Alternative approaches to fabrication of gold-modified TiO2 nanotubes

Three approaches, impregnation–reduction, deposition and direct assembly, are used to fabricate gold-modified TiO₂ nanotubes. Prepared materials are characterized with powder X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), UV–visible absorption spectroscopy and BET, etc. The gold-modified TiO₂ nanotubes prepared via various procedures exhibit distinct difference in structure. By impregnation–reduction approach, gold-modified TiO₂ nanotubes with large gold particles are fabricated. The gold particles are either deposited on or encapsulated in TiO₂ nanotubes. However, by using gold hydrophilic colloidal dispersion as gold precursor, gold particles in the modified TiO₂ nanotubes are very small. Gold particles only adhere to the outer surface of TiO₂ nanotubes after deposition process, whereas adhere to not only the outer but also the inner walls of TiO₂ nanotubes after direct assembly process. A possible mechanism is proposed to illustrate the formation of gold-modified nanotubes that are prepared by direct assembly process.     

BEM calculation of the complex thermal impedance of microelectronic devices

This paper presents a numerical method for modelling the dynamic thermal behaviour of microelectronic structures in the frequency domain. A boundary element method (BEM) based on a Green's function solution is proposed for solving the 3D heat equation in phasor notation. The method is capable of calculating the AC temperature and heat flux distributions and complex thermal impedance for packages composed of an arbitrary number of bar-shaped components. Various types of boundary conditions, including thermal contact resistance and convective cooling, can be taken into account. A simple benchmark case is investigated and a good convergence towards the analytical solution is obtained. Simulation results for a thin plate under convective cooling are compared with a theoretical model and an excellent agreement is observed. In a second example a more complicated three-layer structure is investigated. The BEM is used to analyse the thermal behaviour if delamination of the package occurs, and a physical explanation for the results is given.     

Alternative to the effective transmittance approach for the calculation of polychromatic transmittances in rapid transmittance models

Many current rapid transmittance algorithms, specifically the Optical Path Transmittance (OPTRAN), are based on use of effective transmittances to account for the effects of polychromatic radiation on the transmittance calculations. We document how OPTRAN was modified by replacing the effective transmittance concept with a correction term. Use of the correction term solves some numerical problems that were associated with use of effective transmittances, greatly reduces the line-by-line computational burden, and allows for the efficient inclusion of more gases. This correction method can easily be applied to any other fast models that use the effective transmittance approach.     

The numerical calculation of turbulent boundary layer development

A mathematical model of the two-dimensional, incompressible turbulent boundary layer in arbitrary pressure gradient described and solved in earlier work¹ is solved by an implicit finite difference method. Comparisons of skin friction coefficient and momentum thickness values for the two methods for four test cases of different character indicate that the present method is a useful alternative to the method of characteristics which was used in previous work. One feature of the present method is that allowance is made for the logarithmic character of the velocity profile when constructing one of the finite difference expressions.     

埋置块式基础地基阻抗函数的简化计算方法研究

目前关于地基阻抗的分析和计算方法都比较繁琐,不易为工程设计人员所掌握.基于此,提出了埋置基础地基阻抗函数的简化计算方法.首先,采用锥体模型分析均质半空间内埋置圆盘一维振动波的传播过程,得到了平动和转动时的地基阻抗.在此基础上,利用埋置圆盘组来模拟埋置基础,分析得到了埋置基础地基阻抗函数.最后,通过算例表明此方法计算效率高,误差小,适用于工程计算.     

Efficient calculation of numerical values of a polyhedral function

Some applications require the repeated calculation of numerical values of a polyhedral function at points specified by their co-ordinates. The function is usually defined by some simple interpolation over each of the finite elements of a given mesh. A necessary step for the calculation of the value of the function at a given point is to determine to which element the point belongs. Such a determination can be efficiently accomplished by establishing a correspondence between the cells of some suitably defined regular mesh and the finite elements. Then, for each given point, the cell to which the point belongs is determined and the elements associated with that cell are inspected. This method is described and discussed in the text, and compared with two other less efficient methods with the help of numerical examples.     

