受圆柱面约束螺旋杆伸展为直杆的动力学分析

以大型空间结构的可伸展机械臂从折叠状态被释放的伸展过程为工程背景, 分析受圆柱面单面约束的弹性螺旋杆在惯性力作用下恢复为直杆的动力学过程. 对弹性杆空间大变形的分析不允许利用小变形假设进行简化. Kirchhoff动力学比拟理论是研究细长弹性杆超大变形的有效工具. 但由于圆柱面约束的存在, 不能直接利用无分布力的Kirchhoff 模型, 而必须在方程中增加分布的约束力. 以表述截面姿态的欧拉角为变量, 建立受圆柱面约束弹性杆的动力学方程. 在圆柱面约束条件下, 认为弹性杆在伸展过程中仍维持半径不变的螺旋线形态, 仅螺旋线倾角和杆的扭率随时间变化. 对简化后的非线性微分方程导出解析积分, 以描述伸展运动的动力学过程, 导出螺旋杆伸展速度的变化规律, 以及从初始状态伸展为直杆所需时间的简明的解析形式计算公式.      

弹性杆盘绕折叠的力学分析

以可伸展空间结构元件的盘绕折叠过程为工程背景,分析受圆柱面单面约束的弹性直杆变形为螺旋杆,最终压缩为叠放的平面圆环的变形过程.对此空间大变形的分析不允许利用小变形假设进行简化.由于约束力的存在,也不能直接利用忽略分布力的Kirchhoff弹性杆方程.本文以表述截面姿态的欧拉角为变量,建立受圆柱面约束弹性杆平衡的非线性方程.利用方程的初积分计算杆截面的内力和力矩.忽略盘绕过程的惯性效应,将参数连续改变的螺旋线状态作为杆盘绕过程中的准平衡状态.导出为实现盘绕过程需要施加的轴向压力和扭矩随螺旋角的变化规律.根据一次近似稳定性理论分析得出:两端铰支弹性杆当相对扭率为零时不能保证螺旋线平衡的稳定性.若杆端支承允许存在相对扭转,则轴向压力和扭矩按文中确定的规律变化时可以保证盘绕过程的稳定性.     

非圆截面弹性细杆的螺旋线平衡及稳定性

本文研究端部受力和力矩作用，且存在初曲率和初扭率的非圆截面弹性细杆的螺旋线平衡及其稳定性。描述弹性细杆平衡状态的Kirchhoff方程存在与杆的螺旋线平衡状态相对应的特解。直杆和圆环杆为螺旋线状态的两种特例。文中分析了螺旋线的几何特性与作用力和力矩之间的相互关系，并导出螺旋线平衡的一次近似解析形式稳定性判据。分析表明，松弛状态下弹性杆可处于螺旋线状态，直杆只有在轴向压力的作用下才能保持螺旋线平衡。无初曲率和初扭率弹性杆的螺旋线平衡稳定性必要条件是杆截面绕副法线轴的抗弯刚度大于或等于绕法线轴的抗弯刚度。此条件也适用于带初扭率的圆环杆及更普遍情形。无初曲率和初扭率的圆截面杆的螺旋线平衡恒稳定。     

纯弯曲下薄壁圆柱壳屈曲的非线性分析

为解决薄壁圆柱壳在纯弯曲下由于横截面的椭圆化而引起的屈曲几何非线性问题. 基本假设是改良的Brazier 简单理论,把圆柱壳的纯弯曲变形简化成一个两阶段的过程,分别求得纵向弯曲变形应变能和横截面变形应变能,然后利用最小势能原理求出作用力矩与杆端旋转角度的关系,最后分析可知:壳体长度参数越小,对应的圆柱壳壁越薄,非线性的影响越大;剪力大小参数越小,边界条件对椭圆化变形影响越小,非线性的影响越大.     

