用p-V指数关系确定血管壁的周向应力

通过检测，得到在体轴向伸长比条件下血管段的压力－容积（p-V)数据，利用指数函数关系，求得在一定内压作用下血管壁周向应力沿壁厚的分布。并以正常大鼠腹主动脉为例进行计算，结果表明，在生理压力作用下，残余应力对血管壁周向应力的分布有很大影响，不考虑残余应力将使血管内壁处出现明显的周向应力集中，当考虑存在于血管壁内的残余应力后，周向应力沿壁厚的分布将变得较均匀，例如当内压p=10kPa时，血管内、外壁周向应力值之比，对前者将达10以上，而对后者差不多只有2左右。所得结果与用Fung提出的应变能密度函数的计算结果作比较，发现二者符合得相当好。     

在椭圆横截面弹体正侵彻下有限厚铝靶的破坏模式及响应特性

基于30 mm口径弹道炮平台,开展了3种不同椭圆横截面弹体在200~600 m/s撞击速度范围内正侵彻2A12铝靶的实验,获得了2A12铝靶的破坏形貌及弹体的剩余速度。在此基础上,建立了相应的数值模型,结合实验结果验证了所建模型的有效性,并系统分析了弹体横截面长短轴长度比对靶体的破坏情况及响应特性的影响。研究结果表明:弹体最大横截面面积是影响弹体剩余速度的主要因素,而弹体横截面长短轴长度比对弹体剩余速度的影响较弱;在圆形横截面弹体侵彻下靶体背部形成的花瓣大小和形状一致,空间分布均匀,而在椭圆横截面弹体侵彻下,随着弹体横截面长短轴长度比的增大,靶体背部形成的花瓣数量增加、尺寸变小,且在短轴方向的花瓣数量和靶体表面隆起高度均大于长轴方向的;靶体在圆形横截面弹体侵彻下的径向位移、径向应力和切向应力与其在椭圆横截面弹体侵彻下的显著不同,前者沿周向方向各点的变化规律基本一致,靶体处于简单的压缩状态,切向应力为零,而后者各点的应力状态与弹体横截面长短轴长度比和周向角密切相关,靶体受到压缩和剪切应力的耦合作用。     

动脉压对静脉血管壁周向应力分布的影响

自体静脉是病变动脉管段常用的替代物。移植后因承受压力急剧升高引起的静脉管壁应力改变是影响移植手术的主要因素之一。为了比较移植前(静脉压作用下)和移植后(动脉压作用下)静脉管壁的周向应力分布，本文通过检测一定轴向伸长比条件下静脉管的p(压力)——V(容积)试验数据，利用3参数的应变能密度函数对实验数据进行拟合，进而求得静脉管壁的残余应力和沿血管壁的周向应力分布。对狗的股静脉和颈静脉的分析结果表明，在动脉压作用下静脉管壁周向应力将急剧增大。与处于静脉压环境相比，处于动脉压环境中的颈静脉管周向应力将增大差不多2个数量级。计算结果还显示，静脉管壁残余应力的数值虽然比动脉管壁的相应值小很多，但是与动脉管相同，血管壁残余应力依然对静脉管壁上的周向应力分布影响显著，残余应力的存在将大大削弱在静脉管内壁处的周向应力集中，使周向应力沿静脉管壁厚的变化梯度明显减小。     

Stress field of orthotropic cylinder subjected to axial compression

Based on the constancy hypothesis of material volume, the circumferential and radial stresses of a cylinder specimen are analyzed when the cylinder is subject to a loading along the axial direction. The circumferential and radial stress distribution is a power function of radius parameter when the constitutive relation of specimen material is orthotropic. The stress distribution is a quadratic function of radius parameter for transversely isotropic material. Along the cylinder axial line, the circumferential and radial stresses are maximum and equal to each other. In the circumference boundary surface, the radial stress is zero and the circumferential stress value is minimal. The failure theory of maximum tensile circumferential strain is applied to calculate the critical axial loading. The circumference-boundary-layer failure criterion of orthotropic cylinders is described with the Hill-Tsai strength theory. The obtained strength theory is related to axial stress and mechanical properties of specimen material and to the specimen axialdeformation strain rate and the change rate of strain rate.     

