A STUDY ON THE WEIGHT FUNCTION OF THE MOVING LEAST SQUARE APPROXIMATION IN THE LOCAL BOUNDARY INTEGRAL EQUATION METHOD

The meshless method is a new numerical technique presented in recent years .It uses the moving least square (MLS) approximation as a shape function . The smoothness of the MLS approximation is determined by that of the basic function and of the weight function, and is mainly determined by that of the weight function. Therefore, the weight function greatly affects the accuracy of results obtained. Different kinds of weight functions, such as the spline function, the Gauss function and so on, are proposed recently by many researchers. In the present work, the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method. The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed. Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and a in Gauss and exponential weight functions are in the range of reasonable values, respectively, and the higher the smoothness of the weight function, the better the features of the solutions.     

区间五次Hermite样条多小波Euler-Bernoulli梁单元

首先采用区间五次Hermite样条函数,分别构造了三节点梁的边界和内部节点的多小波尺度函数,然后,基于节点尺度函数在区间内伸缩、平移的思想,构建了梁单元相互嵌套、逐级包含的多尺度位移近似空间序列;最后,采用最小势能原理,得到弯曲梁的平衡方程,从而构造了区间五次Hermite样条多小波Euler-Bernoulli梁单元.算例结果表明,该小波单元可通过改变尺度来重新划分网格,从而可自由调节单个小波单元的计算精度,其计算精度与在相同网格划分下采用任意多个传统三节点Hermite梁单元计算梁构件的完全一致.与其它小波单元相比较,该小波单元具有计算简单明了,物理意义明确,易于理解的特点.     

Performance analysis and application of grid interpolation techniques for fluid flows

Although it is common for automated image processing techniques to claim subpixel accuracy in the identification of particles, or centroids of displacements of groups of particles, additional errors are inevitably introduced when and if these data are reinterpolated back onto a grid mesh whose nodes lie at different locations from the original data. Moreover, these errors can be large compared to the errors introduced in the original image processing step.Two different techniques, convolution with an adaptive Gaussian window (AGW), and a two-dimensional thin-shell spline (STS), have been compared and contrasted for interpolating irregularly spaced data onto a regular grid. Both techniques are global interpolators; the Gaussian kernel applies an ad hoc choice of smooth function, while the thin-shell spline minimises a global functional proportional to the Laplacian of the velocity field. In this way, the smoothness constraint on the spline coefficients may be thought of as akin to a viscous smoothing of the fluid flow.Performance curves are given, enabling the investigator to make an informed choice of interpolating routine and grid interpolation parameters to minimise the interpolation errors, given various external constraints. Some illustrative example applications on real experimental data are described. In general, the importance of matching the interpolation technique to the characteristics of the original data is stressed. It is also pointed out that a correct interpretation of grid interpolated data must be based on a basic knowledge of the performance characteristics of that interpolator. Finally, recommendations are made concerning the development of surface spline techniques for problems involving large numbers of data points.     

h-ADAPTIVE ANALYSIS BASED ON MESHLESS LOCAL PETROV-G ALERKIN METHOD WITH B SPLINE WAVELET FOR PLATES AND SHELLS

Using the two-scale decomposition technique, the h-adaptive meshless local Petrov- Galerkin method for solving Mindlin plate and shell problems is presented. The scaling functions of B spline wavelet are employed as the basis of the moving least square method to construct the meshless interpolation function. Multi-resolution analysis is used to decompose the field variables into high and low scales and the high scale component can commonly represent the gradient of the solution according to inherent characteristics of wavelets. The high scale component in the present method can directly detect high gradient regions of the field variables. The developed adaptive refinement scheme has been applied to simulate actual examples, and the effectiveness of the present adaptive refinement scheme has been verified.     