杆系静不定结构的变形协调条件

本文用数学方法建立杆的变形与节点位移的解析关系式，利用这个解析式，可方便地求出复杂情况下杆系结构的变形协调方程     

重杆在墙角间的平衡问题

 重杆能否仅依赖摩擦力在墙角上保持平衡？本文利用力的平衡条件,及几何关系,并运用摩擦角和自锁的概念,求出了杆平衡的充分条件.     

钱令希教授和庙岭村的水利工程

以平面三角桁架为例,通过放弃应用原始尺寸原理,即在变形后的位形上建立平衡方程,并结合变形协调关系考虑几何非线性,得到了桁架各杆轴力的解,进而给出各杆应力和中间铰位移以及各杆转角的解.最后给出了钢质、木质和橡胶杆桁架的3个算例,还得到了应力的相对误差估计式.分析结果表明应用原始尺寸原理所带来的杆内应力的相对误差与杆内名义应变相同,对于金属桁架在满足强度条件的范围内,应用原始尺寸原理所带来的误差是可以忽略的,而对于橡胶桁架来说其误差是需要考虑的.     

关于原始尺寸原理的适用性

以平面三角桁架为例,通过放弃应用原始尺寸原理,即在变形后的位形上建立平衡方 程,并结合变形协调关系考虑几何非线性,得到了桁架各杆轴力的解,进而给出各杆应力和 中间铰位移以及各杆转角的解. 最后给出了钢质、木质和橡胶杆桁架的3个算例,还得到了 应力的相对误差估计式. 分析结果表明应用原始尺寸原理所带来的杆内应力的相对误差与杆 内名义应变相同,对于金属桁架在满足强度条件的范围内,应用原始尺寸原理所带来的误差 是可以忽略的,而对于橡胶桁架来说其误差是需要考虑的.     

轴向受压螺旋杆的平衡稳定性

在Kirchhoff动力学比拟基础上讨论端部受轴向压力作用的圆截面弹性细杆的螺旋线平衡稳定性问题．弹性杆的平衡状态由Euler角描述的弹性杆平衡方程的特解确定．从Lyapunov或Euler的不同稳定性概念出发,对弹性杆的平衡稳定性的判断可得出不同的结果．根据一次近似扰动方程判断,弹性杆的螺旋线状态和圆环状态恒满足Lyapunov稳定性条件．但螺旋杆在轴向压力到达临界值时,圆环杆在扭转数到达临界值时将产生屈曲而丧失Euler稳定性．导出临界载荷和临界扭转数的计算公式．螺旋杆的临界载荷取决于螺旋线的高度和螺旋角：螺旋角趋近于π／2时螺旋杆转化为带扭率的直杆,其临界载荷的极限值与压杆的Euler载荷一致．文中对两类不同稳定性概念的区别和联系作出解释．     

受圆柱面约束弹性杆的平衡与稳定性

讨论受圆柱面约束的圆截面弹性杆的平衡与稳定性。以描述截面姿态的欧拉角为变量,建立受约束弹性杆的平衡方程。利用方程的初积分导出约束力、截面内力及挠性线的解析表达式。作为特殊的平衡状态,讨论杆的螺旋线平衡的存在条件。用相平面法分析螺旋线平衡的稳定性,导出解析形式的稳定性条件。     

Development of a bluff body wake under the combined influence of curvature and pressure gradient

The present experimental investigation deals with the behaviour of a wake generated by a square cylinder developing in a curved diffuser, a curved duct, a straight duct and a straight diffuser having a same pressure gradient as in the curved diffuser. This enables a systematic study of the effects of curvature and pressure gradient on wake development. It is seen that the curvature makes the wake asymmetric; the wake half width increases on the inner side and decreases on the outer side; the inner side being the region between the centreline and the wall closer to the centre of curvature and the outer side being the region between the centreline and the other wall. It causes a higher entrainment in the inner side as compared to the outer side. An adverse pressure gradient, on the other hand, causes a higher wake growth and velocity defect but reduces the rate of decay of the velocity defect. These are not altered significantly when the curvature and pressure gradient effects are combined. The curvature enhances the Reynolds stresses and the kinetic energy on the inner side and suppresses them on the outer side which makes their profiles asymmetric. These profiles become more and more asymmetric with increase in the streamwise distance. When the effects of curvature and adverse pressure gradient are combined, the profiles become further asymmetric.Department of Aerospace Engineering     

