准各向同性复合材料弹性和强度的各向异性效应（Ⅱ）——应用与…

文献中尚未见到针对准各向同性复合材料的各向异性效应对复合材料结构影响的分析。本文在第（Ⅰ）部分所提出的强度准则模型的基础上，给出了复合材料各向异性特性在含椭圆孔和单个裂纹问题中的具体应用。在椭圆孔问题中分析了远场荷随材料几何参数变化地规律；在含裂纹问题中分析了裂纹扩展方向裂纹方向的变化规律。     

法向荷载作用下椭圆孔不等边裂纹的应力强度因子

采用复变函数方法,研究了在法向均布荷载作用下,含两个不等边裂纹椭圆孔的无限大板平面问题,得到了裂纹尖端的应力强度因子的解析解.并通过有限元软件计算了应力强度因子的数值解,与解析解进行对比,吻合较好.另外,研究了随着裂纹和椭圆孔尺寸变化时应力强度因子的变化规律.可以看出应力强度因子随椭圆孔的长短半轴之比和裂纹长度的增大而增大.     

准各向同性复合材料弹性和强度的各向异性效应(Ⅱ)──应用与细观力学分析*

文献中尚未见到针对准各向同性复合材料的各向异性效应对复合材料结构影响的分析。本文在第(Ⅰ)部分[1]所提出的强度准则模型的基础上,给出了复合材料各向异性特性在含椭圆孔和单个裂纹问题中的具体应用。在椭圆孔问题中分析了远场载荷随材料几何参数变化的规律;在含裂纹问题中分析了裂纹扩展方向随裂纹方向的变化规律。最后,用细观力学方法分析了一类三轴编织复合材料的弹性本构方程和强度准则,以及各向异性效应,得到了与实验和第(Ⅰ)部分理论模型相一致的结果。     

考虑表面效应时孔边均布径向多裂纹Ⅲ型断裂力学分析

理论研究了纳米尺度孔边均布径向多裂纹的Ⅲ型断裂性能.基于Gurtin-Murdoch表面弹性理论和保角映射技术,获得了孔和裂纹应力场的解析解,给出了裂纹尖端应力强度因子的闭合解.基于解答分析了应力强度因子的尺寸效应,讨论了裂纹数量、裂纹/孔径比和缺陷表面性能对应力强度因子的影响.结果表明:当孔和裂纹尺寸在纳米量级时,无量纲应力强度因子具有显著的尺寸效应;应力强度因子随裂纹数量的变化规律受裂纹/孔径比的影响;裂纹/孔径比对应力强度因子的影响受到缺陷表面性能的制约,同时表面性能对应力强度因子的影响也受限于裂纹/孔径比;表面效应对应力强度因子的影响与裂纹数量无关.     

Reissner板中的夹杂和缺陷问题研究

基于保角变换技术和Faber级数展开,研究了含任意形状夹杂或缺陷的无限大Reissner板弯曲问题．将变换域中单位圆内、外解析函数分别展开成Faber级数,并将波动函数展开成第一类和第二类修正的n阶Bessel函数;利用边界位移、剪力和弯矩连续性条件得到问题的高阶线性方程组．以含椭圆形夹杂和缺陷的无限大Reissner板柱面弯曲为例,进一步给出了数值算例和理论分析．结果表明,对于软夹杂,板内力矩随夹杂与板厚尺寸比a/h变化非常敏感;在含硬夹杂条件下,板内力矩随夹杂尺寸变化相对不敏感．     

含有随机分布缺陷的弹性介质

本文对含有随机分布缺陷的固体中弹性场进行了研究.这些缺陷被简化成微空洞或微裂纹等.它们的位置、方位以及尺寸等都是一些随机参量.作者提出了随机点场模型用于描述这些参量的统计特性,并发展了随机缺陷介质的基本场方程及其解法.对于空洞及微裂纹两种缺陷形固体具体得到了弹性场在其中的分布形态.     

Mindlin板条中弹性波传播问题的分析

基于Mindlin弹性厚板理论，采用Hamilton状态空间求解方法，研究了板条横向两侧为自由边界条件下的弹性：波传播问题，给出了问题的分析解，以及各种振动模态和波传播模的存在性．采用本征函数展开法给出了条形板中导波模的频散方程，并与直接根据Mindlin提出的解获得的频散关系进行了比较，通过比较发现：在短波时，频散曲线相差较大，即前几阶低频模式有一定差别。根据Hamilton体系得到的截止频率高一些，长波时频散曲线几乎相同，即高频模式无差别。     

任意形状孔口单边裂纹问题的边界配位解法

本文提出了一组复应力函数,采用边界配位方法对不同形状孔口(包括圆、椭圆、矩形及菱形孔口)的单边裂纹平板的应力强度因子进行了计算.计算结果表明,对长度和宽度远大于孔口和裂纹几何尺寸的试件,配位法与用其他方法所得的无限大板含圆或椭圆孔边裂纹问题的解符合得很好.同时,对其他孔口问题,特别是有限大板情形,本文给出了一系列计算结果.本文所提出的函数及计算过程可以应用于任意形状孔口单边裂纹平板的计算.     

