截尾Gauss概率密度函数中待定参数的确定

给出一种计算描述标量湍流脉动的截尾Gauss概率密度函数的待定参数的方法. 通过将关于待定参数的代数方程组表示成适于求解的形式，综合应用牛顿法、牛顿下山法和阻尼牛顿法等迭代算法，并恰当地选取待定参数的迭代初值，获得了在标量平均值及其脉动均方值的各种取值条件下待定参数的相应数值.     

多自由度非线性动力学方程的能量校准算法

针对非线性动力学方程,通过Taylor展开和Duhamel积分,得到一个具有待定参数的逐步积分求解公式;通过数学变换,将原动力学方程转换为一个能确定待定参数的能量校准方程;最后将该参数回代入逐步积分公式,得到数值解.数值算例的结果说明了该方法的有效性,可以消除算法阻尼和抑制数值解发散,同时,在大步长的条件下也得到了非常准确而且稳定的结果,可以对系统长期性态进行仿真.     

覆水饱和双相介质圆弧场地P波激励下散射问题的理论解

采用波函数展开法对平面P波入射复杂水域地形的空间变异性地震动场进行研究,该水域地形具有覆水层、饱和双相介质、场地非平坦以及第二类分层(场地跨越分层界面)等属性.首先,依据地震波反射和透射特性推导直角坐标系下的自由波场分布;然后,根据场地属性并引入大圆弧法分析极坐标系下的含有待定系数的散射波场;进而,结合土-水分界面和饱和土层分界面边界条件,求解散射波场中的待定系数;最后,通过自由波场和散射波场得到覆水饱和双相介质圆弧场地波函数理论解.基于理论解,通过算例验证了理论推导的合理性及可靠性,分析了地表位移在不同入射条件下的差异性.结果 表明,相对于均匀介质,饱和双相介质会显著影响地表位移分布.此外,入射波频率和角度对地震地面运动特性也有较大的影响.     

结合面静摩擦因数分形模型的建立与仿真

提出一个确定分形维数和分形粗糙度参数(G')的分形函数,并用分形函数逼近结合面的表面粗糙度.根据分形理论和改进后的尺寸分布,推导了静摩擦因数f的解析解.数字仿真结果表明,f随量纲为一的总法向载荷(P')增加而增加.当D较小或较大时,f与(P')之间存在不同的微凸和微凹弧非线性关系,D=1.2时f与(P')的关系基本上是线性的;当D较小时,f随D增加而增加;当D较大时,f随D增加而减小;f随分形粗糙度参数(G')增加而减小,随相关系数K增加而增加,随材料特性(φ)增加而增加.     

岩体节理抗剪强度的巴顿方程评价(英文)

根据实验室的抗剪强度试验, 本文对巴顿方程进行新的讨论并提出新的评价方法。实验室完成了一组岩体结构面的抗剪强度 (τ, σ)试验后, 利用抗剪强度资料来模拟巴顿方程的三个参数 (φ, JRC, JCS)在理论上可以用偏导数求解, 但由于巴顿方程的特殊性, 实际上是不可能的。     

极坐标系下的Legendre谱元方法求解Poisson-型方程

r=0处的坐标奇异性是求解极坐标下Poisson-型方程的关键。本文提出一种极坐标系下基于Galerkin变分的Legendre谱元方法用于求解圆形区域内的Poisson-型方程,物理区域的径向和周向划分若干单元,计算单元均采用Legendre多项式展开;圆心所在单元的径向使用LGR(Legendre Gauss Radau)积分点,其他单元径向使用LGL(Legendre Gauss Lobatto)积分点,从而避免了极点处1/r坐标奇异性,周向单元均采用LGL积分点。利用区域分解技术,可以避免节点在极点附近聚集;最后求解了多个Dirichlet或Neumann边界条件下的Poisson-型方程算例。数值结果表明,谱元方法具有很高的精度。     