Two-dimensional numerical calculation of the flow field about a scoop inlet by the piecewise linear method

The piecewise linear method (PLM) based on time operator splitting is used to solve the unsteady compressible Euler equations describing the two-dimensional flow around and through a straight wall inlet placed stationary in a rapidly rotating supersonic flow. The PLM scheme is formulated as a Lagrangian step followed by an Eulerian remap. The inhomogeneous terms in the Euler equations written in cylindrical coordinates are first removed by Sod's method and the resulting set of equations is further reduced to two sets of one-dimensional Lagrangian equations, using time operator splitting. The numerically generated flow fields are presented for different values of the back pressure imposed at the downstream exit of the inlet nozzle. An oblique shock wave is formed in front of the almost whole portion of the inlet entrance, the incoming streamlines being deflected towards the higher pressure side after passing through the oblique shock wave and then bending down to the lower pressure side. A reverse flow appears inside the inlet nozzle owing to the recovery pressure of the incoming streams being lower than the back pressure of the inlet nozzle.     

An experimental investigation of residual stress in quenched flat plates

The residual stresses induced in a quenched flat plate are measured experimentally. A flat plate approximating the theoretical infinite flat plate, after being heated to a uniform temperature, is quenched uniformly from both sides in order to cause a residualstress distribution. The residual stresses are obtained by successively grinding the plate on one side and measuring the resulting strains on the opposite side. Experiments are performed on plates experiencing no phase transformation—316 stainless steel. Comparison of results is made with the predicted stress distributions from the analysis of Landau and Weiner, which is derived from the time-temperature history of the plate during its quench.     

Flow instabilities during annular displacement of one non-Newtonian fluid by another

This paper describes an experimental setup for axial laminar flow of liquids in the annulus between two eccentered cylinders. The design uses a conductivity method for measuring peak axial velocities around the annulus, and for the determination of displacement efficiency when displacing one fluid by another (displacement efficiency being defined as the ratio of volume of displaced fluid removed from the annulus, to the volume of the annulus, after a given number of annular volumes have been pumped). In an eccentric annulus, lower axial velocity in the narrow side produces “channeling” of the displacing fluid in the wide side and reduces the displacement efficiency. A positive density contrast between the two fluids can increase the efficiency by promoting azimuthal flow of the (denser) displacing fluid towards the narrow side. In this paper we report that gravity driven azimuthal flow is prone to severe instabilities which accelerate the displacement process but may leave behind an immobile strip of the displaced fluid in the narrow side.     

洗衣机节水技术研究及其力学原理

利用全自动洗衣机高速脱水时产生的向心力，将衣物上的水沿脱水桶壁向下排出，由此设计了节水型洗衣机，并对这种洗衣机进行了力学原理分析，给出了关键结构参数，以及关键部件——排水阀的设计．新型洗衣机结构简单，洗涤容量进一步扩大，减少了水和洗涤剂的用量，有利于环境保护．     

Stress distribution and wrinkling of webs under non-uniform and asymmetric edge loading

Non-uniform edge loading can cause unwanted wrinkling of a web. Here, Airy stress functions are obtained by a modified Fourier series method for webs under non-uniform and different edge loading on each side. The stress distributions of a web under non-uniform edge loading only on one side are subjected to the effect of Saint-Venant’s principle. For the web of small aspect ratio under non-uniform edge loading, the stress distribution converges to a uniform distribution or a linear distribution with both the resultant force and the resultant moment being equal to those of the applied loading. Conditions of wrinkling and the corresponding wrinkling modes of a web are found when the edge loadings are different on each side. The non-uniformities and shapes of the applied edge loadings result in different wrinkling conditions. Moreover, the non-uniformities together with the shapes of the applied edge loadings on each side affect the wrinkling conditions.     

