弹性理论几类导数边界积分方程之间的变换关系

导数场边界积分方程通常难以应用，因为存在着超奇异主值积分的计算障碍。弹性理论中有几类不同的位移导数边界积分方程，本文采用算子δij和∈ij(排列张量)作用于这些导数边界积分方程，做一系列变换，原有的超奇异积分被正则化为强奇异积分获解。从而建立了这些位移导数边界积分方程之间的转换关系，它们均可以归结为自然边界积分方程。自然边界积分方程仅存在容易计算的Cauchy主值积分。自然边界积分方程分析可直接获得边界应力和位移导数。     

Hermite梯度重构核近似配点法及其在功能梯度材料板的静力分析中的应用

由于直接配点法在求解边值问题时边界上的求解精度较低,本文提出了Hermite梯度重构核近似配点法（HGCM）来改进边界求解精度。重构核近似是无网格法中一种常用的近似函数,但是其在求解高阶导数时格式复杂且非常耗时。HGCM采用梯度重构核近似构建形函数的任意高阶导数,提高了计算效率;通过Hermite配点法构建离散方程,提高了边界求解精度。这种方法在求解对应变系数四阶偏微分方程的功能梯度材料板的静力问题时精度高,计算效率高,并可进一步推广应用于高阶偏微分方程描述的边值问题。     

重根特征向量导数计算的完备模态法

1 引言特征向量导数是结构动力优化分析和控制系统设计过程中很重要的参数;近些年来,在模型修正以及结构参数识别与诊断中也往往需要特征向量导数的信息:另外,特征向量导数还是“灵敏度分析”的一个重要部分.目前计算特征向量导数的部分方法有Fox(含改进Fox 法)、Nelson 法(含改进Nelson 法)、模态法和扰动迭代法.众所周知,求解特征向量导数的“支配方程”(K-λ_iM)(?)_(i,j)=(λ_iM_(?)+λ_(i,j)M-K_(?))(?)_i=g_i (1)的系数阵为亏秩阵;对于单根为亏秩1;对于m 重根就亏秩m.Fox 法和改进Fox 法是利用     

各种边界条件平行四边形功能梯度板的动力特性解析解

本文基于斜坐标系,建立起平行四边形功能梯度板的基本微分方程及变分方程,用梁函数组合法对平行四边形及菱形功能梯度板进行动力特性分析,提出了适用于每边任取简支、固定、自由边界之一(包括36种边界)平行四边形功能梯度板固有频率与振型的解析解;在简化情况下,给出了各种边界条件平行四边形功能梯度板各阶固有频率解的统一表达式。     

弹性静力问题的无网格弱-强形式结合法

基于改进的移动最小二乘(MLS)二阶导数近似,建立了一种求解弹性静力问题的无网格弱-强形式结合法(MLS-MWS)。该方法采用节点离散求解域,通过MLS构造形函数,将求解域划分为边界域和内部域,并分别使用控制方程的局部弱形式和强形式来建立离散系统方程。对强形式中涉及的近似函数二阶导数计算,提出了一种将其转化为求两次一阶导数的方法,与传统方法相比,该方法计算简单、精度高。MLS-MWS法结合了弱、强形式无网格法的优点,Neumann边界条件容易满足,并且只需在边界区域进行积分。文中应用该方法分析了两个弹性力学平面问题,分析结果表明本文方法具有良好的精度和收敛性。     

爆炸载荷下板条边界斜裂纹的动态扩展行为

为了研究爆炸应力波作用下板条边界斜裂纹的动态扩展行为,首先分析了爆炸应力波在含边界斜裂纹板条中的传播,其次采用动态焦散线实验方法,进行了爆炸载荷下板条边界斜裂纹扩展规律的实验研究.研究结果表明,爆炸应力波作用下,板条试件边界斜裂纹的扩展过程中,裂纹扩展速度、扩展加速度和裂尖动态应力强度因子随时间波动变化,扩展速度最大值...     

三种分形和分数阶导数阻尼振动模型的比较研究

标准的整数阶导数方程不能准确描述粘弹性材料的记忆性参考文献[1]和阻尼的分数次幂频率依赖[2],因此分形导数、分数阶导数及正定分数阶导数被用于描述粘弹性介质中的阻尼振动.该文通过分析模型和数值模拟,比较了三种模型描述的振动过程.结果显示,当p小于约O.75或大于约1.9时(p为非整数阶导数的阶数),分形导数模型衰减最快;当P大于约0.75且小于约1.9时,正定分数阶导数模型衰减最快,衰减最慢的分别为分数阶导数模型(p<1)和分形导数模型(p>1).且正定分数阶导数模型衰减快于分数阶导数模型,当p接近2时,两种模型较为相近.     

