High-order methods for differential equations with large first-derivative terms

A method is developed to solve elliptic singular perturbation problems. Examples are presented in one and two dimensions for both linear and non-linear problems. In particular, examples are presented for fluid flow problems with boundary layers. In the one-dimensional case an approximating equation is developed using just three points. The method first presented is a fourth-order approximation but is extended to become a higher-order method. Results are included for the fourth-, sixth-, eighth- and tenth-order methods. The results are first compared with results found by Segal in an article about elliptic singular perturbation problems. The elliptic singular perturbation problems are compared with a method by Il'in and also with central and backward difference schemes from Segal's article. There was only one case where the results in Segal's paper were as accurate as the results presented in this paper. However, in this case the method used by Segal did not give accurate values for a second problem presented. The results are also compared with results given by Spalding and by Christie. The method of this paper was also tested on the solution of some non-linear diffusion equations with concentration-dependent diffusion coefficients. The results were superior to results presented by Lee and by Schultz. Finally, the method is extended to several two-dimensional problems. The method developed in this paper is accurate, easy to use and can be generalized to other problems.     

基于能量守恒的空间旋转目标消旋力矩计算方法

针对空间旋转目标电磁消旋技术,提出一种计算空间旋转目标消旋力矩的新方法。首先,介绍了电磁消旋的常用计算方法;然后,介绍了能量守恒法的基本思想,从系统能量守恒的角度出发,从整体考虑电磁消旋过程中各物理场之间的相互作用,提出了一种基于能量守恒的消旋力矩计算方法,并通过球壳模型消旋力矩的计算过程对能量守恒法进行阐述。最后,进行了地面消旋实验,对比了实验结果和有限元法、电磁张量法和能量守恒法的计算结果。实验及仿真结果表明,本文提出的基于能量守恒的空间旋转目标消旋力矩计算方法有效。     

求解无斜腹杆桁架的一种新近似法

无斜腹杆桁架越来越多地应用于各类公共建筑,作为一种小型而具有高次超静定结构,它缺乏方法简单且结果合理的计算手段．利用结构力学原理和对称性导出了上述钢桁架内力的近似计算方法．通过精度分析和实例计算证明其结果合理,算法简单,便于应用．     

伺服台台面与恒温箱间的隔热方法

本文提出了伺服转台台面恒温箱与台面之间的隔热方法，通过理论计算和实验结果证实，隔热效果显著，能够达到理想的技术指标。     

Application of the quadrature method to flexural vibration analysis of a geometrically nonlinear beam

The quadrature method (OM) has been used in structural analysis only in recent years. In this study, OM is applied to flexural vibration analysis of a geometrically nonlinear beam. The numerical results by OM agree with the results by the finite element method. It is believed that this is the first attempt to solve a nonlinear dynamic problem by the quadrature method.     

双材料界面应力分析的局部杂交法

本文用云纹干涉法测取双材料高梁受集中载荷时沿ｘ，ｙ轴的位移场ｕ，ｖ．以其作为界面局部微区的边界条件，用有限元计算此微区内界面上的应力分量．与光弹性及全梁有限元法比较，发现局部杂交法的精度最高．     

一种基于Associated Hermite正交函数求解对流扩散方程的算法

提出了一种基于AH(Associated Hermite)正交基函数求解对流扩散方程的无条件稳定算法。该算法将方程的时间项通过Hermite多项式作为正交基函数进行展开,利用Galerkin方法消除时间变量项,从而导出有限维AH域隐式差分方程,突破了传统显式差分格式稳定性条件的限制,最后通过对AH域展开系数的求解得到该对流扩散方程的数值解。在数值算例中,将该算法与传统显示差分法和交替方向隐式差分法进行对比分析,数值计算结果表明,算法无条件稳定且其计算精度与时间步长无关,对于具有精细结构的对流换热问题,该算法具有明显的效率优势,且保持了较高的精度。     

一种易于并行求解Euler方程组的分区技术

在具有复杂边界的计算区域内，求解偏微分方程组时，经常需要分区和并行计算，分区方法直接关系到数值计算的并行化程度，本文在应用时间算子分裂方法求解Euler方程组的过程中，提出了一种非常容易实现并行化计算的分区技术。     

反扰力振动控制理论及其在井塔消振中的应用

应用反扰力振动控制方法，通过施加一个与原扰力在相位上相反的控制力，来抵消原扰力对结构的影响。此法用于实际的矿井井塔建筑结构消振工程，取得了消振９０％以上的显著效果，从而证实了此法的正确性和有效性。此法在动力荷载扰力作用下的建筑结构振动控制工程中，具有重要的应用价值     

粒子法中自由表面粒子识别

针对移动粒子半隐式法MPS（Moving Particle Semi-implicit Method）基于粒子数密度来判断自由表面会出现将内部粒子误判为自由表面粒子的问题,提出了一种结合几何法和体积法的自由表面粒子判定方法。通过对溃坝问题进行数值模拟,结果表明,全新的自由表面粒子判定方法对流体平稳运动以及剧烈运动两种工况,都能准确地判断出自由表面粒子,解决了基于粒子数密度判断方法因粒子分布稀疏产生误判的问题。[JP2]这种全新的自由表面粒子判定方法对今后采用MPS方法计算两相流问题时,两种介质在界面处的传热传质计算有重要意义。     

