应力边界元法解平面热弹性问题

本文提出了求解平面热弹性问题的应力边界元法。利用应力法由平面热弹性问题的基本方程出发,简要地叙述了边界积分方程的建立,给出了位移单值条件。这种方法适用于应力边界值问题。作为数值计算例,计算了圆形区域和具有偏心圆孔的圆形区域的热应力,得到了满意的结果。应力边界元法也可应用于平板弯曲问题。     

边界配点法解中厚板弯曲问题

采用边界配点法解决具有剪切变形的矩形板的弯曲问题,既有效地利用解析法分析的成果,又发挥了离散计算方法的优点,本文给出在均布荷载作用下四边简支,四边固定,两对边简支另两对边固支等边界条件的算例表明:本法的精度高,计算工作量少,能用微型机解决问题,具有工程实用价值,对于其它支承条件、荷载情况,文内提出了求解的途径。     

Green函数法解接触力学问题

基于弹性力学中的Ｂｏｕｓｓｉｎｅｓｑ解当半无限体表面的一个环形面积上作用有均布载荷时分别推导了面上任意点的垂直位移计算表达式。     

球对对称凝固问题的边界元方法数值解

本针对一种自行开发的新型混合有机蓄冷工质,建立了描述凝固过程的数学模型,并应用边界元方法详细给出适用于凝固过程的解,最终得到了在不同Ｓｔｅ,不同球径下,球内凝固完成时的球内温度分布规律,为进一步优化蓄冷系统奠定了理论基础。     

球内对称凝固问题的边界元方法数值解

本文针对一种自行开发的新型混合有机蓄冷工质,建立了描述凝固过程的数学模型,并应用边界元方法详细给出适用于凝固过程的解,最终得到了在不同Ｓｔｅ、不同球径下,球内凝固完成时的球内温度分布规律,为进一步优化蓄冷系统奠定了理论基础     

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.     

利用空间拟合函数实现超象元边界检测

在对成象系统调制传递函数的分析基础上，研究了边界的定义及用空间拟合函数实现超象元边界检测的原理和技术方法，并给出了计算机模拟结果和实验结果。     

动载荷下应力强度因子的边界元计算

用Ｎａｒｄｉｎｉ－Ｂｒｅｂｂｉａ边界元法计算了动载荷下的应力强度因子，与解析解及有限元解相比较，效果较好。最后对计算结果进行了分析讨论。     

正交各向异性平面问题边界元一边境元素法研究

在文献中，本文作者研究了正交向向异性平面问题边界元素法的有关基本理论和计算公工,基上述工作的基础上，本文进一步研究各向异性颊问题边界邻域的应力分析，当采用边界元素法分析应力时，由于边界积分的奇异性，边界领域应力的计算结果往往存在一定误差，为解决此问题，本文提出一处基于修正余能原理的所谓边境元素，包括四节点边境元素，八节点边境元素和三节点边境元素等，在边界元素法求解的基础上，进一步利用本文述边境元素法，得到了非常满意的计算结果。     

正交各向异性平面问题边界元——边境元素法研究

在文献[1]中,本文作者研究了正交各向异性平面问题边界元素法的有关基本理论和计算公式,在上述工作的基础上,本文进一步研究各向异性平面问题边界邻域的应力分析。当采用边界元素法分析应力时,由于边界积分的奇异性,边界邻域应力的计算结果往往存在一定误差。为解决此问题,本文提出一个基于修正余能原理的所谓边境元素,包括四节点边境元素、八节点边境元素和三节点边境元素等。在边界元素法求解的基础上,进一步利用本文所述边境元素法,得到了非常满意的计算结果。      

A Straightforward Direct Traction Boundary Integral Method for Two-Dimensional Crack Problems Simulation of Linear Elastic Materials

This paper presents a direct traction boundary integral equation method (DTBIEM) for two-dimensional crack problems of materials. The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces. The displacements and tractions were used as unknowns on the external boundary, while the relative crack opening displacement (RCOD) was chosen as unknowns on either side of crack surfaces to keep the single-domain merit. Only one side of the crack surfaces was concerned and needed to be discretized, thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method (DBEM). A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly, and the SIFs were evaluated by the extrapolation of the RCOD. Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.     

Domain-Decomposition Singular Boundary Method for Stress Analysis in Multi-Layered Elastic Materials

This paper applies an improved singular boundary method (SBM) in conjunction with domain decomposition technique to stress analysis of layered elastic materials. For problems under consideration, the interface continuity conditions are approximated in the same manner as the boundary conditions. The multi-layered coating system is decomposed into multiple subdomains in terms of each layer, in which the solution is approximated separately by the SBM representation. The singular boundary method is a recent meshless boundary collocation method, in which the origin intensity factor plays a key role for its accuracy and efficiency. This study also introduces new strong-form regularization formulas to accurately evaluate the origin intensity factors for elasticity problem. Consequently, we dramatically improve the accuracy and convergence of SBM solution of the elastostatics problems. The proposed domain-decomposition SBM is tested on two benchmark problems. Based on numerical results, we discuss merits of the present SBM scheme over the other boundary discretization methods, such as the method of fundamental solution (MFS) and the boundary element method (BEM).     

