用变分法估计热爆炸临界状态参数

本文利用作者给出的关于爆炸临界状态的变分原理,并用变分的直接方法,得到了六种不同形状(平板、无限长圆柱,球,无限长方形杆,有限长圆柱,正方体)系统的临界P-K参数和临界温度的近似公式,与精确的数值计算结果比较表明,对点火临界参数,本文公式均能给出较好的估计值。     

四参数全范围da/dN曲线测定方法研究

机械结构设计的损伤容限分析,需要使用材料疲劳裂纹扩展速率曲线性能。在总结传统疲劳裂纹扩展曲线的基础上,本文讨论了四参数全范围da/dN曲线公式;基于断裂力学原理,分别给出了此公式中材料裂纹扩展门槛值ΔKth,断裂韧性K1C和张开函数f的测定方法;利用多元线性回归法对试验数据进行了曲线拟合,得到了四参数全范围da/dN曲线公式的参数估计式;将此公式运用于不同应力比下的裂纹扩展速率试验数据拟合,通过试验数据的拟合结果可以看出:四参数全范围da/dN曲线公式,能够充分有效合理地表征全范围裂纹扩展速率的物理特性和宏观数据规律,且参数估计简便,拟合精度高;从而验证了四参数全范围da/dN曲线公式的有效性和合理性,并将得到广泛应用。     

用于断裂可靠性设计的P—Km—da／dN—△K曲面

本文提出了疲劳裂纹扩展Ｋｍ－ｄａ／ｄＮ－△Ｋ曲面，并给出了Ｐ－Ｋｍ－ｄａ／ｄＮ－△Ｋ曲面实验数据处理及参数估计公式，利用该曲面可进行断裂损伤折算及随机载荷谱作用下构件裂纹扩展寿命估算。最后给出了一实例。     

用于断裂可靠性设计的P-Km-da/dN-ΔK曲面

本文提出了疲劳裂纹扩展Ｋｍ－ｄａ／ｄＮ－ΔＫ曲面，并给出了Ｐ－Ｋｍ－ｄａ／ｄＮ－ΔＫ曲面实验数据处理及参数估计公式；利用该曲面可进行断裂损伤折算及随机载荷谱作用下构件裂纹扩展寿命估算。最后给出了一实例。     

热爆炸临界状态的变分特性

本文利用热爆炸的临界状态是其定态方程分岔点的定义,给出了热爆炸临界参数的一个变分原理。泛函J（,）的极大值恰好是点火临界参数i;其极小值则是熄火临界参数e;其鞍点值是转点参数tr。     

静力预加载结构冲击屈曲的突变模型

基于突变理论给出静力预加载弹性结构冲击屈曲的准则,并将其用于处理Budian-sky-Hutchinson简单力学模型的冲击屈曲分析和受扭圆柱壳的冲击扭转屈曲分析,给出了临界载荷的求解公式。     

切削临界稳定与预报及切削阻尼系数测定——切削动力学研究报告之二

在[1]的基础上本文给出了切削的临界稳定方程组,导出了无再生颤振、两种有再生颤振以及两种特殊情况下再生颤振的(ωτ=180°,270°时)临界稳定和绝对临界稳定公式,在理论上解释了稳定界的跳跃与再生阻尼问题。利用无再生临界稳定条件C_i=-k,作者用自己研制的新装置成功地测取了一系列切削阻尼系数k,为研究k的规律和预报颤振提供了条件。作者以95%的精度预报了两种情况颤振的发生。文中指出了传统公式诸不妥之处。     

悬臂高梁在静动态载荷作用下侧向失稳的实验研究

本文进行了平头圆柱形弹体对铝合金悬臂高梁自由端正撞击引起侧向失稳的实验研究．通过多种不同尺寸梁的实验，研究了梁在静动态载荷下的侧向失稳临界载荷值及屈曲模态．最后给出一个在撞击载荷下，计算悬臂高梁侧向失稳临界冲击动能值的经验公式．     

热爆炸的临界条件和点火时间 (Ⅱ)有反应物消耗情况

本文使用抛物型方程解的比较法,给出了低超临界化学反应系统的点火临界条件,点火临界温度和点火时间。这组近似公式反映了反应物的消耗,系统形状和温度有空间分布对临界特性的影响。它比温度均匀近似更接近实际,温度均匀近似结果可做为本文公式的特例。     

提高能量法确定压杆临界荷载精度的一种方法

 通过杆件的弯矩位移关系消去能量法确定压杆临界荷载公式中的位移导数项，大 大地提高了其计算精度，文后给出的两个算例证明了这一结论.     