高边坡结构可靠度的二次处理有限元分析

本文依据强度折减理论,利用MIDAS/GTS有限元软件,分析计算了高边坡结构的安全系数K,找到边坡滑裂带的位置。在此基础上,对有限元输入数据和输出结果进行二次处理,建立基本随机变量c,f与滑裂带中单元的最大(和最小)主应力σ1(和σ3)的拟合关系f1(和f3),将其代入高边坡结构的功能函数Z中,使Z由隐式形式变为显式。基于该显式表示的Z,利用Monte Carlo法计算滑裂带中所有失效单元的可靠指标β1,并将其单元面积A1作为权重系数,经过加权平均得到边坡结构的整体可靠指标β。上述方法使得结合有限元软件计算边坡结构的整体可靠度得以简化。经实例分析可知,本文提出的方法是合理可行的,可使边坡结构整体可靠性分析得以简化,也可为高边坡结构整体可靠性分析提供理论参考。     

康托洛维奇-里茨杂交法及其应用

本文将Kantorovich法与Ritz法进行适当组合,吸收了二者的主要优点,提出了康托洛维奇法的一种改进方法.以二维问题为例,Kantorovich法在一个方向(例如y方向)的分布完全预先选定,这含有很大的主观任意性,因而限制了近似解的精度,改进法则在y方向仿Ritz法改进为一个含有若干个自由参数的分布函数,由于增加了近似解的自由度,故可改善解的精度.对Kantorovich法的另一改进是在计算高阶近似解时,通过逐项求解待定函数避免了求解更高阶微分方程或含更多方程的方程组,减少了计算量,降低了计算难度.用改进法求解了固体力学里的矩形截面柱体扭转问题和四边固支矩形板的弯曲问题,通过算例充分说明了此方法的特点和优越性.     

部分电极结构单极机的磁流体力学一维流动理论

本文提出了用待定电极壁边值并分区衔接的方法,完整地求解了环管中部分电极单极机的磁流体力学一维流动问题.做为两个特例,研究了环线电极和通常的全电极结构的单极机.对一些典型参数下的流场和感应磁场的分布进行了数值计算.与差分计算的结果比较,在数值和分布两方面都相当符合.着重研究了弥散效应及哈特曼边界层这些磁流体力学的特征现象,并用这些概念去讨论单极机的内部流动现象.结果表明,部分电极结构可以增加环管的流量,改善哈特曼边界层,控制二次流的发展.这些作用对具体的单极机应用有一定实用价值.     

夹层板的复变边界元解法

本文用全纯函数表示微分方程△f(x,y)-λ(~2)f(x,y)=0的一般解,粮据全纯函数的Bekya积分表示法,建立了复数域内的边界积分方程并针对各种边界条件下Reissner型夹层板、Hoff型夹层板进行了数值求解。     

Stochastic Shell Model for Turbulent Mixing of Multiple Scalars with Mean Gradients and Differential Diffusion

In this paper, we develop a shell model for the velocity and scalar concentrations that, by design, is consistent with the eddy damped quasi-normal Markovian (EDQNM) model for multiple mixing scalars. We review the realizable form of the EDQNM model derived by Ulitsky and Collins (J Fluid Mech 412:303–329, 2000), which forms the basis for the shell model. The equations governing the velocity and scalar within each shell are stochastic ordinary differential equations with drift and diffusion terms chosen so that the velocity variance, velocity–scalar cross correlations, and scalar–scalar cross correlations within each shell precisely match the EDQNM model predictions. Consequently, shell averages can be thought of as a representation of the discrete three-dimensional spectrum. An advantage the shell model has over the original EDQNM equations is that the sum of each realization over the shells is a model for the fine-grained, joint velocity/scalar probability density function (PDF). Indeed, this provides some of the motivation for the development of the model. We cannot exploit this feature in the present study of the mixing of two scalars with uniform mean gradients, as the PDF is a joint Gaussian throughout (and hence the correlation matrix completely defines the distribution). The model is capable of predicting Lagrangian correlation functions for the scalar, scalar dissipation and velocity. We find the predictions of the model are in good qualitative agreement with direct numerical simulations by Yeung (J Fluid Mech 427:241–274, 2001). Eventually we will apply the shell model to scalars that are initially highly non-Gaussian (e.g., double delta function) and observe the relaxation towards a Gaussian. As the shell model contains information on the spectral distribution of the scalar field, the relaxation rate will depend upon the length and time scales of the turbulence and the scalar fields, as well as the molecular diffusivities of the species. The full capabilities of the PDF predictions of the model will be the subject of a future publication.     