用BGK格式计算不可压缩流场

简要介绍BGK方法的基本思想,数值方法及其对不可压缩流场数值计算的推广。然后详细介绍将BGK方法应用于平面方框流的结果,将其结果与Ghia的结果进行了详细的比较。本方法还用来模拟后台阶流动,所得结果与相应的实验数据进行比较。以上比较表明本方法的有效性,同时也确定在计算不可压缩流体时参数的正确选择。     

敲击扫描式梁式结构损伤检测方法

受到啄木鸟敲击树干找虫子等敲击现象的启发,论文针对梁式结构提出了一种敲击扫描式损伤检测方法.基于对敲击扫描过程的理论探讨,我们得到了该方法的灵敏度表达式,从而为该方法找到了可靠的理论基础.数值模拟和简单实验表明,该方法不但简单易行,而且在有干扰的环境下也可以有效地检测出结构的损伤.     

X型热膜探头的标定

本文研究了Ｘ型热膜探头的两种主要标定方法，有效角法和多速度偏航法，对两种方法使用时可能引入的误差进行了讨论，并对给定的同一流场用不同方法进行了计算。     

斜交连续梁桥数值分析研究

在分析了矩阵位移法和传递矩阵法的理论基础上，将二者组合而成矩阵混合法。矩阵混合法的实质就是将结构物的一端未知向量通过矩阵的简单乘法传递到另一端，再将已知条件代入求解的过程。在矩阵传递的过程中引入位移法中的前进代入的概念，即将未知向量不断地以新的未知向量替换，可以防止误差的传递和积累。将矩阵混合法运用于斜交连续梁桥内力计算，完成了矩阵混合法在斜交连续梁桥内力计算中的理论推导和程序的设计，给出了实际算例并与有限元法进行了比较。     

Nonlinear and chaotic analysis of a financial complex system

In this paper,determination of the characteristics of futures market in China is presented by the method of the phase-randomized surrogate data.There is a significant difference in the obtained critical values when this method is used for random timeseries and for nonlinear chaotic timeseries.The singular value decomposition is used to reduce noise in the chaotic timeseries.The phase space of chaotic timeseries is decomposed into range space and null noise space.The original chaotic timeseries in range space is restructured.The method of strong disturbance based on the improved general constrained randomized method is further adopted to re-deternination.With the calculated results,an analysis on the trend of futures market of commodity is made in this paper.The results indicate that China＇s futures market of commodity is a complicated nonlinear system with obvious nonlinear chaotic characteristic.     

二维复合材料结构模态分析的边界元法

将边界元方法用于分析二维复合材料结构的自由振动模态，利用特解处理体积力（惯性力）仅需静态基本解就可求解问题，对一各向同性悬臂梁，用该法得到的结果与用有限元或各向性边界元法得到的结果符合得很好，但该法可解各向异性问题，对层状复合材料简支梁，用该法得到了数值结果与用一维层状复合材料梁的理论解的比较表明，当结构的长厚比大于２０时，二者符合得很好，当结构的长厚比小于２０时，一维层状材料梁的理论将产生很大的     

排水粉喷桩(2D工法)加固软土地基对桩周土体强度的影响

排水粉喷桩(简称2D工法)作为一种新的软土地基处理方法,在淮盐公路软基处理中得到试用,效果良好;但是目前对其桩间土强度的变化规律还不是很清楚,本文首次通过大量现场试验,采用静力触探、十字板剪切等试验手段,测得了排水粉喷桩施工后桩间土强度变化的规律。结果显示在排水粉喷桩施工后,桩间土强度先降低,之后随着龄期的增长而提高。     

黏性不可压缩流体流动前沿的数值模拟

提出了模拟注射成型中黏性、不可压缩流体流动前沿的新方法. 将Hele-Shaw流动应用于非 等温条件下的黏性、不可压缩流体，建立了流动分析模型，用充填因子的输运方程描述流动 前沿. 应用高阶Taylor展开式计算每一时间步长的充填因子，用Galerkin方法导出了计算 充填因子各阶导数的递推公式. 给出了时间增量的选取方法，证明了它的稳定性. 针对Han 设计的试验模具，用相同的材料及工艺条件模拟充填过程，比较了传统方法和该方法的模 拟结果与实验结果的差异. 算例分析表明，该方法可以有效地提高注射成型中流动前沿的 模拟精度和计算效率.     

A compact finite difference method for solving Burgers' equation

In this paper, a high‐order accurate compact finite difference method using the Hopf–Cole transformation is introduced for solving one‐dimensional Burgers' equation numerically. The stability and convergence analyses for the proposed method are given, and this method is shown to be unconditionally stable. To demonstrate efficiency, numerical results obtained by the proposed scheme are compared with the exact solutions and the results obtained by some other methods. The proposed method is second‐ and fourth‐order accurate in time and space, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

一种基于小波变换的信号突变征兆提取方法及其应用

获取故障征兆是诊断系统必须解决的首要问题。应用小波变换理论提出了一种信号突变征兆提取方法，并将它应用于转台故障诊断中。实验结果表明，这种方法在信号突变征兆提取上具有明显效果。