壁湍流相干结构尺度及边界层内的SL标度律

利用高分辨率、高帧率PIV系统对湍流边界层中相干结构的多种空间尺度和边界层内SL 标度律在不同尺度下的具体表达形式进行了实验研究. 实验在两个动量损失厚度雷诺数 (Re_{\theta}=628.5和Re_{\theta}=1032.9)下测量平板湍流边界层中缓冲 层、对数区和外区的二维瞬时速度场. 应用 小波分析以及传统的统计学方法，在垂直于平板和平行于平板的平面内考察平板湍流边界层 中存在的相干结构的流向和展向尺度，并与已知的相干结构尺度实验结果进行了对比分析. 利用在动量损失厚度雷诺数628.5下测得的数据，对多种脉动结构(脉动速度结构等) 的空间关系及其标度律进行了研究. 第2项工作直接利用湍流边界层空间速度分布，对多种 流场尺度结构内部的She-Leveque(简称SL)标度律及自相似律进行了验证. 结果表明，各 单一流场尺度结构内部，流向脉动速度{\pmb u}'、法向脉动速度{\pmb v}'及 脉动涡分量\d {\pmb v}'/\d {\pmb x}的统计结构量均存在明显的标度律，标度 指数的形式与自相似律和SL标度律均非常吻合，只是常数随流场尺度的不同而不同， 且呈现一定的规律性. 但对于结构量的五阶矩随距离l的研究表明，自相似律和SL 标度律成立的范围并不完全一致，同时标度律成立的范围大小与流场尺度有明显关系.     

结构破坏的尺度律

文中综述了结构破坏的尺度律和尺寸效应的研究进展,尤其将重点放在准脆性材料的分析上,因为它们的尺寸效应是重要和复杂的．在回顾了尺寸效应研究的悠远发展史以后。着重讨论了三种主要类型的尺寸效应,即由于强度随机性引起的统计尺寸效应、能量释放的尺寸效应和由于微裂纹或断裂的分形特性可能引起的尺寸效应．得出了这些理论应用的明确结论．之后讨论了如何运用已知的尺寸效应律来测量材料的断裂特性,并采用内聚裂纹模型（cohesivecrackmodel）、非局域化有限元模型和离散元模型等对尺寸效应进行模化．文中还进而分析了尺寸效应在压缩失效和车相关材料行为下的有关问题,并讨论了在断裂扩展区描述含微裂纹材料所需的损伤本构关系．最后也讨论了尺寸效应对准脆性材料的多种应用,这些材料包括,如混凝土、海冰、纤维复合材料、岩石和陶瓷等．本文包含了参考文献377篇     

弹丸撞击圆板的尺度律实验研究

本文对周边固支软钢圆板，用柱形平头弹丸以２４ｍ／ｓ和２８ｍ／ｓ的速度进行撞击实验，研究板变形的尺度律。板和弹的尺寸严格按１、２和４的比例制作，撞击能量只使板产生塑性大变形而不穿孔。实验结果表明，变形偏离经典尺度律，其规律是较大的撞击能量，出现的偏差也较大。经分析，材料的应变律效应是产生偏差的主要原因。     

固体跨尺度压痕标度律的研究与展望

压痕标度律是对通过压痕试验方法测定固体材料力学性能参量问题所给出的一般性结论, 具有重要的理论意义, 是探寻材料力学性能潜在规律的方法论研究. 本综述论文系统而简要地介绍如下主要内容: 采用传统理论对传统固体材料压痕标度律的研究回顾; 采用跨尺度力学理论对先进固体材料的跨尺度压痕标度律的研究回顾. 总结并得到了如下主要结论: 传统固体材料压痕标度律可由一空间曲面完整描绘, 若进一步已知某类无量纲独立参量的取值范围, 则该空间曲面可退化为系列平面曲线族; 先进固体材料(新材料)的跨尺度压痕标度律可由一个三维函数关系完整描绘, 若存在某类独立无量纲参量取值范围已知, 则该三维函数关系将退化为系列空间曲面族. 压痕标度律的未来研究发展仍将重点集中在建立新材料的跨尺度压痕标度律上, 以试图从根本上解决新材料力学性能标准规范难以建立的理论问题. 除此之外也将重点关注建立各类功能新材料的多尺度及跨尺度压痕标度律规律.      

