)相比 ,该方法收敛性强 ,应用范围广 ,可适用于高电导率对比地层。由于不必进行直接的大型矩阵求逆运算 ,因此与积分方程的直接解法 (IE)相比 ,该方法计算速度更快 ,所需内存更少。采用矩阵求逆方法计算了成层介质中的二维 Green函数 ,并对含 Green函数的积分进行了简化 ,从而加快了计算速度。数值计算结果显示 ,在地层电导率对比度达到 2个数量级时 MSAM仍收敛 ,且计算结果与直接求解积分方程的结果一致 ,因此 MSAM是一种有效的计算轴对称二维井间电磁场的方法     

轴快流CO2激光器气体压力控制

激光切割对激光功率模式、功率密度和功率稳定性要求很高,采用轴快流CO2激光器时,控制工作气体压力工作在最佳状态并保持其恒定是激光器输出连续、稳定功率的必要条件和关键技术之一。在深入研究激光器工作原理和影响激光输出功率因素的基础上,采用带积分分离的智能PID控制算法对工作气体压力进行调节。该过程控制算法简单实用,可以有效地提高气体压力控制精度,改善功率控制精度和稳定性,并用实验加以验证。     

穿透裂纹和表面半椭圆裂纹模型的失效评定曲线比较

针对弹塑性材料裂纹管道的J积分计算建立了等效穿透裂纹和表面半椭圆裂纹2种有限元模型。在等效穿透裂纹模型中应用了1／4节点单元，在表面裂纹模型中采用了线弹簧单元。用这2种模型计算J积分，分别对3个实际含裂纹管段建立了失效评定曲线。比较了2种模型的失效评定曲线和R6通用曲线的差别，指出穿透裂纹模型偏于保守，建议在油气管道断裂的工程评定中采用半椭圆表面裂纹模型。     

Nonlinear coupled problems in dynamics of shells

The coupled system of three partial differential equations governing a flexible shallow shell dynamics is analysed. No any prior assumptions about the temperature distribution through the shell thickness are applied. The efficiency of the method used here when applied to the solution of integral-differential equations with different dimensions (three-dimensional equations related to the Kirchhoff-Love model) and of different type (heat transfer equations and the hyperbolic equations of shell theory) is demonstrated. Many computational results are reported and discussed.     

Computational Implementation of Asymmetric Integral Imaging by Use of Two Crossed Lenticular Sheets

We propose an asymmetric integral imaging method to adjust the resolution and depth of a three‐dimensional image. Our method is obtained by use of two lenticular sheets with different pitches fabricated under the same F/#. The asymmetric integral imaging is the generalized version of integral imaging, including both conventional integral imaging and one‐dimensional integral imaging. We present experimental results to test and verify the performance of our method computationally.     

T-stress in orthotropic functionally graded materials: Lekhnitskii and Stroh formalisms

A new interaction integral formulation is developed for evaluating the elastic T-stress for mixed-mode crack problems with arbitrarily oriented straight or curved cracks in orthotropic nonhomogeneous materials. The development includes both the Lekhnitskii and Stroh formalisms. The former is physical and relatively simple, and the latter is mathematically elegant. The gradation of orthotropic material properties is integrated into the element stiffness matrix using a “generalized isoparametric formulation” and (special) graded elements. The specific types of material gradation considered include exponential and hyperbolic-tangent functions, but micromechanics models can also be considered within the scope of the present formulation. This paper investigates several fracture problems to validate the proposed method and also provides numerical solutions, which can be used as benchmark results (e.g. investigation of fracture specimens). The accuracy of results is verified by comparison with analytical solutions.     

Material constant sensitivity boundary integral equation for anisotropic solids

In this paper, the material constant sensitivity boundary integral equation is presented, and its numerical solution proposed, based on boundary element techniques. The formulation deals with plane problems with general rectilinear anisotropy. Expressions for the computation of sensitivities for displacements, tractions, strains and stresses are derived, both for boundary and interior points. The sensitivities can be computed with respect to the bulk material properties or to the properties of part of the domain (inclusions, coatings, etc.). To assess the accuracy of the proposed approach, the computed results are compared to analytical ones derived from exact solutions obtained by complex potential theory, when possible, or finite difference derivatives otherwise. Copyright © 2005 John Wiley & Sons, Ltd.