基于小波多分辨滤波特性的结构损伤识别

小波分析作为一个很好的损伤识别工具,可以看作是传统傅立叶变换的扩展,小波变换采取了可调整的时频窗口,因此小波变换的优势是它具有了“可变焦”性能对局部信号进行多尺度的刻画。小波基的伸缩和平移系列,使小波变换可看作是一组带通滤波器。本文全面分析了小波变换多尺度带通滤波器特性以及在结构在线损伤识别中的应用。结构损伤的出现体现在结构物理参数的改变,相对应的动力响应信号将会产生局部时变特性。利用小波分析的多尺度带通滤波器在不同尺度下对结构振动信号作滤波分析。通过观察不同带宽内振动信号的时频变化来判断结构损伤的存在。     

Characteristic time scales of velocity and pressure events

Numerical and wind tunnel simulations of full-scale wind loads on structures are usually performed at a lower Reynolds number and different turbulence parameters. One way to assess the validity of such simulations is through matching magnitudes, duration and/or spectral characteristics of simulated pressure peaks with full-scale data. Because wavelet analysis provides a time/frequency decomposition, it has been proposed as an analysis tool for the intermittent and transient pressure peaks. This work aims at answering the question as to whether different wavelets yield the same-scale decomposition of pressure peaks and velocity events and could, thus, be used as a tool for the analysis of extreme loads on structures. The results show that, by isolating the peaks or events with a modified Gaussian window prior to applying the wavelet transform, the dependence of the measured time scale on different wavelet functions is reduced. The time scales of the pressure peak and the velocity event are estimated to be about the same indicating that one contributing factor, at the peak scale, to the pressure peak lies in the variation of the incoming flow at the same scale.     

4th-order spline wavelets on a bounded interval

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A numerical method for the evaluation of Fourier integrals

This paper suggests the use of spline function interpolation in the evaluation of Fourier integrals. At the same time, the numerical results of some common functions by various interpolation methods and a simplified method of construction of spline function for various boundary conditions are also presented.     

Spatially Localized Models of Extended Systems

We investigate the construction of low-dimensional spatiallylocalized models of extended systems. Specifically, theKuramoto–Sivashinsky (KS) equation on large one-dimensional domainsdisplays spatiotemporally complex dynamics that are remarkablywell-localized in both real and Fourier space, as demonstrated by a(spline) wavelet representation. We show how wavelet projectionsmay be used to construct various localized, relativelylow-dimensional models of KS spatiotemporal chaos. There ispersuasive evidence that short, periodized systems, internally forcedat their largest scales, form minimal models for chaotic dynamics inarbitrarily large domains. Such models assist in the understandingof extended systems.     

The Wavelet-Based Technique in Dispersive Wave Propagation

The paper expounds a wavelet-based technique. The techniques is applied to the dispersive wave equation by describing wave propagation by a composition of fundamental (harmonic) wavelets. The linear Klein–Gordon equation is analyzed and associated approximate wavelet solutions are considered for fixed resolution levels. Discretized wavelet families are computed explicitly using a basis of time harmonic wavelets. Some applications at various low resolution levels show that the technique proposed provides new opportunities for wave propagation analysis     

Quantification of phase shift in the simulation of shallow water waves

Numerical simulation of nonlinear waves to reproduce the laboratory measurements has been a topic of great interest in the recent past. The results reported in the literature are mainly focused on qualitative comparison or on the relative errors between the numerical simulation and measurements in laboratory and hence lack in revealing the existence of phase shift in nonlinear wave simulation. In this paper, the simulation of nonlinear waves in mixed Eulerian and Lagrangian framework using finite element method (FEM) is investigated by applying two different velocity calculation methods viz, cubic spline and least squares (LS). The simulated wave surface elevation has been compared with the experimental measurements. The coherence analysis has been carried out using the wavelet transformation, which gives a better understanding between the numerical and the experimental results with respect to the time–frequency space, compared with the conventional Fourier transformation. It is observed that the application of cubic spline approach leads to a higher phase difference for steeper waves. The present study has shown that the phase difference exists at the higher modes rather than at the primary period. For waves with steepness (wave height/wave length) higher than 0.04, LS approach is found to be effective in capturing the higher‐order frequency components in the event of nonlinearity. In addition, the comparison of numerical simulations with that from PIV measurements for the tests with solitary waves is also reported. Copyright © 2009 John Wiley & Sons, Ltd.     

