Direct method of solution for general boundary value problem of the Laplace equation

A general boundary value problem for two-dimensional Laplace equation in the domain enclosed by a piecewise smooth curve is considered. The Dirichlet and the Neumann data are prescribed on respective parts of the boundary, while there is the second part of the boundary on which no boundary data are given. There is the third part of the boundary on which the Robin condition is prescribed. This problem of finding unknown values along the whole boundary is ill posed. In this sense we call our problem an inverse boundary value problem. In order for a solution to be identified the inverse problem is reformulated in terms of a variational problem, which is then recast into primary and adjoint boundary value problems of the Laplace equation in its conventional form. A direct method for numerical solution of the inverse boundary value problem using the boundary element method is presented. This method proposes a non-iterative and unified treatment of conventional boundary value problem, the Cauchy problem, and under- or over-determined problems.     

弹性力学的样条边界元法

本文对弹性力学问题提出一个样条边界元法。文中用三次B样条函数来逼近边界未知量,并且利用域外奇点法建立了样条边界元法的计算格式。这种计算格式十分简单,容易在微机或小机上实现。利用域外奇点法建立起来的计算格式,完全可以避免奇异积分。计算结果表明,样条边界元法是一个经济有效的计算方法。     

The traction boundary contour method for linear elasticity

This paper presents a further development of the boundary contour method. The boundary contour method is extended to cover the traction boundary integral equation. A traction boundary contour method is proposed for linear elastostatics. The formulation of traction boundary contour method is regular for points except the ends of the boundary element and corners. The present approach only requires line integrals for three‐dimensional problems and function evaluations at the ends of boundary elements for two‐dimensional cases. The implementation of the traction boundary contour method with quadratic boundary elements is presented for two‐dimensional problems. Numerical results are given for some two‐dimensional examples, and these are compared with analytical solutions. This method is shown to give excellent results for illustrative examples. Copyright © 1999 John Wiley & Sons, Ltd.     

On boundary conditions for a certain class of problems in mixture theory

An additional boundary condition is proposed for solid-fluid mixtures for the situation in which a mixture boundary is in a saturated state. This condition on the boundary is derived from a thermodynamic characterization of the state and takes the form of a relationship between the total stress tensor, the stretch tensor and the volume fraction of the solid. This additional condition is sufficient to make several boundary value problems involving mixtures, determinate.     

三维一致粘弹性人工边界及等效粘弹性边界单元

基于粘弹性人工边界推导了三维一致粘弹性人工边界单元的刚度及阻尼矩阵,利用单元矩阵等效原理采用普通有限单元构造了等效粘弹性边界单元来模拟三维粘弹性边界。均匀半空间算例与成层半空间算例证明三维粘弹性边界单元具有与集中粘弹性人工边界相近的精度,并且施加更为简便。     

Self similar unsteady boundary layers

Summary This paper deals with unsteady laminar boundary layers contiguous to self-similar flows. The following general result is obtained: when the self-similar structure of the external flow is apparent in the boundary layer system of coordinates, and when there is no heat transfer through the wall, then the boundary layer is self-similar too. This property can be applied to a lot of known self-similar motions. Some examples are considered for which the final form of the boundary layer equations is formulated.     

Numerical stability in regular BEM schemes for elastostatic problems

The regular boundary element method is employed for the static analysis of boundary value problems of elasticity. This method allows one to reduce a given boundary value problem to a system of regular integral equations of the first kind with respect to source functions not located on the boundary. This paper is concerned with the numerical stability analysis of regular boundary element methods. In particular, the existence and stability of approximate solutions for integral equations of the first kind with continuous kernels are discussed. The special regularization technique for treating such a class of integral equations is developed. Numerical examples illustrate proposed algorithms and demonstrate their advantages.     