在体轴向伸长比条件下血管壁的周向应力分布

本文通过检测在体轴向伸长比条件下血管段的压力－容积数据,利用应变能密度函数,求得血管壁周向应力沿壁厚的分布。文章的正常大鼠腹主动脉为例进行计算,结果发现,在生理压力作用下（例如ｐ＝１３．３ｋＰａ）,不考虑残余应力确实出现在血管内壁处的周向应力集中,血管内、外壁处的应力值之比可达１５左右,而存在于实际动脉管中的残余应力会使血管壁中的周向应力沿壁厚的分布明显趋于均匀,血管处的周向应力之比差不多只有２左     

Using the logarithmic strain measure for solving torsion problems

The problems of free and constrained torsion of a rod of solid circular cross-section are solved numerically using a tensor linear constitutive relation written in terms of the energy compatible Cauchy stress and Hencky logarithmic strain tensors. The only function used to determine the properties of the isotropic incompressible material of the rod is a power-law function that approximates the shear diagram and corresponds to an elastoplastic material with power-law hardening. The solution obtained shows that, despite the tensorial linearity of the state law, the use of the logarithmic strain measure allows one to describe qualitatively the effect of significant elongation of the rod in free torsion (the Poynting effect) as well as the arising normal longitudinal, radial, and circumferential stresses, whose values are commensurable, at large deformations, with the maximum tangential stresses in the cross-section. Computational dependences of the torsional moment on the angle of twist in free and constrained torsion are obtained. These dependences are found to be significantly different from each other; the limitmoment and the correspondingmaximum angle of twist for free torsion are found to be considerably lower than those for constrained torsion. It follows that the shear strength, which is traditionally calculated from the maximum torsional moment, becomes indeterminate. For constrained torsion, the dependence of the longitudinal compressive force on the angle of twist is obtained.     

边坡下伏地下圆形洞室的弹性应力解析

根据洞室与边坡的相对位置,将其分为深埋地下洞室与浅埋地下洞室,并分别建立了计算模型。将浅埋圆形洞室视为分布荷载作用下半无限体表面附近的孔洞的应力分析问题,采取复变函数的保角映射得到了浅埋洞室的应力解析解。将深埋洞室视为一个双向受压无限板孔应力集中问题,得到了边坡下伏深埋圆形洞室的应力解析解。以某填筑边坡下地下圆形洞室为例,计算得到了浅埋圆形洞室周边的径向应力与环向应力分布,计算结果表明洞室圆心水平线上的环向压应力随着与洞周距离的增加逐渐减小,但径向压应力却是首先增加,然后才逐步减小。洞顶圆周出现环向拉应力,随着越来越接近地表,环向应力逐步转变为压应力并且越来越大,而径向应力逐渐变大。洞周环向拉应力在洞顶与洞底数值最大,洞室左右两端洞周环向压应力数值最大;洞周径向应力在洞顶、洞底数值较小,左右两端洞周应力最大。     

血管残余应力的一种确定方法

动脉无载荷状态下存在残余应力,分析血管壁在载荷状态下的应力分布必须计及血管壁的残余应力。本文通过检测动脉不同轴向伸长比条件下的压力—容积(p—V)数据,根据其p—V实验曲线的“S”型特征,提出了一种用反正切函数关系对试验数据点进行拟合,进而导得动脉管壁周向残余应力沿壁厚分布的方法。文章对10只正常大鼠颈动脉的分析结果表明,大鼠颈动脉周向残余应力沿血管壁厚呈单调上升趋势。残余应力在内壁处为负呈压缩状态,在外壁处为正呈拉伸状态,并且内外壁处应力绝对值大小基本相等,大约在2．5kPa左右。文章结果对进一步分析动脉管壁在载荷作用下的应力分布提供必要的信息。     

Thermal gradient effect on the free vibration of a cardioid cross-section cylindrical shell

For the first time, a new cross-section profile and efficient method are developed for the vibration analysis of isotropic and orthotropic cylindrical shells having circumferentially varying profile of a cardioid cross-section expressed as an arbitrary function, under thermal gradient effect. The governing equations of orthotropic cylindrical shells with varying thermal gradient around its circumference are derived as a boundary-value problem and solved numerically as an initial-value problem, based on the framework of Flügge's shell theory, transfer matrix approach and Romberg integration method. As a semi-analytical procedure, the trigonometric functions are used with Fourier's approach to approximate the solution in the longitudinal direction and also to reduce the two-dimensional problem to one-dimensional one. The thermal gradient is assumed to arise due to the variation of Young's moduli and shear modulus, along the circumferential direction of the shell. The results are obtained to indicate the effects of cardioid cross-section on the natural frequencies and corresponding mode shapes in the thermal environment as well as the sensitivity of the vibration behavior to the thermal gradient ratio and the orthotropy of the shell is also investigated for different types of vibration modes. In general, close agreement between the obtained results and those of other researchers has been found.     

