Estimation of variance components of local stereological volume estimators: a pilot study

Local stereological techniques can be used for particle volume estimation based on information collected on a section plane through a reference point of the particle. We present methods for variability estimation of the local stereological volume estimators. This variability arises during the stereological estimation procedure and in the particle population. Both of these components can be estimated separately from planar sections. Our aim is to give a preliminary analysis of the possibility to include the particle structure interaction into the estimation procedure. For this reason, not only the section profiles, but also their locations, have to be recorded. The methods are applied for the sectional data obtained from neurons in the hippocampal brain region subiculum of four 3-month-old male Wistar rats. The proposed procedure enables one to obtain information about particle volume distribution.     

A rigid-plastic finite-element formulation for the analysis of general deformation of planar anisotropic sheet metals and its applications

General three-dimensional deformation of a planar anisotropic rigid-plastic sheet metal which obeys Hill's quadratic yield function is considered in the present analysis. The explicit expressions of the yield criterion and the related equations are given in the surface curvilinear co-ordinate system. A convective co-ordinate system is used in order to take into account the effect of geometric change during one step in the incremental analysis. The expression of the effective strain increment during one step is obtained in closed form by introducing assumptions on the deformation path and by proper consideration of the rotation of the axes of anisotropy during deformation. Considering the equilibrium at the deformed state, a variational formulation is derived to determine the deformation during a step. The corresponding finite-element equations are found in order to analyze the general deformation of planar anisotropic sheet metals. Two computational examples are chosen and computed by using the developed FEM program in order to verify the present formulation. The flange deformation in deep drawing of a circular diaphragm of planar anisotropy is analyzed and compared with the existing solution. The effects of planar anisotropy in the circular diaphragm bulge test are also investigated.     

Effect of planar anisotropy on wrinkle formation tendencies in curved sheets

Wrinkle formation tendencies in the form of short-wavelength shallow buckling modes are investigated for sheet materials exhibiting planar anisotropy. The critical state for the onset of these short-wavelength shallow modes are determined from plastic bifurcation theory. A local analysis is performed by considering the current deformed state of a sheet element in a doubly-curved, biaxial plane stress state. The planar anisotropy is prescribed using recently proposed anisotropic yield criteria. Parametric studies are performed to assess the effects of the various material and geometric parameters on wrinkling.     

The effect of anisotropy on wrinkling of tube under rotary draw bending

Rotary draw tube bending is one of the most complex tube forming processes subject to different process parameters such as material properties and geometry. This process is being practiced in more and more applications in industry due to its high efficiency, high forming precision and quality. However, improper process parameters can lead to wrinkling which restrict the thin walled tube bending. Therefore, the prediction and prevention of wrinkling is very important. Despite its importance, the effect of anisotropy on the occurrence of wrinkling was not considered in the literature up to now. In this investigation, a quantitative study on the wrinkling of thin walled tube bending is carried out through a finite element model of the process using velocity integral parameter, which is used for the detection of wrinkles. The other methods usually warn the wrinkling initiation with no precise location prediction. In addition, the effects of some process parameters, specially normal and planar anisotropy on the tube wrinkling are investigated. It is shown that increasing normal and planar anisotropy (increasing r0 and r90 values) result in a decrease in tube wrinkling.     

A reappraisal of the wedge-drawing test

The wedge-drawing test is re-evaluated in the light of improved methods of lubrication. The test is used to study the radial drawing of anisotropic sheet materials and the experimental results correlate well with theoretical predictions based on the orthotropic theory of plasticity. In the theoretical analysis planar anisotropy is considered as well as normal anisotropy. The materials tested were soft and half-hard aluminium, soft 70/30 brass, killed steel and titanium. It is clearly demonstrated that the wedge-drawing test does not simulate the instability conditions existing in deep-drawing. While in deep-drawing increasing R-values can lead to large increases in limiting drawing ratio, this is not the case in wedge-drawing.     

Estimation of linear functionals by maximum likelihood*

A classical problem of stereology is estimation of linear functionals of particle size distributions from intersections on planar probes. The maximum likelihood method of estimation is outlined and compared with classical linear methods and with numerical interpolation methods. A population of spherical particles is distributed in an infinite matrix with position defined by a Poisson field. Diameters of circular intersections on a planar probe constitute a generalized Poisson process. Maximum likelihood theory fits a parametric family of planar density functions to observed diameter frequency data. The integral of an appropriate kernel with respect to the fitted density function is the linear functional estimate. The approach can handle composite data involving observation at several magnifications. Estimation of complementary cumulative density of pores in uranium oxide fuel pellets illustrates the maximum likelihood method of data collected with two microscopes at four magnifications.     