Effects of imaging system blur on measurements of flow scalars and scalar gradients

Planar imaging of flow scalars is widely used in fluid mechanics, but the effects of imaging system blur on the measured scalar and its gradients are often inadequately quantified. Here, we present a 1-D analytical study that uses simplified models of the scalar profiles and imaging system blur to estimate the measurement errors caused by finite resolution. One objective of this paper is to give the experimentalist a methodology for quantitatively assessing the impact of imaging system blur on the accuracy of scalar measurements. The scalar profiles are modeled as either error or Gaussian functions, and the imaging system resolution is cast in terms of the line-spread function (LSF), which is modeled as Gaussian. The analysis gives the errors induced in the scalar structure thickness, gradient, and dissipation, for varying degrees of blur, the latter of which is quantified by , the standard deviation of the Gaussian LSF. The results show that, to keep errors in the peak scalar gradients and dissipation to less than 10%, the 20%-width of the scalar structures should be at least 7.5. Typical flow imaging experiments require fast (i.e., low f/#) optics that may suffer from significant blur and, therefore, this requirement may be difficult to meet in many applications. It is also shown that the resolution requirements for measuring the dissipation are more restrictive than for structure thicknesses. Further simulations were made to assess the effects of having clustered, or closely spaced, dissipation structures. Compared to the single structure results, there is a less severe resolution requirement to obtain scalar structure length scales, but a more severe requirement on the scalar gradient and dissipation.     

界面上圆形衬砌结构对平面SH波散射

研究界面上的圆形衬砌结构对平面SH波散射与动应力集中问题.在一个含有半圆形衬砌缺口的弹性半空间水平面上,Green函数是受时间谐和的出平面线源载荷作用的位移基本解.采用沿界面“剖分”圆形衬砌结构的方法,并利用界面连续性条件建立起问题的定解积分方程组,进而得到圆形衬砌上的动应力集中解.最后给出了关于界面圆形衬砌结构上动应力集中系数的数值结果,并对界面圆形衬砌结构的动应力集中系数的影响进行了讨论.     

EXPERIMENTAL RESEARCH OF THE WHOLE TENSILE CURVE FOR BITUMINOUS MORTAR

细观尺度上, 沥青混合料是由沥青胶浆、粗骨料和孔隙等构成的多相复合材料, 而沥青胶浆的力学参数为沥青混合料进行细观尺度研究的重要部分, 对抗拉强度有着决定性的影响. 本文通过设计制作加载夹具针对不同温度和不同加载速率的条件, 对9 组试件进行拉伸试验, 得到沥青胶浆拉伸全曲线. 通过对沥青胶浆拉伸全曲线的研究和计算, 确定了沥青胶浆的最大破坏应力σ_max、刚度K_nn 和破坏位移U, 这些参数为采用粘聚带本构模型模拟沥青混合料的开裂行为提供了力学参数.     

Stiffness of planar tensegrity truss topologies

This paper proposes and demonstrates a symbolic procedure to compute the stiffness of truss structures built up from simple basic units. Geometrical design parameters enter in this computation. A set of equations linear in the degrees-of-freedom, but nonlinear in the design parameters, is solved symbolically in its entirety. The resulting expressions reveal the values of the design parameters which yield desirable properties for the stiffness or stiffness-to-mass ratio. By enumerating a set of topologies, including the number of basic units, and a set of material distribution models, stiffness properties are optimized over these sets. This procedure is applied to a planar tensegrity truss. The results make it possible to optimize the structure with respect to stiffness properties, not only by appropriately selecting (continuous) design parameters like geometric dimensions, but also by selecting an appropriate topology for the structure, e.g., the number of basic units, and a material distribution model, all of which are discrete design decisions.     