非线性弹性介质中冲击波斜反射的研究(Ⅱ)

利用前文结果求解了冲击波在固壁及滑动刚壁两种边界面上的斜反射问题。在滑动刚壁的情,很可能出现马赫反射图象。     

基于固定网格和拓扑导数的结构拓扑优化自适应泡泡法

为继承传统拓扑优化泡泡法变量少、精度高等优点,并克服其网格重划频繁、孔洞合并操作繁琐等不足,提出了一种基于固定网格和拓扑导数的自适应泡泡方法.该方法的主要特点是:(1)采用有限胞元固定网格分析方法计算结构力学响应,在优化过程中无需网格更新和重划分,就能保证较高的分析精度;(2)根据拓扑导数信息指导结构区域中孔洞的引入,不仅消除了优化结果对孔洞初始布局的依赖性,还能有效控制设计变量的数量;(3)引入拓扑导数阈值和孔洞影响区域新概念,实现了孔洞引入频次和位置的自适应调节,保证了拓扑优化过程的数值计算稳定性;(4)采用光滑变形隐式曲线描述孔洞边界,不仅设计参数少、变形能力强,而且便于处理孔洞间的融合/分离操作以及与固定网格分析方法的有机结合.理论分析和数值算例表明,改进后的自适应泡泡法能够消除传统泡泡法因采用拉格朗日网格和参数化B样条曲线模型而存在的实施困难,采用很少的设计变量就可获得边界光滑清晰的优化结果.      

关于位移法计算有侧移斜梁的研究

针对用位移法计算有侧移斜梁时遇到的几个问题进行了研究，利用运动学原理对斜 梁位移进行分析，采用力法对几种常见载荷作用下的斜梁进行理论推导，得到了几 个重要结论: 一是斜梁的侧移计算公式，二是一端固定、一端定向支承(支杆与斜梁斜交时)的有侧移单 跨斜梁的转角位移方程、固端弯矩分别与两端固定支承的水平梁的相同，所以计算此类斜梁 时可以按两端固定支承的单跨水平梁处理.     

Mixing in a stably stratified medium by horizontal shear near vertical walls

Stratified environmental flows near boundaries can have a horizontal mean shear component, orthogonal to the vertical mean density gradient. Vertical transport, against the stabilizing force of gravity, is possible in such situations if three-dimensional turbulence is sustained by the mean shear. A model problem, water with a constant mean density gradient flowing in a channel between parallel vertical walls, is examined here using the technique of large eddy simulation (LES). It is found that, although the mean shear is horizontal, the fluctuating velocity field has significant vertical shear and horizontal vorticity, thereby causing small-scale vertical mixing of the density field. The vertical stirring is especially effective near the boundaries where the mean shear is large and, consequently, the gradient Richardson number is small. The mean stratification is systematically increased between cases in our study and, as expected, the buoyancy flux correspondingly decreases. Even so, horizontal mean shear is found to be more effective than the well-studied case of mean vertical shear in inducing vertical buoyancy transport as indicated by generally larger values of vertical eddy diffusivity and mixing efficiency.     

沉积物中甲烷水合物饱和度测定及其力学特性研究

在自主研制的实验装置上合成甲烷水合物,采用时域反射技术(TDR)实时监测甲烷水合物生成过程中饱和度的变化,并与系统的压力降法计算的饱和度进行了对比。结果表明TDR法简单易行,结果可靠。对含甲烷水合物沉积物进行了一系列不排水三轴压缩实验,结果表明,含甲烷水合物沉积物的抗剪强度随着有效围压的增加和水合物饱和度的增加而增大;粘聚力随着甲烷水合物饱和度的增加而明显增加,但内摩擦角变化并不显著。在此基础上,提出了抗剪强度与有效围压和水合物饱和度的关系模型。     

Plane-parallel advective flow in a horizontal incompressible fluid layer with rigid boundaries

The exact solution of the Navier-Stokes equations that describes the plane-parallel advective flow in a plane incompressible fluid layer with rigid boundaries at which either the linear distribution of temperature of different signs or the linear horizontal temperature gradient is given is presented.     