Comparative study of dynamic analysis techniques in vehicle simulation

Several dynamic analysis techniques are compared with a planar vehicle model. Cartesian formulation, suspension superelement technique, velocity transformation, and recursive formula are compared. The relation between the recursive formula and velocity transformation is investigated. When those techniques are applied to a planar vehicle with two independent suspensions, the efficiency of those methods was compared. The computational efficiency of the recursive formula was higher than those of other methods for the specific planar vehicle example.     

Prediction of forming limits using Hosford's modified yield criterion

A new generalized anisotropic yield criterion has been suggested by Hosford. This criterion has been used in prediction of forming limits by Graf and Hosford using M-K analysis for a material with normal anisotropy. In this paper the effect of planar anisotropy has been incorporated and the procedure for calculation of forming limits has been modified using the approach suggested by Parmar and Mellor. The results are compared with those of Graf and Hosford in the case of planar isotropy to validate the model and procedure. The results are also compared with the predictions of the M-K model using Hill's old and new (after Parmar and Mellor) yield criteria as well as experimental values obtained under conditions of both in-plane and punch stretching.It is observed that the effect of planar anisotropy is negligible while the predictions are strongly dependent on exponent “a” (exponent in yield criterion). Predictions with a = 5, 6 or 8 match the experimental results much better than predictions using the M-K model with Hill's old criterion, or even the new criterion used by Parmar and Mellor.     

Two-dimensional fast Fourier transform and power spectrum for wear particle analysis

Statistical parameters, such as R_a and R_q, have been widely used to investigate the roughness of wear particle surfaces in the literature. It has been reported that wear particle analysis based only on numerical characterization is often insufficient to distinguish certain types of wear debris. In this study, two-dimensional fast Fourier transform, power spectrum and angular spectrum analyses are applied to describe wear particle surface textures in three dimensions. Laminar, fatigue chunk and severe sliding wear particles, which have previously proven difficult to identify by statistical characterization, have been studied. The results show that spectral analysis effectively identifies the surface texture pattern (e.g. isotropy or anisotropy) and can be applied to classify these three types of wear particles.     

Effect of sheet anisotropy on the wear in deep-drawing process of a cylindrical cup

In the present investigation, the deep-drawing process of a cylindrical cup is simulated using the finite element method, with the aim of investigating the effect of sheet anisotropy on wear depth in the die which is exposed to the most severe tribological condition in this process. Both the blank and the die are assumed to be deformable. For the blank, the elasto-plastic behavior is considered, while the die material is assumed to be elastic. The sheet is anisotropic, so Hill quadratic yield criterion is employed. Two kinds of anisotropy, i.e. planar anisotropy and normal anisotropy are considered in this study. To study the effects of sheet anisotropy on the wear depth on the die shoulder qualitatively a parameter called relative wear depth (RWD) is introduced. Different distributions of Lankford coefficients are chosen and several conclusive results are presented.     

X射线激光自支撑Mo滤光膜的制备及特性研究

用直流平面磁控溅射方法在抛光玻璃衬底上淀积 Mo薄膜 ,将薄膜在真空环境中进行热处理 ,用扫描探针显微镜 ( SPM)方法观察了薄膜的表面形貌 ,X-射线衍射方法分析了薄膜中应力各向异性特征及其与淀积时溅射气体压强和真空热处理的关系。发现薄膜中晶粒具有明显的择优取向 ,内应力沿径向对称分布 ,切向应力比径向应力更具有压应力特性 ,应力的各向异性特征与溅射原子的入射方向有关。真空热处理对薄膜中压应力的释放作用不明显 ,然而能有效地释放薄膜中的张应力。用 HF酸腐蚀衬底的方法制备了自支撑 Mo薄膜 ,发现脱膜前后薄膜表面微观形貌未产生大的变化。     

Debonding of particles in anisotropic materials

Effects of geometrical anisotropy as well as plastic anisotropy are studied in relation to debonding of rigid inclusions embedded in a metal. Full finite strain analyses are carried out for a cell model under plane strain conditions, and the average overall stress–strain response of the cell is calculated. For increased triaxiality the onset of matrix–particle debonding occurs at a significantly reduced overall strain of the cell. The point of initial debonding is nearly unaffected by variations of the shape of the inclusions, but complete debonding occurs earlier if the inclusions are elongated perpendicular to the main tensile direction. The same effect is observed, if the spacing of the inclusions is larger in the main tensile direction than in the transverse direction. For the orientations of plastic anisotropy considered, the debonding initiates and grows at a much lower overall strain than if the material was plastically isotropic. It is found for mixed geometrical and plastic anisotropy, that plastic anisotropy promotes debonding initiation, whereas the occurrence of complete matrix–particle debonding is quite sensitive to the type of geometrical anisotropy.     

