改进广义移动最小二乘近似的无网格法

无网格法是求解微分方程定解问题的一种新数值方法.移动最小二乘近似只要求近似函数在各节点处的误差的平方和最小,对近似函数导数的误差没有任何约束.而广义移动最小二乘近似要求近似函数及其导数在所有节点处的误差的平方和最小.为了降低计算工作量,本文构造了要求近似函数在全部节点处和任意阶导数在部分节点处误差的平方和最小的改进广义移动最小二乘近似.数值计算显示本文提供的方法关于函数值和各阶导数值都具有很高的精度.     

A NEW TWO-POINT ADAPTIVENONLINEAR APPROXIMATION METHOD FOR RELIABILITY ANALYSIS

I. INTRODUCTION Reliability analysis is becoming increasingly important in structural design. Over the years, manyresearchers have been involved in the evaluation of failure probability and many methods have beenpresented for structural reliability anal…     

有理逼近和Pad\'e逼近的高阶紧致型方法

对高阶紧致(high order compact)方法进行了详细的讨论和简洁的评述. 这就是: 回顾了方法的发展历史, 指出了方法优点, 分析了方法的基本特征、构造方式和应用现状, 预示了它的近期发展和研究形势. 特别地, 就方法的数学基础------有理逼近和Pad\'e逼近进行了归纳. 在文章中提供了丰富的方法信息和大量的有关公式.      

改进的移动最小二乘法

近年来发展的无网格方法大多采用移动员小二乘法来构造试函数，而应用移动最小二乘法形成的方程组有时会是病态的甚至奇异的，从而限制了它的发展和应用。本文采用带权正交函数作为基函数对移动最小二乘法做了改进，避免出现病态方程组，且在计算过程中不需要进行短阵求逆运算，提高了计算速度。之后，借鉴牛顿法、平衡法和摄动法对由移动最小二乘法得到的非线性代数方程组提出了新的求解方法。     

相关识别中的曲面拟合法

本文讨论了相关识别中的曲面拟合法。利用相关系数在真实匹配点附近的统计特性,通过对相关系数进行曲线（一维）或曲面（二维）拟合,根据其一阶导数确定最大相关系数所在的位置,快速得到亚像素匹配点。与逐步搜索法相比,该方法大大减少了运算次数,提高了数字图像相关运算的速度。     

Geometrical optics approximation of light scattering by large air bubbles

For large spherical bubbles in water,geometrical optics approximation is considered a better method for calculating light scattering patterns.In this paper,the basic theory of geometrical optics approximation is clarified.The change of phase for bubbles is calculated when total reflection occurs,which is different from particles with relative refractive indices larger than 1.Verification of the method was achieved by assuming a spherical particle and comparing present results to Mie scattering and Debye calculation.Agreement with the Mie theory was excellent in all directions when the dimensionless size parameter is larger than 50.Limitations of the geometrical optics approximation are also discussed.     

压电桁架作动器/传感器优化配置算法研究

针对自适应压电桁架结构振动控制,建立了作动器/传感器优化配置数学模型,并提出一种优化配置的新方法。为了减少结构分析次数,该方法将近似概念、对偶法和遗传算法相结合,首先采用多点近似技术建立原问题的序列近似问题,再对近似问题中的作动器/传感器位置离散变量和控制增益连续变量采用遗传算法和对偶方法分别寻优的分层优化策略。为了提高近似问题对原问题的逼近程度,本文提出一种适于离散变量结构优化的分段多点近似函数。算例表明本文方法能够以很少的结构分析次数得到最优解。     

复变量移动最小二乘法及其应用

提出了复变量移动最小二乘法，并详细讨论了基于正交基函数的复变量移动最小二乘 法. 然后，将复变量移动最小二乘法和弹性力学的边界无单元法结合，提出了弹性力学的复 变量边界无单元法，推导了相应的公式，并给出了数值算例. 基于正交基函数的复变量移动 最小二乘法的优点是不形成病态方程组、精度高，所形成的无网格方法计算量小. 复变量边 界无单元法是边界积分方程的无网格方法的直接列式法，容易引入边界条件，且具有更高的 精度.     

A unified asymptotic theory of the anelastic approximation in geophysical gases and liquids

An asymptotic theory of the anelastic approximation is developed for fluids having arbitrary equations of state under two assumptions: weak compressibility and small Brunt–Väisälä frequency. We show that both Boussinesq approximation (BA) and anelastic approximation (AA) may be included in a unique quasi-incompressible approximation (QIA) already constructed by Durran for polytropic gases. The only difference between AA and BA is that, in the BA, the equations are with slowly varying coefficients, while in the AA the coefficients are fast varying. Applications are made to atmospheric air and to sea-water.     

An approximation method to relate the linear viscoelastic functions

A method based on rational approximations is presented to interpolate the data from sinusoidal experiments in linear viscoelasticity. Bounds to the corresponding dynamical function and a discrete approximation to the spectrum are established. From this approximation the related viscoelastic functions can be computed. The method is checked by considering two theoretical models of physical interest and a satisfactory accuracy is achieved.     

Crucial properties of the moment closure model FENE-QE

We investigate four crucial properties for testing and evaluating a moment closure approximation of the FENE dumbbell model for dilute polymer solutions: non-negative configuration distribution function, energy dissipation, accuracy of approximation and computational expense. Through mathematical analysis, numerical experiments and comparisons with closure model FENE-P and FENE-YDL, we prove that the FENE-QE approximation has non-negative configuration distribution function, approximates the energy dissipation behavior of original kinetic theory and provides good accuracy. To improve the efficiency of this closure approximation, we introduce a piecewise linear approximation technique that greatly reduces the computational cost. This extension of FENE-QE, FENE-QE-PLA, is the closure model we recommend for simulating dilute polymer solutions.     