应力有限元分析中边界应力计算的一种方法

本文利用边界元法中边界应力的计算方法对有限元应力分析中原边界应力计算方法加以改进,并给出几种不同格式的边界应力计算公式和算例。该方法使用较方便,计算结果的精度比原方法有一定提高。     

非局部弹性杆固有频率求解的传递函数法

基于Eringen提出的非局部弹性模型，采用幂指数型核函数，导出直杆的振动方程，该振动方程与应用Eringen非局部微分本构关系得到的杆的振动方程一致，并应用传递函数法，进行了直杆的动力学分析，计算了它的固有频率和相应振型，结果表明本文方法具有一般性和通用性，并且求解问题过程统一，精度高，能够处理多种边界条件。     

多角形域上第一类边界积分方程的高精度配置法

本文提出了一种多角区域上的第一类边界积分方程的高精度算法:离散之前采用特殊周期变换,消去边界积分方程未知函数在积分端点的奇异性,然后使用常元配置法求解,该方法在内点获得超收敛o(h3)。此外,通过Richardson整体外推,可进一步提高内点解的精度。实际计算结果表明,该方法优上同一问题的Galerkin方法甚至机械求积法。     

A Hybrid T Matrix/Boundary Element Method for Elastic Wave Scattering from a Defect Near a Non-planar Surface

The in-plane P-SV scattering of elastic waves by a defect and a close non-planar surface is considered. A hybrid T matrix/boundary element approach is used, where a boundary integral equation is used for the non-planar surface and the Green’s tensor in this integral equation is chosen as the one for the defect and thus incorporates the transition (T) matrix of the defect. The integral equation is discretized by the boundary element method in a standard way. Also models of ultrasonic probes in transmission and reception are included. In the numerical examples the defect is for simplicity chosen as a circular cavity. This cavity is located close to a non-planar surface, which is planar except for a smooth transition between two planar parts. It is illustrated that the scattering by the cavity and the non-planar surface becomes quite complicated, and that shielding and masking may appear.     

多角形域上第一类边界积分方程的高精度配置法

本文提出了一种多角区域上的第一类边界积分方程的高精度算法离散之前采用特殊周期变换,消去边界积分方程未知函数在积分端点的奇异性,然后使用常元配置法求解.该方法在内点获得超收敛O(h3).此外,通过Richardson整体外推,可进一步提高内点解的精度.实际计算结果表明,该方法优于同一问题的Galerkin方法甚至机械求积法.     

A Method for Determining X-ray Elastic Constants for the Measurement of Residual Stress

Abstract: The X-ray diffraction method is arguably the most convenient method of measuring residual stresses in terms of cost, spatial resolution, measurement time and the accuracy of measurement. The normal methods for calibrating X-ray diffractometers are not conveniently applied to automated scanning systems, however, and so a new approach is required. In this study, a scanning X-ray diffractometer was calibrated and the X-ray elastic constant for a steel alloy was determined using a customised four-point bending rig. The bending rig, in turn, was calibrated by dead loading. This study also described a simple alternative method for determining the X-ray elastic constant, without the use of specialised software. After calibration, the error band of the diffractometer was found to be less than ±10 MPa. As this is ±5% of the yield stress for a typical steel, this level of accuracy was deemed to be acceptable for the measurement of residual stress.     

Fabrication of a Stable New Polymorph Gold Nanowire with Sixfold Rotational Symmetry

Gold is known as the most noblest metal with only face‐centered cubic (fcc) structure in ambient conditions. Here, stable hexagonal non‐close‐packed (ncp) gold nanowires (NWs), having a diameter of about 50 nm and aspect ratios of well over 400, are reported. Au NWs are grown in the confined system of nanotubular TiO₂ arrays via photoelectrochemical reduction of HAuCl₄ precursors. Some of the resulting Au NWs are proved to have sixfold rotational symmetry, observed by transmission electron microscopy tilting experiments. This new polymorph is identified as a hexagonal ncp‐structure with lattice parameters of a = 2.884 Å and c = 7.150 Å, showing quite a large interplanar spacing (c/a ≈ 2.48). That is, Au atoms are close‐packed along the ab plane, but each plane is not closely stacked along the c axis like in graphite. The structure is usually expected to be unstable, but the present ncp‐2H gold is stable under ambient conditions and intense electron beam irradiation, and shows thermal stability up to 400 °C. Moreover, the resulting physical properties as a result of the corresponding change in electronic structures are investigated by comparing the optical properties of fcc and ncp‐2H Au NWs.