评“关于椭圆扁平程度的探究”

<正>在离心率教学中一种常见现象是按照书上定义进行讲授,然后总结离心率的各种求法．离心率的几何意义是表示椭圆的扁平程度,但椭圆方程中只出现a,b,从图形上看用它们之间的比值表示椭圆的扁平程度不是很自然吗,为何要用焦距与长轴长的比?当然也有不少学生根本提不出问题,按照书上写的和老师讲的,做对题就可以了,何必管那么多．多数教师认为,     

对一类求离心率e的范围问题的探究

圆锥曲线的离心率是描述曲线形状的一个很重要的量．椭圆的离心率能刻画其扁平程度,而双曲线的离心率反映的是其张口大小的量．由于离心率P分别与椭圆及双曲线的特征量a、b、c有量的直接联系,所以对离心率e的考察在每一次检测中几乎都会出现．     

New stochastic model for dispersion in heterogeneous porous media: 1. Application to unbounded domains

A new model of solute dispersion in porous media that avoids Fickian assumptions and that can be applied to variable drift velocities as in non-homogeneous or geometrically constricted aquifers, is presented. A key feature is the recognition that because drift velocity acts as a driving coefficient in the kinematical equation that describes random fluid displacements at the pore scale, the use of Ito calculus and related tools from stochastic differential equation theory (SPDE) is required to properly model interaction between pore scale randomness and macroscopic change of the drift velocity. Solute transport is described by formulating an integral version of the solute mass conservation equations, using a probability density. By appropriate linking of this to the related but distinct probability density arising from the kinematical SPDE, it is shown that the evolution of a Gaussian solute plume can be calculated, and in particular its time-dependent variance and hence dispersivity. Exact analytical solutions of the differential and integral equations that this procedure involves, are presented for the case of a constant drift velocity, as well as for a constant velocity gradient. In the former case, diffusive dispersion as familiar from the advection–dispersion equation is recovered. However, in the latter case, it is shown that there are not only reversible kinematical dispersion effects, but also irreversible, intrinsically stochastic contributions in excess of that predicted by diffusive dispersion. Moreover, this intrinsic contribution has a non-linear time dependence and hence opens up the way for an explanation of the strong observed scale dependence of dispersivity.     

高烈度下双裂缝主控结构面危岩的断裂破坏机制分析

灰岩地区危岩具有典型类砌体结构特征,结构面发育复杂,其破坏本质是主控结构面在荷载作用下的断裂扩展失稳问题.基于地貌演化分析了灰岩地带陡崖复杂结构面形成与演化,获得了双裂缝主控结构面危岩的地质模型.构建了此类危岩的力学模型和断裂力学模型,按照最大周向应力准则,基于危岩自重、裂隙水压力及地震荷载作用,构建了双裂缝主控结构面危岩的断裂稳定系数表达式.通过案例分析验证了其合理性;各烈度对应的断裂稳定系数随贯通度增加而下降,基本地震烈度为Ⅷ度和Ⅸ度时,危岩处于不稳定状态;危岩稳定性受到主控结构面的裂隙贯通度与地震诱发的耦合作用影响,临界失稳贯通度随地震烈度的提高而降低;Ⅶ度地震的临界失稳贯通度理论值为25.8%,略小于贯通度实际值27.7%,略偏安全,其建立的断裂稳定系数表达式具有较好的适用性.研究结果可为推动此类危岩合理化防治提供重要的理论支撑.     

Longitudinal waves in partially saturated porous media: the effect of gas bubbles

The problem of the propagation of longitudinal waves in a liquid-saturated porous medium when there are gas bubbles present is considered. The decay factor and the phase velocity of Frenkel–Biot waves of the first and second kind are found as a function of the frequency in the linear approximation. It is shown that, in the neighbourhood of the resonance frequency of the bubbles, longitudinal Frenkel–Biot waves change their form. A wave of the first kind is transformed from a fast wave at low frequencies into a slow wave at high frequencies. The dispersion curve of a wave of the second kind consists of two branches – a “low-frequency” branch, the oscillations of which possess the classical properties, and a “high-frequency” branch, which is a weakly decaying high-velocity mode. The frequency dependences of the ratio of the mass velocities of a gas-liquid mixture and of a porous matrix, and also of the perturbations of the stress in the matrix and the pressure in the mixture, are constructed. It is shown that the “high-frequency” branch of a wave of the second kind is characterized by the in phase motion of the gas-liquid mixture and of the porous matrix, while their mass velocities are close, which explains the weak decay of this mode of oscillations. An analytical expression is obtained for the “boundary frequency”, which determines the offset of the “high-frequency” branch of the dispersion curve of the wave of the second kind.     

