Intensity, slope and curvature discontinuities in loading distributions at the contact of two plane bodies

The optical method of caustics was used for the evaluation of intensity, slope and curvature discontinuities of the most general load distribution along a straight boundary in a semi-infinite plane simulating the elastic contact of two bodies under conditions of generalized plane stress. The load distribution was assumed as composed of normal as well as tangential loads.A simple procedure based on the geometric properties of caustics formed at the vicinity of such discontinuities in loading was developed, which yielded all the necessary information for the evaluation of such discontinuities. Interesting properties related to the shape, position and orientation of the caustics were established. Thus, a simple experimental procedure was developed for measuring the influence of friction along the contact area of two bodies.     

Method of caustics for the study of cracked plates made of viscoelastic materials

The optical method of caustics was used for the evaluation of the stress intensity factor at the crack tip in a viscoelastic plate made of polycarbonate of bisphenol A and containing a single external crack under conditions of generalized plane stress. It was assumed that the crack developed in a linear viscoelastic material. The reflected rays from both lateral faces, as well as the transmitted rays of a normally incident light beam were significantly dispersed at the close neighborhood of the crack tip because of the excessive lateral constraint and the strong variation of the refractive index, and concentrated along singular curves (caustics) at some distances from the plate. The reflected caustics formed two branches. While the internal branch, which was formed by reflections from the front face, depended only on the elastic modulus (E) and Poisson's ratio (v) of the material, the external branch, formed by reflections from the rear face, depended on E and v, as well as on the refractive index of the material (n). The transmitted rays formed the same type of caustic as that which was formed by reflections from the rear face, but with a different size.

By studying the relative position and shape of the two reflected branches and their variation with time, information was derived concerning the viscoelastic state of the material at fracture. The transmitted light caustic was used as a check on the results.

A series of viscoelastic tests in pure tension at various stress and strain levels yielded the variation of the mechanical (E, v) and optical (n, c_r, c_f) properties of the material with applied stress and strain. The values of these quantities at each stress level allowed the plotting of the relative positions of the two branches of the reflected caustics. Comparison of the actual position of the caustics at the crack tip with the caustic nomogram yielded the viscoelastic behavior of the material during the progress of loading. It was shown that by increasing the loading mode a strong viscoelastic behaviour was apparent which influenced considerably the fracture mode of the plate.     

Error analysis in evaluating stress intensity factors by reflected caustics

Based on the general theory of errors, a detailed analysis of errors in determining the stress intensity factors by the method of reflected caustics was developed.A classification of errors with respect of their sources, as well as their influence on the experimentally determined value of stress intensity factors in cracked plates was undertaken. A practical guidance was given for minimising the individual or global errors of the optical set-up used by the method of caustics.Finally, the influence of the optical magnification factor on the size of the caustics was also analysed and an optimal choice of the optical set-up was indicated.     

Ductile fracture in glassy polymers

The optical method of caustics was used to study the highly deformed region at the crack tip of a tension plate made of polycarbonate (PCBA) up to fracture. This polymer was selected for its typical quasi-plastic behaviour. The modified Dugdale-Barenblatt (D-B) model was used in order to take into account the influence of the non-linear region of quasi-plastic behaviour of PCBA. Furthermore, it has also been observed that the tensile specimens of PCBA were curved significantly before fracture and this phenomenon is typical of all ductile materials. Comparison of the caustics formed from reflected and transmitted rays allowed the accurate evaluation of the curvature of the cracked plate during loading. The influence of curvature being excluded, the remaining parts of the caustics were related to the stress distribution at the crack tip. The size and the dimensions of the caustics were fitted into one of the six typical stress configurations in the plastic zones studied by the modified Dugdale-Barenblatt model and the form of stress distribution in the plastic zone for each loading step was determined. It was shown that the modified D-B model is capable of describing the plastic behaviour in cracked plates made of ductile materials. Furthermore, the method of caustics was capable of evaluating the influence of curvature of the cracked plate during loading.     

The reflected caustics method for the evaluation of mode III stress intensity factor

The optical method of reflected caustics, which has been applied to the evaluation of stress intensity factors in cracked plates deformed under mode I and II, is extended in this paper to the evaluation of the same factor in cracked plates subjected to mode III deformation. It is shown that the method of reflected caustics is capable of detecting and evaluating this factor, whereas all the other experimental methods, i.e. photoelasticity, holographic interferometry and especially the method of transmitted caustics are incapable to yield this quantity. Based on the first-order approximation of the elastic solution around the crack tip and on Sneddon's formulas, the theory of formation of the reflected caustics is developed and the characteristic geometric properties of this envelope curve are defined. It is shown that this envelope is again a generalized epicycloid, whose characteristic dimensions are directly related to K_III. Experimental evidence with specimens made of optically isotropic materials (plexiglas), elastically loaded, has corroborated the theoretical results.     