Looking for “laminars”: Measuring intermittency on the America’s Cup race course

The determination of intermittency from experimental results has been achieved in the past by a number of approximate methods, the most prolific of which involves the use of a detector function based on the square of first and second derivatives of the flow velocity with respect to time. The disadvantages of such methods are that they rely on appropriate time domain binning of the data, they are calibration dependent, they involve error propagating numerical differentiation and 50% intermittency is incorrectly diagnosed as an extremely high level of turbulence. Where experimental records are of limited time spans, calibration is difficult, measurement errors are significant and a 50% intermittency measurement is required for design purposes, the detector method loses its utility. However, recent experimental and theoretical work by Ferchichi and Tavoularis [1] has revealed a remarkably Gaussian probability distribution for the thermal passive scalar. The degree of self-similarity (analysed through the flatness of the signal) can then be used as a measure of intermittency. Flatness analysis has been used in this study on full scale data obtained experimentally on an International America’s Cup Class (IACC) yacht to overcome the problems of intermittency measurement. A generalised signal conditioning technique has been proposed.     

基于FPK方程的减摆器的非线性阻尼测试方法

受高斯白噪声外激的一阶非线性动力学方程能通过求解对应的FPK方程得到精确稳态解．本文基于这一结果导出减摆器非线性阻尼力与系统速度输出的概率结构的关系,将动力学系统中非线性阻尼力参数的测试问题转化测量系统的概率结构,并通过仿真进行了验证．     

Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

This work honors the 75th birthday of Professor Ionel Michael Navon by presenting original results highlighting the computational efficiency of the adjoint sensitivity analysis methodology for function‐valued operator responses by means of an illustrative paradigm dissolver model. The dissolver model analyzed in this work has been selected because of its applicability to material separations and its potential role in diversion activities associated with proliferation and international safeguards. This dissolver model comprises eight active compartments in which the 16 time‐dependent nonlinear differential equations modeling the physical and chemical processes comprise 619 scalar and time‐dependent model parameters, related to the model's equation of state and inflow conditions. The most important response for the dissolver model is the time‐dependent nitric acid in the compartment furthest away from the inlet, where measurements are available at 307 time instances over the transient's duration of 10.5 h. The sensitivities to all model parameters of the acid concentrations at each of these instances in time are computed efficiently by applying the adjoint sensitivity analysis methodology for operator‐valued responses. The uncertainties in the model parameters are propagated using the above‐mentioned sensitivities to compute the uncertainties in the computed responses. A predictive modeling formalism is subsequently used to combine the computational results with the experimental information measured in the compartment furthest from the inlet and then predict optimal values and uncertainties throughout the dissolver. This predictive modeling methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution for the a priori known mean values and uncertainties characterizing the model parameters and the computed and experimentally measured model responses. This approximate a priori distribution is subsequently combined using Bayes' theorem with the “likelihood” provided by the multi‐physics computational models. Finally, the posterior distribution is evaluated using the saddle‐point method to obtain analytical expressions for the optimally predicted values for the parameters and responses of both multi‐physics models, along with corresponding reduced uncertainties. This work shows that even though the experimental data pertains solely to the compartment furthest from the inlet (where the data were measured), the predictive modeling procedure used herein actually improves the predictions and reduces the predicted uncertainties for the entire dissolver, including the compartment furthest from the measurements, because this predictive modeling methodology combines and transmits information simultaneously over the entire phase‐space, comprising all time steps and spatial locations. Copyright © 2016 John Wiley & Sons, Ltd.