基于裂纹尖端二阶弹性解的断裂过程区尺度

基于Westergaard应力函数裂纹尖端二阶弹性解,推导了裂纹尖端微裂区的轮廓线和特征尺寸的解析表达式;采用幂函数模型描述的拉应变软化模型,确定了在最大拉应力强度理论和最大拉应变强度理论下断裂过程区（FPZ）临界值的解析表达式;将基于Westergaard应力函数一阶弹性解及二阶弹性解、Muskhelishvili应力函数和Duan-Nakagawa模型确定的FPZ临界值进行了比较．结果表明裂纹尖端微裂区和FPZ临界值随着Poisson比的减小而增加并逐渐趋近于应用最大拉应力强度理论确定的结果;二阶弹性解确定的裂纹尖端微裂区和FPZ临界值大于一阶弹性解的值;FPZ临界值随着拉应变软化指数的增加而增加;二阶弹性解确定的FPZ临界值的精度远高于一阶弹性解确定的值.     

Low-frequency acoustic characteristics of biological tissues

The laws of propagation of elastic waves of different types in biological tissues in the acoustic frequency range have been theoretically and experimentally investigated. The contributions of the imaginary and real components of the complex modulus of elasticity to the elastic wave velocity are analyzed. It is shown that in soft tissues, low-frequency elastic disturbances are propagated chiefly by shear (transverse) waves. The geometric dispersion of the elastic wave velocity has been investigated in experiments on gel model systems; the results of the measurements are in agreement with the theoretical dispersion curve.     

Elastic wave propagation in a cylindrical bore situated in a micropolar elastic medium with stretch

Propagation of surface elastic waves in a cylindrical bore through a micropolar elastic medium with stretch is analysed in two cases. In the first case, the cylindrical bore is considered empty while in the second case, the bore is filled with homogeneous inviscid liquid. In both the problems, period equations are obtained in closed form. The problem of Banerji and Sengupta [2,3] has been reduced as a special case. Numerical calculations have been performed for a particular model and results obtained are presented graphically. It is noticed that the effect of micropolarity on dispersion curve is significant while the effect of micro-stretch on dispersion curve is not appreciable.     

A practical analytic model for predicting the performance of an encapsulated polymer composite

A novel model is presented for simulating the characteristics of a micro-encapsulated composite. The procedure initiated utilizing particle size analysis (PSA) to obtain the volume based average diameter and average spacing between the microcapsules in the composite. Results of this procedure were verified by scanning electron microscopy (SEM). Then, a simple model was presented to predict the healing percent of a triangular crack propagating in the composite. In order to obtain more detailed results, a probabilistic model was also suggested for the planar and triangular cracks, which gave the probability of crack incidence for different number of capsules to be intersected. Results of this method were then validated in comparison with the results independently obtained using a simulation by computer programming. The comparison showed close agreement between the analytical results and the simulations which present the current model and simulations as a promising method for investigating the characteristics of the encapsulated self-healing composites.     

Analysis of extension propagation process of interface crack between belts of a radial tire using a finite element method

A radial tire is a very complex structure made from rubber elastomers and fiber–rubber composite materials. During its use, extension propagation of interface crack between belts can occur, which obviously affects its durability and life. In the present paper, a new mathematical model of extension propagation of interface crack in complex composite structures is presented. The model can reveal the extension propagation dependence of interface crack on the relative size of energy release rates at the left and right crack tips and on the interfacial material properties. The extension propagation model of interface crack, Irwin’s virtual crack close technique and the finite element analysis method are used together in simulating numerically the extension propagation process of a interface crack between belts of a radial tire. The present study numerical results show that the extension propagation model of interface crack proposed in this paper can more realistically characterize the complexity of the extension propagation process of interface crack in complex composite structures.     

Forward mixing model in a rotating disc contactor for kerosene–acetic acid–water system

The application of an extraction column model which takes into account the influence of the forward mixing model is brought forward by generation of values of the mass transfer and axial dispersion coefficients required by the model. Values of these coefficients were generated from solute concentration profile measurements in a rotary disc contactor (RDC). The use of the Handlos–Baron drop mass transfer model was justified. The resulting continuous phase transfer coefficients were found to be dependent largely on disc speed. The accuracy of the forward mixing model for kerosene–acetic acid–water system was adequately presented and explained by the axial dispersion coefficient.