Stress Analysis for an Elastic Semispace with Surface and Graded Layer Coatings under Induced Torsion

In this paper, the axisymmetric torsional problem of a coating structure consisting of a surface coating, a functionally graded layer and a substrate under a rigid cylindrical punch is investigated. The coating and substrate are homogeneous materials with distinct physical properties while the intermediate layer is inhomogeneous with its shear modulus changing exponentially along the thickness direction. The Hankel integral transform technique is employed to reduce the torsional problem to a singular integral equation with a Cauchy kernel. The circumferential shear stress and displacement fields in the coating structure are calculated by solving the integral equation numerically. The results show that the stiffness ratio has significant effect on the distribution of the circumferential stress and displacement at the interface.     

刚性圆管中血液周期振荡流的切应力分布

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的压力梯度与切应力之间的关系式。在此基础上，详细讲座了圆管中轴向流速和切变率谐波的变化规律，指出流速谐波和切变率谐波的幅值都将随着谐波次数的增大而逐渐减小。为了使所得结果便于应用。文章通过管轴向中心线流速与压力梯度之间的关系式，进一步给出一种利用管轴向中心线流速计算管内切应力分布的简便方法。该方法用于检测活体血管内血液振荡流的切应力分布，具有操作简单，精度较高的优点。最后，以人体颈动脉为例，讨论血液周期振荡流的切应力的分布特性。发现在任意时刻，除了邻近管壁处切应力急剧增大到一定数值之外，沿管截面切应力分布相当均匀且接近于零，呈现出与定常流不同的切应力分布特征。     

A General Formulation of Stress Distribution in Cylinders Subjected to Non-Uniform External Pressure

This work presents a two-dimensional stress analysis for elastic solid cylinders subjected to combined loading. The loading is generally formed with a number of concentrated and partially distributed forces all applied radially on the outer surface. The distributed forces cause pressures with non-uniform intensity along the circumferential direction. The cylinder is assumed to be long so that a state of plane-strain is valid. To obtain the stress distribution for the problem of partially distributed forces a new approach is followed first introduced in this paper. It is based on the expressions formed after using the theory of simple radial stress distribution when point-forces are applied on the cylinder and leads to the solution after direct integration. The total stresses due to both concentrated and distributed forces are obtained using the method of superposition. Apart from its simplified formulation, this general solution is always preferable since it proved to have a great advantage. As a result of not containing Fourier series, it eliminates some problems of convergence of the series at the boundaries that appear due to the Gibbs phenomena when the boundary conditions are a discontinuous function. Numerical results are presented for some interesting cases of loading conditions. This revised version was published online in August 2006 with corrections to the Cover Date.     

扇形截面杆扭转问题的差分线法

导出了扇形截面杆扭转问题偏微分方程的差分线法常微分方程组, 并解析求解了该方程组, 得到了扭转应力函数的半解析解, 计算了扭转应力及扭转刚度. 计算过程中, 用追赶法计算 常微分方程组的特解, 用公式计算三对角矩阵的特征值与特征向量, 利用实对阵矩阵的特征 向量相互正交的特性避免矩阵求逆计算, 利用复化梯形公式计算扭转刚度. 整个求解过程在 角度方向离散微分方程和用复化梯形公式进行面积积分时引入了误差, 其他求解过程是精确 的. 计算结果与已有结果进行了对比, 显示了算法的正确性. 该算法对工程中扇形截面扭 转杆的设计有一定的实用价值.     

脉动血压对在体轴向极限强约束血管壁应力分布的影响

本文详细分析正弦脉动压力载荷对动脉管壁应力分布的影响。结果表明,对某确定时刻,包含在运动方程中的惯性项对血管壁应力的影响很小,可忽略不计;在体轴向极限强约束下,血管壁周向应力随时间的变化曲线与压力曲线同相位和同周期,而且振幅不随频率的快慢而改变。一个心动周期内,血管内、外壁处周向应力随时间变化的平均值只与脉动压力载荷的平均值有关,而振幅主要与脉压有关,在内壁处随平均压的改变有一定变化,但在外壁处受平均压的影响很小。     

Measurement of residual stress in a multi-layer semiconductor heterostructure by micro-Raman spectroscopy

Si-based multilayer structures are widely used in current microelectronics. During their preparation, some inhomogeneous residual stress is induced, resulting in com-petition between interface mismatching and surface energy and even leading to structure failure. This work presents a methodological study on the measurement of residual stress in a multi-layer semiconductor heterostructure. Scanning electron microscopy (SEM), micro-Raman spectroscopy (MRS), and transmission electron microscopy (TEM) were applied to measure the geometric parameters of the multi-layer structure. The relationship between the Raman spec-trum and the stress/strain on the [100] and [110] crystal orientations was determined to enable surface and cross-section residual stress analyses, respectively. Based on the Raman mapping results, the distribution of residual stress along the depth of the multi-layer heterostructure was suc-cessfully obtained.     