Grain boundary energy anisotropy: a review

This paper reviews findings on the anisotropy of the grain boundary energies. After introducing the basic concepts, there is a discussion of fundamental models used to understand and predict grain boundary energy anisotropy. Experimental methods for measuring the grain boundary energy anisotropy, all of which involve application of the Herring equation, are then briefly described. The next section reviews and compares the results of measurements and model calculations with the goal of identifying generally applicable characteristics. This is followed by a brief discussion of the role of grain boundary energies in nucleating discontinuous transitions in grain boundary structure and chemistry, known as complexion transitions. The review ends with some questions to be addressed by future research and a summary of what is known about grain boundary energy anisotropy.     

On the effects of thermomechanical processing on failure mode in precipitation-hardened aluminium alloys

This paper concentrates on the influences of thermomechanical processing on fracture behaviour of Al-Mg-Si-Cu (AA6061) alloys. Important factors are grain boundary structure and extent of matrix- and grain boundary precipitation. Large grain boundary phases in the as-air-cooled alloy, explains its much smaller fracture strain with respect to the water-quenched alloy. With increasing artificial ageing time, the bulk fracture strain of the air-cooled alloy exhibits a minimum. This is due to grain boundary precipitate growth and coarsening affecting the fraction of strain confined to the grain boundary region. For the recrystallized microstructure aged to peak strength, the fraction of intergranular fracture is much larger for the air-cooled alloy. This can be understood on the basis of a much wider precipitate free zone and a smaller grain boundary precipitate volume fraction for the air-cooled alloy, increasing the fraction of strain confined to the grain boundary region by about one order of magnitude with respect to the water-quenched alloy. A much coarser distribution of intermetallic phases in the extruded microstructure is responsible for a larger degree of slip localization. This enhances the tendency for shear- and intergranular fracture, reducing the ductility and thus the fracture strain with respect to that of the recrystallized microstructure.     

Distribution of misorientations and grain boundary planes in grain boundary engineered brass

Abstract

The present paper reports the application of a five parameter determination of grain boundary types to grain boundary engineered α brass. Approximately 20 000 grains constituted the total sample population, giving rise to more than 77 000 grain boundary line segments. This is the first time that the orientation of a large sample population of grain boundary planes has been measured in a grain boundary engineered material. The most important findings of the investigation were that the distribution of planes showed a prevalence of 〈 110 〉 tilt boundaries, especially asymmetric tilt types, and the presence of 〈 111 〉 twist boundaries. This distribution is a consequence of the low energy of these boundary types. Furthermore, more than three-quarters of boundaries could be considered to be 'potentially special'. The presence of these boundaries greatly fragmented the grain boundary network. This fragmentation is probably a key factor in the development of superior properties in a grain boundary engineered material.     

闪光X光噪声图象的局部统计滤波

本文介绍一种噪声图象的滤波方法 ,它不需要先验的图象模型 ,而且也不会损伤边界和细小的细节 ,在相加性和相乘性噪声的情况下 ,计算与边界方向有关的子集的局部平均值和方差 ,相应地沿着边界方向的噪声就被去掉 ,同时对边界有一定的增强效果     

Grain boundary grooving in molybdenum bicrystals

The morphologies of grain boundary grooves formed after annealing of three Mo bicrystals at the temperature close to the melting point were studied with the aid of scanning force microscopy. The ratio of grain boundary to surface energy was calculated from the surface slopes measured at the root of the groove. This ratio was about 0.3 for the grain boundary grooves with the sharp roots, and it was significantly lower than 0.3 for the grooves with the blunted roots. It was shown that the blunting of the root of the grain boundary grooves is associated with the grain boundary migration during annealing. A model of grain boundary grooving accompanied by the instantaneous boundary shift was formulated. The surface topographies predicted by the model were in a good agreement with the experimentally measured ones. It was shown that grain boundary grooving process can be completely suppressed at the singular surfaces. This, together with the grain boundary migration during annealing results in characteristic groove morphology with the blunted root and leads to a significant underestimation of the grain boundary energy calculated from surface slopes.     