薄板小波有限元理论及其应用

利用样条小波尺度函数构造了常用的三角形和矩形薄板单元的位移函数,得到了利用小波函数表示的形函数。采用合理的局部坐标,对单元进行压缩,使单元在局部坐标区间上有其值,成功地推导出了分域的三角形和矩形薄板小波有限元列式。在此基础上,提出了弹性地基薄板的小波有限元求解方法。通过两个算例对薄板的挠度和弯矩进行了计算,数值结果表明,求解结果具有收敛快、精度高的特点。     

一种新的小波及其在结构损伤检测中的应用

结构受冲击将引起某些部位的震荡、裂纹甚至断裂,从而导致结构刚度下降.此时振动信号会出现奇异性或携带突变信息,而这些突变信息反映了结构的损伤情况.加之冲击信号测试环境一般较为复杂,环境噪声对测试存在一定的影响.然而,利用合理的小波变换技术去噪可以识别出损伤情况.本文通过对冲击振动的信号特性进行分析构造了一种新的基本小波,并论证了该小波的基本特征.最后运用小波分析的信号奇异检测理论结合实例将该小波用于冲击振动仿真分析中.计算结果表明,利用该小波进行结构损伤信号分析能清晰地识别结构损伤的时刻.采用该小波函数的构造方法,可避免通常采用Daubechies系列小波作为信号分析而要繁琐地选择不同小波函数的过程.     

Spectral analysis of localization in nonlocal and over-nonlocal materials with softening plasticity or damage

The paper shows that spectral wave propagation analysis reveals in a simple and clear manner the effectiveness of various regularization techniques for softening materials, i.e., materials for which the yield limits soften as a function of the total strain. Both plasticity and damage models are considered. It is verified analytically in a simple way that the nonlocal integral-type model with degrading yield limit depending on the total strain works correctly if and only one adopts an unconventional nonlocal formulation introduced in 1994 by Vermeer and Brinkgreve (and in 1996 by Planas, and by Strömberg and Ristinmaa), which is here called, for the sake of brevity, ‘over-nonlocal’ because it uses a linear combination of local and nonlocal variables in which a negative weight imposed on the local variable is compensated by assigning to the nonlocal variable weight greater than 1 (this is equivalent to a nonlocal variable with a smooth positive weight function of total weight greater than 1, normalized by superposing a negative delta-function spike at the center). The spectral approach readily confirms that the nonlocal integral-type generalization of softening plasticity with an additive format gives correct localization properties only if an over-nonlocal formulation is adopted. By contrast, the nonlocal integral-type generalization of softening plasticity with a multiplicative format provides realistic localization behavior, just like the nonlocal integral-type damage model, and thus does not necessitate an over-nonlocal formulation. The localization behavior of explicit and implicit gradient-type models is also analyzed. A simple analysis shows that plasticity and damage models with gradient-type localization limiter, whether explicit or implicit, have very different localization behaviors.     

Quasicontinuum Models of Dynamic Phase Transitions

We propose a series of quasicontinuum approximations for the simplest lattice model of a fully dynamic martensitic phase transition in one dimension. The approximations are dispersive and include various non-classical corrections to both kinetic and potential energies. We show that the well-posed quasicontinuum theory can be constructed in such a way that the associated closed-form kinetic relation is in an excellent agreement with the predictions of the discrete theory.     