The Remarkable Nature of Cylindrically Anisotropic Elastic Materials Exemplified by an Anti-Plane Deformation

A material is cylindrically anisotropic when its elastic moduli referred to a cylindrical coordinate system are constants. Examples of cylindrically anisotropic materials are tree trunks, carbon fibers [1], certain steel bars, and manufactured composites [2]. Lekhnitskii [3] was the first one to observe that the stress at the axis of a circular rod of cylindrically monoclinic material can be infinite when the rod is subject to a uniform radial pressure (see also [4]). Ting [5] has shown that the stress at the axis of the circular rod can also be infinite under a torsion or a uniform extension. In this paper we first modify the Lekhnitskii formalism for a cylindrical coordinate system. We then consider a wedge of cylindrically monoclinic elastic material under anti-plane deformations. The stress singularity at the wedge apex depends on one material parameter γ. For a given wedge angle α, one can choose a γ so that the stress at the wedge apex is infinite. The wedge angle 2α can be any angle. It need not be larger than π, as is the case when the material is homogeneously isotropic or anisotropic. In the special case of a crack (2α=2π) there can be more than one stress singularity, some of them are stronger than the square root singularity. On the other hand, if γ < there is no stress singularity at the wedge apex for any wedge angle, including the special case of a crack. The classical paradox of Levy [6] and Carothers [7] for an isotropic elastic wedge also appears for a cylindrically anisotropic elastic wedge. There can be more than one critical wedge angle and, again, the critical wedge angle can be any angle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Solution of three-dimensional natural convection about a vertical square rod in a cylindrical enclosure

The problem of three-dimensional laminar natural convection in a vertical enclosure with an inner square rod is treated by a numerical method in boundary-fitted co-ordinates. The inner and outer cylinders are heated and cooled, respectively, to maintain different constant surface temperatures. The horizontal enclosure surfaces are maintained at adiabatic conditions. The Prandtl number is that of air, 0·703, and the Rayleigh numbers span the conduction, transition and boundary layer regimes of flow. The radius ratio is 1, and the aspect ratio (cylinder length divided by maximum annular gap) is 1. The results of the study provide data useful in the design and performance assessment of nuclear reactor spent fuel shipping casks.     

3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux

A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips (diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that the velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.     

Analytical dynamic displacement response of rigid pavements to moving concentrated and line loads

This paper presents the formulation of a plate of infinite dimensions (without boundary conditions) on an elastic foundation, subjected to a moving concentrated and line load of constant amplitude and speed, using a triple Fourier transform. The solution is carried out integration by residues. A closed-form solution of displacement field has been obtained for a moving load with subsonic, transonic and supersonic speeds. It is found that the maximum response of the slab occurs beneath the moving load and travels with the load at the same speed. It is also shown that a critical speed exists. If the moving load travels at critical speed, slab displacement becomes infinite in amplitude.     

Geometric Currents in Piezoelectricity

As a simple model for piezoelectricity we consider a gas of infinitely many non-interacting electrons subject to a slowly time-dependent periodic potential. We show that in the adiabatic limit the macroscopic current is determined by the geometry of the Bloch bundle. As a consequence we obtain the King-Smith and Vanderbilt formula up to errors smaller than any power of the adiabatic parameter.     

Fluid flow through a network of thin pipes

We study the fluid flow through a network of intersected thin pipes with prescribed pressure at their ends. Pipes are either thin or long and the ratio between the length and the cross-section is considered as the small parameter. Using the asymptotic analysis with respect to that small parameter the effective behaviour of the flow is found. At each junction an explicit formula for computing the value of the pressure is found. The interior layer phenomenon in vicinity of the junction is studied. We generalize the junction formula on the case of adiabatic compressible flow.     

正弦波温度边界下多孔介质方腔内非热平衡对流传热数值模拟

采用局部非热平衡模型,在方腔左侧壁面温度正弦波变化、右侧壁面温度均一的边界条件下,通过SIM-PLER算法数值研究了固体骨架发热多孔介质方腔内的稳态非达西自然对流,主要探讨了不同正弦波波动参数N及方腔的高宽比M/L对方腔内自然对流与传热的影响规律。计算结果表明:正弦波温度边界使得方腔内的流场出现了复杂的变化,流体及固体区域左侧壁面附近出现了周期性的正负变化的温度场分布,左侧壁面局部Nusselt数出现了周期性的震荡现象;存在一个最佳温度波动参数N=1,此时多孔介质方腔内的整体散热量达到最大值;增加方腔高宽比会显著地削弱方腔内的自然对流传热过程,小高宽比也会在一定的程度上削弱多孔介质方腔内的对流传热。     

Laminar fluid flow and heat transfer in a duct of cross-shaped cross-section

Fully-developed flow calculations were performed on ducts of cross-shaped cross-section, which may be regarded as possible candidates for compact heat exchanger configurations. A parametric study was made on the friction and heat transfer characteristics in terms of the parameter α associated with the decrease in the cross-sectional area (namely, α=0 for a square duct and α→1 for infinite parallel plates). As increasing α, both the Nusselt number and friction coefficient decrease toward their minimum levels, but then, increase gradually, and overshoot those of a square duct. Consequently, the heat transfer coefficient shows a significant increase for α>0.4, suggesting an excellent performance of heat transfer surfaces in the duct of cross-shaped cross-section.     

Flow parameter approach to modeling the flow of heated gases through high resistance porous media

A constitutive relationship is developed to characterize the flow of high velocity, compressible, heated gases through concrete. This relationship equates a nondimensional flow parameter with pressure and temperature ratios across the medium. The key premise is that the resistance to flow through a porous medium can be modeled with friction coefficients analogous to the method used for simpler geometries. The utility of a porous media compressible flow parameter is appraised by comparing it with the Forchheimer equation modified for an ideal gas. There is little difference in adiabatic flow rates predicted by the two relationships. The Forchheimer equation does not account for the effects of heating. The flow parameter predicts mass flows through a slab of concrete to decrease by nearly 50% when this medium is heated from 25 to 350C.