带积分边界条件的Poisson方程边值问题的近似解

对带积分形式边界条件的Ｐｏｉｓｓｏｎ方程边值问题，当它的边界充分小时，其边值问题的解可用不带积分形式边界条件的边值问题的解来近似。本文将用泛函分析方法证明这个结论     

Grain boundary reorientation in copper

The present route to grain boundary engineering (GBE) is usually based on multiple annealing twinning which can only be applied to a certain subset of materials, namely those that twin prolifically. A more general approach has been highlighted recently, following experimental evidence that certain boundary planes in iron bicrystals are ‘special’, and that this classification is not based on misorientation. It was suggested that, under suitable conditions, individual interfaces could reorient the most energetically advantageous orientations. This approach concurs with a similar concept of ‘grain boundary plane engineering’, proposed previously. In the present article we explore this concept and report the effect of long duration, low temperature annealing on the distribution of boundary misorientation and planes in copper. The new findings give support to the possibility of grain boundary structure optimisation via controlled annealing. To have established that grain boundary plane reorientation is feasible opens up new avenues and challenges in the field of grain boundary research. This could have significant impact both scientifically in terms of understanding grain boundary structure and technologically in the field of GBE.     

Dynamic element discretization method for solving 2D traction boundary integral equations

A sufficient condition for the existence of element singular integral of the traction boundary integral equation for elastic problems requires that the tangential derivatives of the boundary displacements are Hölder continuous at collocation points. This condition is violated if a collocation point is at the junction between two standard conforming boundary elements even if the field variables themselves are Hölder continuous there. Various methods are proposed to overcome this difficulty. Some of them are rather complicated and others are too different from the conventional boundary element method. A dynamic element discretization method to overcome this difficulty is proposed in this work. This method is novel and very simple: the form of the standard traction boundary integral equation remains the same; the standard conforming isoparametric elements are still used and all collocation points are located in the interior of elements where the continuity requirements are satisfied. For boundary elements with boundary points where the field variables themselves are singular, such as crack tips, corners and other boundary points where the stress tensors are not unique, a general procedure to construct special elements has been developed in this paper. Highly accurate numerical results for various typical examples have been obtained.     

无限域波动问题的有限元模型

本文基于半解析波动方程,推导了无限域粘弹性人工边界单元。在有限元波动模型中,统一了节点计算稳定性问题;提出了合理的人工边界反射系数公式,为有限元模型提供了理论基础。SH波数值分析表明本文有限元模型具有多向波动透射能力。     

A Σ3 grain boundary in an epitaxial chalcopyrite film

We have grown epitaxial grain boundaries of CuGaSe₂ by metal organic vapour phase epitaxy onto a GaAs substrate containing a Σ3 grain boundary. SEM micrographs show a dense grain boundary. TEM micrographs prove that the grain boundary in the film is the direct continuation of the grain boundary in the substrate. HRTEM shows that the grain boundary in the film is a twin as well and thus a Σ3 boundary. Thus, by using a Σ3 grain boundary in the cubic GaAs substrate as a template a Σ3 grain boundary is obtained in the tetragonal CuGaSe₂ film. Kelvin Probe Force Microscopy gives no indication of a space charge around this grain boundary, while in Hall measurements a small barrier of a few 10 meV is evident. This is an experimental indication for the existence of neutral grain boundaries as predicted theoretically.     

无界区域上Stokes问题的自然边界元与Mini元耦合法

奉文讨论用自然边界元与mini元耦合法求解描述平面尢界区域上不可压缩粘滞低速流动的定常Stokes问题.首先以圆为人工边界,利用自然边界归化将原问题转化为耦合变分问题,并证明该变分问题的存在唯一性,然后在人工边界上采用分段线性边界元,在有界区域上应用mini元分别进行离散化,合成总刚度矩阵,从而建立耦合法的线性方程组,最后,证明其收敛性和误差估计,并通过数值实验以表现该方法的实际有效性及其理论分析的正确性.     

The activation areas for grain boundary sliding

The activation areas for grain boundary sliding in Al, Pb, Sn, Zn, and Cu are compared with those for creep in the same materials. It is found that the activation area-stress relation for grain boundary sliding is similar to that for creep. This observation is consistent with a dislocation or ledge mechanism of grain boundary sliding.