Variational approaches for dynamics and time-finite-elements: numerical studies

This paper presents general variational formulations for dynamical problems, which are easily implemented numerically. The development presents the relationship between the very general weak formulation arising from linear and angular momentum balance considerations, and well known variational priciples. Two and three field mixed forms are developed from the general weak form. The variational principles governing large rotational motions are linearized and implemented in a time finite element framework, with appropriate expressions for the relevant tangent operators being derived. In order to demonstrate the validity of the various formulations, the special case of free rigid body motion is considered. The primal formulation is shown to have unstable numerical behavior, while the mixed formulation exhibits physically stable behavior. The formulations presented in this paper form the basis for continuing investigations into constrained dynamical systems and multi-rigid-body systems, which will be reported in subsequent papers.     

Mathematical model of drying of deformable materials and numerical calculation method

A further development of numerical methods for calculating the nonlinear interdependent processes of heat and mass transfer in capillary-porous materials with account for their stressed-strained state is given.     

制冷装置毛细管数值计算方法研究

对毛细管模型进行简化,避免计算制冷剂物性,提出由制冷剂流量确定毛细管长度和已知毛细管长度确定制冷剂流量的数值方法,并用这2种方法分析影响毛细管特性的主要因素。将模拟结果与试验结果进行比较,发现模拟值高于试验值,相对误差在10％以内。该简化计算方法可应用于工程计算。     

Empirical,analytical and numerical approaches to failure analysis of a frictional power transmission composite roller

The current study investigated the impact of different parameters on the failure of a frictional power transmission mechanism composed of a steel tyre and a two-layer composite rotating roller. Empirical, analytical and finite element methods were employed to study the mechanism. As for the empirical approach, a few rollers were made with different materials for the outer layer of the composite driver roller in order to examine the probable causes of the failure. In addition, thermography was conducted to find the increase in the temperature due to the working conditions. Analytical formulations were also employed so, as to understand the correlation between stress distribution and deformation regime in the contacting parts. Moreover, through relating the analytical to the empirical data, a homogenous representative cylinder was defined as equivalent to the composite cylinder. In order to reveal the details of stress and deformation distribution inside the roller parts, numerical analysis was performed employing finite element method. The results of such modeling helped us understand the relationship between the tuneable parameters and output results. Furthermore, by relating FEM results to the empirical data, probable causes of the failures were explained. According to the interpretation of the results and the data obtained via the introduced approaches, a few suggestions were presented as applicable in designing proper two-layer composite rollers.     

Study on numerical approaches for the evaluation of J-Integral Results in 3D problems

For numerical analyses of fracture mechanics problems often a combination of the finite element method with a post processor program for the evaluation of J-integral values is used. Instead of calculating a line integral as originally proposed by RICE it is reasonable to evaluate surface or volume integrals (for two or three dimensional calculations, respectively) in this case. In this paper 3D-formulations proposed by DE LORENZI and ATLURI are considered and several possibilities of the numerical realisation of these formulations are described. While the De Lorenzi proposal is contained as subroutines in the GRS-version of the standard finite element program ADINA, the Atluri formulation is used in separate post-processing programs developed by GRS. As a first application three-dimensional calculations of a compact-tension-shear specimen are considered.     

An effective numerical stress intensity factor calculation with no crack discretization

An effective numerical procedure for calculating stress intensity factors (SIF) in plane problems based on a modified boundary element technique not requiring any crack discretization was proposed by Snyder [1]. Instead of the usual fundamental solution, he used Green's function for the problem of a traction-free central crack in an anisotropic plate.In the first part of the present paper, the corresponding Green's function for the isotropic problem, not explicitly included in [1], is presented. In addition to the central crack, a semi-infinite edge crack is considered. Both Green's functions are given for the case of the anti-plane state of strain as well. In the first step of the proposed procedure, the tractions and displacements along the outer boundary are calculated. In the second step, the SIF for modes I, II and III are derived in terms of simple boundary integrals over quantities known from the previous step. Contrary to Snyder's derivation, the determination of the SIF is based on the asymptotic displacement field at the crack tip. The method can easily be extended to multiple crack problems by using the subregion technique. Some illustrative examples demonstrate the effectiveness of the method.