裂缝介质渗流多尺度混合有限元数值模拟研究

针对裂缝介质具有多尺度特点,建立了Darcy/Stokes-Brinkman多尺度耦合模型,采用多尺度混合有限元方法,对裂缝介质渗流问题进行了研究.阐述了多尺度混合有限元方法的基本原理,并推导得到Darcy/Stokes-Brinkman方程的多尺度混合有限元计算格式.数值计算结果表明,大尺度Darcy模型能够捕捉到小尺度上裂缝网络渗流特征;与网格粗化、传统有限元方法相比,多尺度混合有限元方法的基函数具有能反映单元内参数变化的优点,在保证计算精度的同时能够减少计算量,对于裂缝油藏具有良好的适用性.     

微纳米尺度下材料性能多尺度模拟方法进展

微纳米材料的力学行为正日益引起研究者的关注.微纳米材料的性能取决于从微观、细观到宏观多个空间、时间尺度上不同物理过程非线性耦合演化的结果,发展相应的多尺度数值模拟方法已成为该领域研究工作的一个热点.本文对微纳米材料模拟中比较典型的几种协同多空间尺度和协同多时间尺度方法进行了介绍,着重介绍这些方法的的基本思想、应用情况, 以及各自的优缺点,并对微纳米材料多尺度方法的发展趋势进行总结和评述.      

数字式惯性平台稳定回路的离散变结构控制

为了实际实现具有良好跟踪精度和抗干扰能力的惯性平台稳定回路,建立了平台伺服电机的离散时间模型,设计了由单片机和高速DSP组成的数字控制系统,与惯性平台组成了基于采样数据的平台稳定控制回路,研究了离散变结构控制趋近律的选取方法,采用改进趋近律设计了离散变结构控制律,提出了一种数字式平台稳定回路的离散变结构控制方法,通过实物实验得出了平台伺服电机转轴摩擦力矩模型系数的估计值,并将其引入到控制系统中.仿真实验结果表明,该回路系统对于摩擦力矩和系统参数不确定性具有一定的抗干扰性能,对于阶跃干扰力矩输入具有良好的动态特性,且静态力矩刚度提高到1.2×104 N.m/rad,系统对于斜坡和加速度输入信号实现了平稳跟踪,跟踪误差最大值分别为0.0056 rad和0.0597 rad.     

微/纳尺度接触问题计算方法研究进展

接触问题广泛存在于现实生活的众多领域,近来随着微/纳米技术的不断发展,接触力学在基础理论和研究方法上面临许多新的挑战.本文在摩擦学的范畴内,对近年发展的若干求解微/纳尺度接触问题的计算方法及理论进行了综述.按发展先后及所解决问题的尺度范围划分,主要有3类评估微/纳尺度接触性能的计算方法:(1)连续介质力学方法;(2)分子动力学模拟; (3)多尺度方法.介绍了这3类计算方法的典型理论和主要数学描述,给出了这些方法对解决若干微/纳观接触问题如黏着效应、粗糙表面描述、表面摩擦及润滑、表面热效应、生物接触等的主要应用.最后, 探讨了微/纳尺度接触问题计算方法可能的发展方向及应用领域.      

新修正偶应力层合板理论中的几个基本假设对自由振动计算的影响

基于新修正偶应力理论,在对微细观尺度的复合材料层合梁/板进行力学响应计算时,往往采用一系列假设来简化模型。现有文献都全部或部分应用了这些假设,但对这些假设是否会对计算结果造成影响尚未进行充分讨论分析。本文建立了未经简化的新修正偶应力Reddy层合板模型,并对其自由振动进行了分析。通过数值算例的对比,讨论了常用的几个简化假设对微细观复合材料四边简支方板自振频率的影响以及适用范围。算例结果表明,常用的几个简化假设对于微尺度层合薄板自由振动的影响很小,对于厚板的低阶频率影响也很小,但对厚板的高阶频率影响显著。     