基于粒子系统与纹理映射的空气分离可视化模拟

空气分离工艺流程复杂,导致流体在机械装备内的流动难以模拟与表达。为实现空气分离系统吸附、换热与精馏等工艺过程的可视化,提出了一种基于粒子流源与纹理映射的空气分离可视化模拟方法：采用关键帧间坐标系递推变换,描述运动部件位置及运动的变化;采用自定义粒子流源,模拟流体的传热传质属性;采用多尺度纹理映射,描述流体的流动迹线。开发了基于虚拟现实技术的可视化系统,实现了空气分离的性能模拟与可视化。     

Measuring through the microscope: Development and evolution of stereological methods

Obtaining, by means of microscopy, meaningful measurements pertaining to spatial structures requires methods which allow three-dimensional quantitative information to be derived from the reduced information available on the two-dimensional flat sections of the structure. The most powerful methods to that effect are those of stereology which are based on mathematical principles. This paper reviews the early invention of these methods, which sought to solve practical problems, and their further evolution as more rigorous mathematical foundations were developed. It is demonstrated that stereological methods are essentially sampling methods and that newer trends provide new and sound solutions to old and elusive problems, such as anisotropy or particle number and size.     

平面2R机器人中的混沌运动现象

利用混沌数值分析法中的Poincare截面积法和最大Lyapunov指数分析法，对平面2R机器人基于多变量比值微分控制时的混沌运动现象进行了研究。分析出该动力系统由倍周期倒分岔进入混沌运动状态；并获得了混沌运动产生的参数条件。所得结果对进一步改善机器人的混沌控制和动力学特性具有指导意义。     

Multiobjective optimization for force and moment balance of a four-bar linkage using evolutionary algorithms

In this study, force and moment balance of a planar four-bar linkage is implemented using evolutionary algorithms. In the current problem, the concepts of inertia counterweights and physical pendulum are utilized to complete balance of all mass effects, independent of input angular velocity. A proposed multiobjective particle swarm optimization, and non-dominated sorting genetic algorithm II are applied to minimize two objective functions subject to some design constraints. The applied algorithms produced a set of feasible solutions called pareto optimal solutions for the design problem. Finally, a fuzzy decision maker is utilized to select the best solution among the obtained pareto solutions. The results show that optimal solutions minimize the weights of applied counterweights and eliminate both shaking forces and moments transmitted to the ground, simultaneously.     

A design-based proof of Wicksell's integral equation

Wicksell's integral equation (1925) describes, for an aggregate of spherical particles, the relation between the distribution of sphere diameters and the distribution of diameters of circular profiles observed on a planar section. Usually, this integral equation is proved under the assumption that the particle aggregate is a realization of a stationary stochastic process while the position of the planar probe is allowed to be arbitrary. In this note, it is shown that, under the alternative assumption that diameters of circular profiles are sampled by means of a planar FUR (fixed orientation uniform random) probe, Wicksell's equation holds for a deterministic aggregate of spherical particles with arbitrary positions and sizes. Since the proof is based on the randomness generated by the sampling (the design), the proof may be characterized as design-based. It can thus be concluded that Wicksell's equation may be applied to any aggregate of spherical particles if diameters are sampled by means of random (FUR) planar probes.     

Finite element method for sheet forming based on an anisotropic strain-rate potential and the convected coordinate system

A variational formulation and the associated finite element (FE) equations have been derived for general three-dimensional deformation of a planar anisotropic rigid-plastic sheet metal which obeys the strain-rate potential proposed by [11.]. By using the natural convected coordinate system, the effect of geometric change and the rotation of planar anisotropic axes were efficiently considered. In order to check the validity of the present formulation, a cylindrical cup deep drawing test was modeled for a 2008-T4 aluminum alloy sheet sample. Eating simulations were performed and planar anisotropic material properties were experimentally determined. Even though quantitative agreement was not fully achieved, reasonably good agreement was found between the FE simulation and the experiment in thickness strain distribution and caring. No numerical difficulty due to planar anisotropy was encountered, and the computational procedure was found to be very stable, requiring only moderate computational time. The results have shown that the present formulation for planar anisotropic deformation can provide a good basis for the analysis of sheet metal forming processes for planar anisotropic materials, especially for aluminum alloy sheets.     

ADJACENT MARTIX METHOD OF IDENTIFYING ISOMORPHISM TO PLANAR KINEMATIC CHAIN WITH MULTIPLE JOINTS AND HIGHER PAIRS

The adjacent matrix method for identifying isomorphism to planar kinematic chain with multiple joints and higher pairs is presented. The topological invariants of the planar kinematic chain can be calculated and compared by adjacent matrix. The quantity of calculation can be reduced effectively using the several divisions of bars and the reconfiguration of the adjacent matrix. As two structural characteristics of adjacent matrix, the number of division and division code are presented. It can be identified that two kinematic chains are isomorphic or not by comparing the structural characteristics of their adjacent matrixes using a method called matching row-to-row. This method may be applied to the planar linkage chain too. So, the methods of identifying isomorphism are unified in the planar kinematic chain that has or hasn't higher pairs with or without multiple joints. And it has some characters such as visual, simple and convenient for processing by computer, and so on.