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Résumé Snyder a proposé une procédure numérique pour le calcul des facteurs et intensité de contraintes dans les problèmes plans, en se basant sur une modification de la technique des éléments aux limites ne requérant pas de discrétisation de la fissure. Au lieu d'une solution fondamentale habituelle, il a utilisé une fonction de Green pour traiter le problème d'une fissure centrale libre de contraintes dans un plaque anisotrope.Dans la première partie de la présente étude, on présente la fonction de Green qui correspond à un problème isotrope, qui n'était pas explicitement couvert par le travail de Snyder. Outre le cas de la fissure centrale, on considère le cas de la fissure de bord dans un milieu semi-infini. Les deux fonctions de Green relatives au cas d'un état de déformation antiplanaire sont également communiquées. Dans une première étape de la procédure proposée, on calcule les sollicitations et déplacements le long du contour extérieur; dans une deuxième étape, on établit les facteurs d'intensité de contraintes relatifs aux modes I, II et III en terms d'intégrals sur un contour simple défini par les valeurs résultant de l'étape précédente. Contraitement à l'approche de Snyder, on détermine le facteur d'intensité des contraintes sur base du champs de déplacement asymptotique à l'extrémité de la fissure. Par la technique des sous-régions, on peut aisément étendre la méthode à des problèmes de fissuration multiples. L'efficacité de la méthode est illustrée par divers exemples.

     

二维非均质材料应力场的数值化计算方法

等效夹杂方法是求解含杂质材料弹性应力场的一种有效方法,但是其解析求解只适用于椭球/椭圆类杂质问题。本文提出一种基于等效夹杂方法的数值化计算方法,介绍了其基本理论,并引入共轭梯度法求解该方法的一致性条件线性方程组。该方法通过计算区域的数值离散,能够实现对二维任意形状杂质弹性场的求解。将该方法得到的结果与解析解进行比较,验证了该方法的有效性。讨论了数值化等效夹杂方法在效率以及收敛性上的表现。通过对比证明,利用共轭梯度法实现该方法,能在保持精度的同时,相较于高斯消元法具有较大的效率优势。最后通过半椭圆杂质和氧化锆/氧化铝共挤复合材料算例验证了该方法处理任意形状杂质的能力。     

某型号固体火箭发动机喷管型面设计与数值计算

根据某型号固体火箭发动机总体设计要求及限制条件,给出了喷管型面设计方法。采用计算流体动力学(CFD)方法,用单方程（Spalart-Allmaras）湍流模型,分析计算了不同入口压力下喷管内流场特性和壁面压力、温度分布等。根据流场计算结果求出了发动机瞬时推力,并与地面推力试验结果进行了对比。     

Antenna model of the horizontal grounding electrode for transient impedance calculation: Analytical versus boundary element method

The paper deals with a simple and efficient procedure for the calculation of the transient impedance of the horizontal grounding electrode. This work represents an extension of a previous paper, published by the authors, on the antenna modeling of the grounding electrode with corresponding Pocklington integro-differential equation. The governing equation is solved in the frequency domain, both numerically and analytically, thus obtaining the solution for the current induced along the electrode. The numerical solution is undertaken via Galerkin–Bubnov scheme of the Indirect Boundary Element Method. Scattered voltage along the electrode is then calculated using Generalized Telegrapher?s equation. Time domain scattered voltage is evaluated via the Inverse Fast Fourier Transform. Subsequently, transient impedance is determined as a ratio of time domain voltage and current at the feeding point. Results obtained via different methods seem to agree satisfactorily.     

Formulation of a numerical process for acoustic impedance sensitivity analysis based on the indirect boundary element method

The objective of the work presented in this paper is the formulation, implementation and validation of an algorithm for computing the acoustic sensitivity with respect to the unequal impedance boundary conditions in an indirect boundary element method (IBEM). The IBEM integral equations are considered for all possible acoustic boundary conditions including velocity, pressure, unequal impedance, and simultaneous velocity and unequal impedance boundary conditions. The numerical system of equations is developed using a variational approach. The sensitivity formulation is based on analytically differentiating the system of equations formed by the variational approach with respect to the unequal acoustic impedance boundary conditions. Numerical sensitivity results obtained using the formulation developed in this paper are compared to analytical solutions in order to validate the new formulation.