15×10~4m~3超大型油罐应力测试与数值模拟分析

兰州原油末站大型油罐群,是我国首次在饱和黄土地基修建的大型储油设施。依托其中一座15×104 m3超大型非锚固油罐,开展了现场充水测试罐壁静态应力的试验研究。通过粘贴在油罐罐壁的应变计,测试充水过程中罐壁应力的变化规律,并采用有限元对15×104 m3超大型油罐进行应力分析。测试结果表明:罐壁的环向应力随充水水位的增加基本呈线性关系。数值模拟计算表明,罐壁环向应力最大值发生在第二圈罐壁和第三圈罐壁相连接的位置。由于罐壁上部设置了抗风圈和加强圈,有效地控制了罐壁的径向位移,使罐壁环向应力和竖向轴向应力在加强圈和抗风圈附近发生波动。将有限元数值模拟计算的罐壁环向应力分布情况与实测应力进行比较,两者总体吻合较好。上述研究结果可为超大型储罐在黄土地基的设计和建造提供技术依据和设计参数验证。     

Scattering of guided waves by circumferential cracks in composite cylinders

A somewhat generalized numerical procedure is used in this paper to study the problem of wave scattering by circumferential cracks in composite pipes. The study is motivated by the need to develop a model for the quantitative, ultrasonic non-destructive evaluation of cracks in pipes. For this purpose, a stiffness-based Rayleigh–Ritz type approach is employed first to obtain the approximate wave numbers and wave modes. Using the wave function expansions of the incident and scattered fields in the axial direction and decomposing the problem into separate symmetric and anti-symmetric problems, a three-dimensional wave scattering problem is reduced to two, independent two-dimensional problems over the circular cross-section. Both these problems can be reduced further to quasi-one-dimensions by discretizing the cross-section into finite elements and using a transfer matrix approach in the circumferential direction. This simplification greatly reduces the computational time. A comparison of the results for an isotropic pipe demonstrates the reliability and accuracy of the modified numerical procedure. Numerical results for the reflection and transmission coefficients of different incident wave modes are also presented for a 2-ply composite pipe with a crack. The crack may have an arbitrary circumferential length and radial depth. Simple extrapolations from one wave to another wave, separately incident on a crack, are demonstrated to be impossible due to different mode conversions by the crack.     

永磁激励下磁流变安全联轴器物理场数值仿真计算与分析

设计了一种新型磁流变安全联轴器,该联轴器以磁流变胶作为传力介质,以Halbach永磁排列作为磁场激励源。在COMSOL Multiphysics环境下建立了三维有限元分析模型;利用Bingham磁致本构模型对自行研制的磁流变胶的剪切屈服应力和粘度进行最小二乘5次多项式拟合,得到了剪切屈服应力和粘度随磁通密度的变化曲线参数;并将磁流变胶的拟合参数及其磁化特性嵌入COMSOLMultiphysics有限元计算环境中,最终得到磁流变胶所在区域的磁通密度云分布以及两个指定位置的剪切屈服应力和粘度在极坐标下的周向分布。研究结果表明:安全联轴器里层区域的磁通密度分布明显具有Halbach排列特点和明显的区域分布特性;磁通密度、剪切屈服应力、粘度在两个指定位置的周向分布具有明显的对称性;可以通过去掉外层磁流变胶所在区域来达到结构的小型化和轻量化,也能够保证联轴器的传递扭矩不发生较大幅度的降低。本研究能够在联轴器的设计阶段提供一定的指导。     

On the physics of viscoplastic fluid flow in non-circular tubes

Flow of Bingham plastics through straight, long tubes is studied by means of a versatile analytical method that allows extending the study to a large range of tube geometries. The equation of motion is solved for general non-circular cross-sections obtained via a continuous and one-to-one mapping called the shape factor method. In particular the velocity field and associated plug and stagnant zones in tubes with equilateral triangular and square cross-section are explored. Shear stress normal to equal velocity lines, energy dissipation distribution and rate of flow are determined. Shear-thinning and shear-thickening effects on the flow, which cannot be accounted for with the Bingham model, are investigated using the Hershey-Bulkley constitutive formulation an extension of the Bingham model. The existence and the extent of undeformed regions in the flow field in a tube with equilateral triangular cross-section are predicted in the presence of shear-thinning and shear-thickening as a specific example. The mathematical flexibility of the analytical method allows the formulation of general results related to viscoplastic fluid flow with implications related to the design and optimization of physical systems for viscoplastic material transport and processing.