Difference schemes basing on coefficient approximation

Introduction AdiscreteprocedureofthevariablecoefficientODEisdividedintotwosteps:Firstthe coefficientisfrozenasaconstantoneverydiscretesubinterval,soaseriesofapproximate differentialequationsareobtainedonglobalsolutioninterval.Secondly,thesetofalgebraic eq…     

旋转运动柔性梁的假设模态方法研究

采用假设模态法对旋转运动柔性梁的动力特性进行研究，给出简化的控制模型. 首先采用Hamilton原理和假设模态离散化方法，在计入柔性梁由于横向变形而引起的轴向变形的二阶耦合量的条件下，推导出基于柔性梁变形位移场一阶完备的一次近似耦合模型，然后对该模型进行简化，忽略柔性梁纵向变形的影响，给出一次近似简化模型，最后将采用假设模态离散化方法的结果与采用有限元离散化方法的结果进行了对比研究. 研究中考虑了两种情况：非惯性系下的动力特性研究和系统大范围运动为未知的动力特性研究. 研究结果显示，当系统大范围运动为高速时，在假设模态离散化方法中应增加模态数目，较少的模态数目将导致较大误差. 一次近似简化模型能够较好地反映出系统的动力学行为，可用于主动控制设计的研究.     

Wave interaction with multiple articulated floating elastic plates

Flexural gravity wave scattering by multiple articulated floating elastic plates is investigated in the three cases for water of finite depth, infinite depth and shallow water approximation under the assumptions of two-dimensional linearized theory of water waves. The elastic plates are joined through connectors, which act as articulated joints. In the case when two semi-infinite plates are connected through a single articulation, using the symmetric characteristic of the plate geometry and the expansion formulae for wave-structure interaction problem, the velocity potentials are obtained in closed forms in the case of finite and infinite water depths. On the other hand, in the case of shallow water approximation, the continuity of energy and mass flux are used to obtain a system of equations for the determination of the full velocity potentials for wave scattering by multiple articulations. Further, using the results for single articulation and assuming that the articulated joints are wide apart, the wide-spacing approximation method is used to obtain the reflection coefficient for wave scattering due to multiple articulated floating elastic plates. The effects of the stiffness of the connectors, length of the elastic plates and water depth on the propagation of flexural gravity waves are investigated by analysing the reflection coefficient.     

旋转悬臂梁的刚柔耦合动力学建模与频率分析

对固结于转动刚体上外接柔性梁的刚柔耦合动力学建模和频率特性进行了研究,在精确描述柔性梁非线性变形的基础上,利用Hamilton变分原理和假设模态法,在计入柔性梁由于横向变形而引起的轴向变形二阶耦合量的条件下,推导出考虑"动力刚化"项的一次近似耦合模型。首先忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量,对简化模型做无量纲化处理,分析梁固有频率对模态截断数的依赖性;其次研究在一次近似简化模型和零次近似简化模型下,调谐角速度与共振现象的关系;最后分析一次近似耦合模型的动力特性。研究发现,为保证计算的精度,模态截断数应随无量纲角速度的增大而增加,合理的模态截断数具有收敛值;一次近似简化模型下悬臂梁横向弯曲振动不存在共振调谐角速度,一次耦合模型下柔性梁并没有出现屈曲失稳现象。现有典型文献的相关结论是值得商榷的。     

基于近似模型的非线性区间数优化方法及其应用

在不确定优化中,非线性区间数优化方法由于需要嵌套优化,造成计算效率低下而阻碍其应用于工程实际.本文提出了一种基于径向基函数近似模型的求解方法,以提高非线性区间数优化方法的计算效率.该方法利用拉丁超立方实验设计方法采样,建立目标函数和各约束的径向基函数近似模型.利用近似模型代替嵌套优化中的真实模型,再用非线性区间数优化方法进行求解,从而提高了非线性区间数优化方法的计算效率,使得该算法在工程应用方面成为可能.用一个测试函数验证了该方法的可行性,最后将方法应用于车身薄壁梁的耐撞性优化.     

结构参数大修改时的特征值重分析方法

就结构参数发生大修改的情况提出了两种高精度的特征值重分析方法：Ｐａｄｅ　逼近法和推广的Ｋｉｒｓｃｈ混合法．利用这两种方法,计算了一个具有２０２个结点,３５７个梁单元的平面框架的近似特征值．计算结果表明,所提出的方法是结构参数修改时的特征值重分析的有效方法．     

Taylor Approximation of Integral Manifolds

Integral manifolds generalize invariant manifolds to nonautonomous ordinary differential equations. In this paper, we develop a method to calculate their Taylor approximation with respect to the state space variables. This is of decisive importance, e.g., in nonautonomous bifurcation theory or for an application of the reduction principle in a time-dependent setting.     

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. A simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure for the Born cross-sections that employs the Elwert–Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. We also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.     

二级多点近似方法在整星结构优化设计中的应用

以整星结构为研究对象,针对含有离散变量的混合变量优化问题,应用二级多点近似方法给出从卫星拓扑布局设计到尺寸的一体化优化求解过程。首先,对整星结构进行仿真和振动试验,设计满足总体指标要求且已得到在轨验证。其次,建立以极小化卫星质量为目标的多工况优化模型后利用分段多点逼近函数建立了显式近似问题。最后,采用遗传算法和变尺度法分别对离散/连续两类变量寻优,并以拓扑构型一致性和目标函数的下降程度作为收敛的判定依据。结果显示,在满足频率和静力的约束下,卫星质量降低了7.9%,且结构分析迭代次数仅为50~60次,从而验证了该方法在求解整星结构多变量多工况下的一体化设计问题时具有很高的计算效率和准确性。