应变局部化分析中两类不同材料模型的讨论

特定情况下单相固体材料率相关模型与多孔介质中的渗流作用均对问题的动力应变局部化分析产生内尺度律效应，对两类问题基本解之间的关系进行讨论，给出了两类不同材料模型解之间的若干联系．     

Metric Invariants in Dynamical Systems

The scaling function and the linear model for a circle endomorphism are two important smooth invariants under conjugacy. We discuss these two invariants and some relations between them. Furthermore, we use these relations to discuss some realization results in this direction. The discussion in this paper avoids quasiconformal mapping theory and Gibbs theory and g-measure theory, which are used in our previous discussions, therefore, is straightforward and simple.This paper is dedicated to Professor Shui-Nee Chow on the occasion of his 60th Birthday.Mathematics Subject Classification 2000: Primary 37E10, Secondary 34C14     

Generalized variational principles with several arbitrary parameters and the variable substitution and multiplier method

The functional transformations of variational principles in elasticity are classified as three patterns: Ⅰ relaxation pattern, Ⅱ augmented pattern and III equivalent pattern.On the basis of pattern Ⅲ, the generalized variational principles with several arbitrary parameters are formulated and their functionals are defined. They are: the generalized principle of single variable u with several parameters, the generalized principle of two variables u, σ with several parameters, the generalized principle of two variables u, ε with several parameters, and the generalized principle of three veriables u, ε, σ with several parameters. From these principles, a series of new forms of equivalent functionals can be obtained. When the values of these parameters are properly chosen, a series of finite element models can be formulated.In this paper, the question of losing effectiveness for Lagrange multiplier method is also discussed. In order to "recover" effectiveness for multiplier method, a modified method, namely, the variable substitution and multiplier method, is proposed.     

The use of renormalization for calculating effective permeability

There is a need in the numerical simulation of reservoir performance to use average permeability values for the grid blocks. The permeability distributions to be averaged over are based on samples taken from cores and from logs using correlations between permeabilities and porosities and from other sources. It is necessary to use a suitable effective value determined from this sample. The effective value is a single value for an equivalent homogeneous block. Conventionally, this effective value has been determined from a simple estimate such as the geometric mean or a detailed numerical solution of the single phase flow equation.If the permeability fluctuations are small then perturbation theory or effective medium theory (EMT) give reliable estimates of the effective permeability. However, for systems with a more severe permeability variation or for those with a finite fraction of nonreservoir rock all the simple estimates are invalid as well as EMT and perturbation theory.This paper describes a real-space renormalization technique which leads to better estimates than the simpler methods and is able to resolve details on a much finer scale than conventional numerical solution. Conventional simulation here refers to finite difference (or element) techniques for solving the single phase pressure equation. This requires the pressure and permeability at every grid point to be stored. Hence, these methods are limited in their resolution by the amount of data that can be stored in core. Although virtual memory techniques may be used they increase computer time. The renormalization method involves averaging over small regions of the reservoir first to form a new averaged permeability distribution with a lower variance than the original. This pre-averaging may be repeated until a stable estimate is found. Examples are given to show that this is in excellent agreement with computationally more expensive numerical solution but significantly different from simple estimates such as the geometric mean.     

Prediction of vibration characteristics of blisks using similitude models

This study investigates the determination approach of distorted scaling laws for predicting the dynamic characteristic of an aero engine’s blisk. Based on the dynamic scaling laws of typical thin-walled structures, an assumption of geometrically complete scaling laws is firstly proposed and numerically validated. For distorted models of disk thickness, in order to simplify the design procedure, a simplification condition is proposed and applied to the first 10 orders’ distorted scaling laws (blade-dominated vibrations) by combining sensitivity analysis. Next, the 11th–14th orders’ distorted scaling laws are determined for disk-dominated vibrations. Numerical validation demonstrates that distorted scaling laws possess a good accuracy. Finally, the applicability of these new scaling laws is validated by the experimental data. The results indicate that, by using the new scaling laws, the simple models can predict vibration characteristics of blisk by employing similitude models.     