Kinematics of the motorcar body side deformation process during front-to-side vehicle collision and the emergence of a hazard to car occupants

The kinematics of the process of deformation of the motorcar body side in the culminating phase of a front-to-side vehicle collision has been examined as a possible basis for analyzing and modeling the process of emergence of a hazard to car occupants during a road accident. The course of such accidents has a complex nature and their models are necessarily based on the approximation of non-linear elastoplastic characteristics of impact processes, especially during the transition from the compression phase to the restitution phase of the deformation process. For such characteristics to be obtained, a lot of experimental tests have to be carried out. This paper addresses the short-duration processes with a high degree of complexity.

A front-to-side motorcar collision model has been prepared, which made it possible to analyze the process of deformation of the car body side and the emergence of a hazard and injuries to car occupants. The results of calculation of the deformation rate and range in various car body zones, velocity of the test dummy placed on driver’s seat and velocity of possible dummy’s impact against the car body side being deformed may be taken as a basis for designing effective occupant protection systems. The kinematics of the phase of vehicle contact and deformation process was modeled with taking into account results of experimental tests, including the curves characterizing the largely non-linear processes that are decisive for the deformation of the car body side. The deformation processes analyzed on these grounds showed at the same time the range of penetration of the deformed body part into the car interior, which causes a hazard to vehicle occupants. The calculation results have shown e.g. that the car body side is deformed to a depth of 0.2 m as quickly as within 0.02–0.03 s. At such a car body side deformation range, the car body part being deformed hits occupant’s body in his/her hips and pelvis area with a velocity of about 6 m/s.

     

On the stable posture of a pair of parallel cylinders in a uniform flow *

The stable posture of a pair of parallel circular cylinders in a uniform flow was experimentally studied when it was free to rotate about an axis at the middle of the two cylinders. The cylinder pair comes to rest facing the oncoming flow side by side, the line connecting the centers of the two cylinders being perpendicular to the flow, when s/d = 0.5, where s is the distance between the center of rotation and the central axis of each cylinder and d is the diameter of the cylinder. When s/d = 1.0 or 1.5, the cylinder pair is stable both in tandem, with one cylinder behind the other, and in side-by-side arrangements to the oncoming flow. When s/d 2.0, the cylinder pair is stable only in tandem arrangements.     

Photoelastic determination of stresses in the tube plate of a 70-mw steam generator

This article describes the examination, by three-dimensional photoelasticity, of the tube plate of a sodium steam generator. The tube plate is flat on the side of the tube bundle (121 tubes) and spherical (concave) on the other side. The photoelastic model was made by precision casting, there being no glued joints at the points which are important from the point of view of stresses, such as the tube-tube plate junctions. Both the stress distribution along important sections and the stress concentrations in different types of tube-tube plate junctions due to the internal pressure were determined. The investigation described in this article was carried out in the framework of the Association—Euratom TNO/RCN on Fast Reactors, on behalf of the TNO—Neratoom Sodium Technology Project.     

Experimental unsteady flow study in a patient-specific abdominal aortic aneurysm model

The velocity field in a patient-specific abdominal aneurysm model including the aorto–iliac bifurcation was measured by 2D PIV. Phase-averaged velocities obtained in 14 planes reveal details of the flow evolution during a cycle. The aneurysm expanding asymmetrically toward the anterior side of the aorta causes the generation of a vortex at its entrance, covering the entire aneurysm bulge progressively before flow peak. The fluid entering the aneurysm impinges on the left side of its distal end, following the axis of the upstream aorta segment, causing an increased flow rate in the left (compared to the right) common iliac artery. High shear stresses appear at the aneurysm inlet and outlet as well as along the posterior wall, varying proportionally to the flow rate. At the same regions, elevated flow disturbances are observed, being intensified at flow peak and during the deceleration phase. Low shear stresses are present in the recirculation region, being two orders of magnitude smaller than the previous ones. At flow peak and during the deceleration phase, a clockwise swirling motion (viewed from the inlet) is present in the aneurysm due to the out of plane curvature of the aorta.