Wavelet analysis on particle dynamics in a horizontal air–solid two-phase pipe flow at low air velocity

High-speed particle image velocimetry (PIV) is first used to measure two components of the fluctuating particle velocities for different particle sizes and solid mass flow rates at low air velocity in a horizontal pipe. Then, the continuous wavelet transform and orthogonal wavelet multi-resolution techniques are employed to analyze and decompose the fluctuating particle velocities to provide both quantitative and qualitative information on the particle fluctuation velocity of various frequencies. It is revealed that the fluctuating energy of axial particle velocity is mainly contributed from the wavelet components of low frequency, accounting for about 84%, near the bottom part of the pipe cross-section. However, the contribution to the fluctuating energy of vertical particle velocity accounts for about 82% from the wavelet components of high frequency. The auto-correlation analysis suggests a quasi-periodical large-scale axial particle fluctuating velocity. On the other hand, the spatial correlation analysis indicates that the low-frequency components of the axial particle velocity exhibit a large correlation near the bottom part of the pipe cross-section. From the probability density function (PDF) distribution, it is found that the low-frequency components of the axial particle velocity exhibit larger fluctuation, and this fluctuation reduces as the frequencies increase near the bottom part of the pipe cross-section. Near the top part of the pipe cross-section, however, a larger fluctuating axial particle velocity appears in the high-frequency range.     

一种准确度高的土工测试数据拟合新方法

针对目前岩土工程土工测试数据处理方法的不足,给出了一种能够减少端点导数误差的三次样条拟合方法.三次样条函数拟合是曲线拟合的一个公认的较好方法,它具有很好的分段光滑性.但当端点的导数值无法精确得到时,会给样条拟合的准确性带来较大的影响.为了尽量减少这种误差的出现,本文提出先用多项式函数对前、后各一小部分测量数据点进行拟合后,再对函数求导,得到所需端点导数带入三次样条函数,最终得到更加准确的拟合结果.采用文中建立的拟合方法,对地基沉降实测数据进行分析,拟合结果表明本文方法的工程适用性强、拟合准确度高.     

影响无网格方法求解精度的因素分析

基于移动最小二乘法的无网格方法的计算精度除受到节点的分布密度和基底函数的阶次影响外，还受到其它因素的影响，其中权函数的选取、权函数影响域的大小及位移边界条件的引入对计算精度影响较大。本文分析了几种常用权函数在数值计算时的特点，包括计算精度、收敛情况、计算效率等，同时分析了影响域大小及边界条件的引入对计算精度的影响。通过分析给出了确定权函数及其影响域大小的方法。当受约束的自由度较多时，通过配点法引入位移边界条件会引起计算结果的振荡，通过施加稳定项可以消除振荡现象，通过对带孔方板的受力分析证明了其可行性。应用以上结论对J23—10曲柄压力机机身进行了受力分析，应力集中部位的计算结果得到了较高的精度。     

地下工程爆破振动信号能量分布特征的小波包分析

根据爆破振动信号具有短时非平稳的特点 ,利用小波包分析技术对地下工程爆破振动信号的能量分布特征进行了研究。首先 ,简略介绍了小波变换与小波包分析的特点 ;其次 ,基于MATLAB(MaterialsLab oratory)对段药量和爆源距离等不同条件下记录的 8条爆破振动信号进行小波包分析 ,得到了爆破振动信号在不同频带上的能量分布图 ;最后 ,分析了爆破振动信号能量的分布特征。本分析手段为研究地下工程爆破地震效应特别是振动速度 频率相关安全准则提供了一种有效的分析技术。     

光纤陀螺信号处理方法的比较研究

给出了光纤陀螺信号漂移的数学模型，并针对信号噪声的特点，采用了“加权术平均”、“五点三次平滑算法”、“小波分析”三种不同的处理方法进行信号的消噪处理，通过对仿真结果的比较研究，肯定了小波变换算法在信号消噪处理中的适用性，并且编写了实时信号处理软件，提高了光纤陀螺的精度，为促进光纤陀螺的研制开发起到了积极的作用。