Stability of plane-parallel convective fluid flow in a horizontal layer relative to spatial perturbations

The stability of stationary plane-parallel convective flow between horizontal planes along which a constant temperature gradient is given, is investigated relative to spatial perturbations. It is shown that the flow crisis is caused by spiral perturbations in a broad range of Prandtl number values (P > 0.24). Spiral perturbations are developed in unstably stratified fluid layers adjoining the upper and lower layer boundaries, and are of Rayleigh nature.     

Stability of the advective flow in a horizontal rectangular channel with adiabatic boundaries

The steady-state advective flow in a long horizontal rectangular channel with rigid adiabatic boundaries in the presence of a uniform longitudinal pressure gradient is investigated. The stability of this flow with respect to perturbations of various types is studied. The dependence of the critical Rayleigh number on the Prandtl number is found for various aspect ratios.     

Convective flow with uniform vorticity in a vertical layer

The free convective circulation of liquid in plane vertical slits of circular and square cross section with a longitudinal horizontal temperature gradient at the boundaries was investigated experimentally. It was found that under such heating conditions there is a uniform-vorticity flow with a region of quasirigid rotation, which has the shape of a disk in a circular slit and the shape of a cross in a square slit; in each longitudinal section of this zone the liquid moves along concentric trajectories with constant angular velocity. Dimensionless numbers for the problem were established by tests with various liquids and cavities of different dimensions. In dimensionless form, the angular velocity of the vortex and the temperature gradient in it depend linearly on the temperature difference at the boundaries of the layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 160–165, May–June, 1984.     

Onset of convection regimes with double period in a periodic field of external forces

We investigate the onset of secondary convective flows in the Rayleigh problem (in a horizontal layer of a viscous incompressible liquid with free boundaries) in the presence of a parameter that varies with time and has a period T, namely the temperature gradient or the intensity of the gravitational field.Translated from Zhurnal Prikladnoi Mekhanlki i Tekhnicheskoi Fizlki, No. 6, pp. 65–70, November–December, 1972.     

Stability of thermocapillary advective flow in a slowly rotating liquid layer under microgravity conditions

The stability of thermocapillary flow developed in a slowly rotating fluid layer under microgravity conditions is investigated. Both boundaries of the layer are free and assumed to be plane. The tangential thermocapillary Marangoni force exerts on the boundaries, where heat transfer takes place in accordance with the Newton law, the temperature of the medium in the neighborhood of the boundaries being a linear function of the coordinates. The axis of rotation is perpendicular to the liquid layer, rotation is weak so that the centrifugal force can be neglected. Being the solution of the Navier-Stokes equations, the thermocapillary flow in question can be described analytically. The neutral curves which describe the wavenumber dependence of the critical Marangoni number for various Taylor numbers and various directions of the horizontal temperature gradient on the layer boundaries are obtained within the framework of the linear stability theory. The behavior of finite-amplitude perturbations beyond the stability threshold is studied numerically.     

Stability of a binary-mixture advective flow in a plane horizontal layer with perfectly heat conducting boundaries

The stability of a steady-state advective flow of a binary mixture in a plane horizontal layer with perfectly heat conducting solid boundaries in the presence of a uniform longitudinal temperature gradient is investigated. The problem is solved with account for thermodiffusion. The limits of the stability of the steady-state flow with respect to long-wave disturbances are found analytically. The stability of the main flow with respect to plane and spiral disturbances with finite wavelengths is studied numerically. The stability maps in the “Rayleigh number-Sorét parameter” plane are constructed for a number of typical liquid and gaseous mixtures.     

On the convective instability of a liquid in an inclined layer of a porous medium

In this paper we study the stability of the equilibrium of a liquid heated from below, wherein the liquid saturates a planar layer of a porous medium arbitrarily inclined to the direction of gravity. We consider the cases for which the boundaries of the layer are heat-conducting and also thermally insulated. In a horizontal layer with heat-conducting boundaries equilibrium is destroyed by perturbations of cellular structure [1], In a vertical layer the minimum critical temperature gradient corresponds to perturbations of plane-parallel structure. The transition to cellular perturbations in the case of heat-conducting boundaries takes place at an arbitrarily small angle of inclination of the layer to the vertical. For the thermally insulated layer the crisis of equilibrium is connected with plane-parallel perturbations at all angles of inclination.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 127–131, May–June, 1973.The author thanks G. Z. Gershuni for stating the problem and his interest in the work.