Near-wall scaling for turbulent boundary layers with adverse pressure gradient

A new extended inner scaling is proposed for the wall layer of wall-bounded flows under the influence of both wall shear stress and streamwise pressure gradient. This scaling avoids problems of the classical wall coordinates close to flow separation and reattachment. Based on the proposed extended velocity and length scales a universal nondimensional family of velocity profiles is derived for the viscous region in the vicinity of a wall that depend on wall distance and a parameter α quantifying the importance of the streamwise pressure gradient with respect to the wall shear stress in the momentum balance. The performance of the proposed extended scaling is investigated in two different flow fields, a separating and reattaching turbulent boundary layer and a turbulent flow over a periodic arrangement of smoothly contoured hills. Both flows are results of highly resolved direct numerical simulation (DNS). The results show that the viscous assumptions are valid up to about two extended wall units. If the profiles are scaled by the extended inner coordinates, they seem to behave in a universal way. This gives rise to the hope that a universal behavior of velocity profiles can be found in the proposed extended inner coordinates even beyond the validity of the extended viscous law of the wall.      

Nondimensional frequency scaling of aerodynamically-tensioned membranes

Membrane wings have applications that involve low Reynolds number flyers such as micro air vehicles. The time-averaged and time-dependent deformations of the membrane affect the aerodynamic characteristics of the wing, primarily in the region beyond the maximum aerodynamic efficiency of the wing. This paper investigates an appropriate nondimensional vibration frequency scaling of a spanwise tensioned membrane with free (unattached) leading and trailing edges at low Reynolds numbers relative to nondimensional aeroelastic parameters. Silicone rubber membranes with varying spanwise pre-tension, aerodynamic tension (due to wing angle-of-attack and flow dynamic pressure), modulus of elasticity, span, and thickness are studied. Experimental results are compared to a proposed scaling that simplifies the aerodynamic loading as a uniform pressure distribution acting on the membrane. Data is further compared and discussed relative to previous published results of membrane wings with finite wing spans (three-dimensional flow) and fixed (rigid) leading edges.     

低Pr数流体自然对流边界层流动的直接数值模拟

在太阳能采暖通风系统中,空气在太阳辐射作用下于吸热壁上所形成的非稳态自然对流边界 层流动是决定系统热性能的关键所在. 对于线性分层的低普郎特数($Pr<1$)流体而言,标度分 析表明在起始阶段边界层的发展是与高度无关而只依赖于时间的,而处于稳态时,各项标度 关系与处于起始阶段终结时刻的大不相同,且都与高度和时间无关,而只与$Pr$数和线性分 层度相关. 直接数值模拟计算结果表明由标度分析所得的各项标度关系揭示了流动的特性参 数与控制参数之间的决定性内在联系. 但同时也表明标度关系并没有充分体现出 对$Pr$数的所有依赖关系,这一不足可利用直接数值模拟计算结果得到弥补.     

Size effect upon grained materials tensile strength: The increase of the statistical dispersion at the smaller scales

The present paper provides a statistical model to the size effect on grained materials tensile strength; it is based on an Extreme Value Theory approach. Since the weakest link in grained materials is usually represented by the interface between the matrix and the aggregates, it is assumed that the flaw distribution can be represented by the aggregate distribution, expressed as a probability density function (pdf) of the grain diameters. Under the hypothesis that the strength of the material depends on the largest flaw, the tensile strength is computed as a function of the specimen size. In this way, two remarkable results are obtained: (i) a size effect for the average tensile strength that substantially agrees with the multifractal scaling law (MFSL) proposed by the first author and (ii) an increase of scatter of the tensile strength values when testing small specimens. Both these trends are confirmed by experimental data available in the literature.     

Intermittency and scaling in turbulent convection

Both the velocity and temperature measurements taken in turbulent Rayleigh-B‘‘enard convection experiments have been analyzed. It is found that both the velocity and temperature fluctu-ations are intermittent and can be well-described by the She-Leveque hierarchical structure. A positive correlation between the vertical velocity and the temperature differences is found both at the center, near the sidewall and near the bottom of the convection cell, supporting that buoyancy is significant in the Bolgiano regime. Moreover, the intermittent nature of the temperature fluctuations in the Bol-giano regime can be attributed to the variations in the temperature dissipation rate. However, the relations between the velocity and temperature structure functions and their correlations implied by the Bolgiano-Obukhov scaling are not supported by experimental measurements.