Symmetric bending of cracked plates studied by caustics

The optical method of reflected caustics was applied to the study of singularities in the stress field appearing at the crack tip of symmetric plates containing a symmetric crack and submitted to bending loads. The method of caustics was used in connection with the most effective plate theories, that is the theories of Kirchhoff-Williams and Reissner-Sih as they apply to problems of cracked plates.     

Effects of non-singular stress terms and birefringent coefficient on caustics under various fracture mode loadings

This report investigates the effect of the first few higher-order, non-singular stress terms and the coefficient of optical anisotropy on the shapes of the initial curves and the caustics in birefringent plates under Mode I and Mode II static loading conditions. For Mode I and Mode II loading conditions, Williams stress function is employed to generate various theoretical initial curves and caustics. Some experimentally obtained double caustics are compared to the theoretically generated double caustics. The agreement is found to be good as far as the shapes of caustics are concerned although it is not easy, if not impossible, to distinguish the effect of each higher-order terms.     

On the experimental solution of plane elasticity problems by the method of caustics

The optical method of caustics is used for the complete experimental determination of the stress field inside a plane isotropic elastic medium. Two experiments are required for this determination.     

用切口尖端应力方法分析V形切口的应力强度因子

为了基于传统有限元法分析圆轴中的V形切口尖端的奇异性应力场的高精度数值解,建立一种切口尖端应力方法,用于计算V形切口的应力强度因子.该方法不需要在V形切口尖端采用反映应力奇异性的奇异单元.求解时,首先给定参考问题的广义应力强度因子,然后利用待求问题的应力值与参考问题的应力值之间的比值来求解待求问题的广义应力强度因子.算例采用切口尖端应力方法分析圆轴中的V形切口问题.计算结果表明,该方法计算精度较高,能方便地用于求解相关的工程问题.     

应用X射线衍射法测定轴类工件中的残余应力

根据测试距车轴表面2mm深度处残余应力的要求,推导了剥层测残余应力的修正公式,利用生死单元法模拟了车轴车削的过程,验证了该修正公式的正确性,并采用X射线衍射法测定了距某车轴表面2mm深度处的轴向和周向残余应力。结果表明:X射线衍射法和修正公式能有效测出距车轴表面2mm深度处的残余应力;轴向残余应力最大值(绝对值)和周向残余应力最大值(绝对值)分别出现在0°测点和90°测点,其值分别为-139.15MPa和-105.21MPa,轴向残余应力和周向残余应力各点的差值均小于EN13261标准规定的40MPa。     

The topography of the core-region around cracks under modes I, II and III of fracture

The core region, defined as the limiting zone of validity of the various brittle fracture criteria, has been intuitively assumed as a circle. Its experimental determination is based here on a simple asymptotic elastic theory and a verification by the method of reflected caustics. This definition covers the three modes of deformation at the surroundings of the crack tip. For each mode the initial curve of the caustic, which for isotropic elastic materials is always a circle, yields the limits of validity of the linear elastic theory and corresponds to the boundary of the core region. Experimental evidence with profilometers and projected-grating techniques indicates a similar nature of the deformed surfaces adjacent to the crack tip, as this given by the asymptotic analysis theory of stress and displacement distribution around the crack-tip.     

镦粗工艺理论与技术的研究进展

综述了在镦粗工艺新理论与新技术方面的研究进展,完善与发展了塑性力学镦粗工艺理论,提出圆柱体平板间镦粗时的刚塑性力学模型的拉应力理论和静水应力力学模型的切应力理论,并经定性物理模拟,光塑试验及数值模拟证明,提出广义滑移线法,将经典滑移线理论拓展到能求解所有2维问题和轴对称塑性变形问题,发展了主应力法,提出力学分块法。     

柔性机器人系统碰撞动力学建模

讨论柔性机器人与其工作环境发生碰撞时的动力学建模问题。以空间链式柔性机器人为研究系统,该机器人由n杆n铰构成,柔性杆的变形用假设模态法表示。引入冲量势,运用拉格朗日方程推导出柔性机器人系统受外冲击的广义冲量－动量方程。结合碰撞恢复系数方程,进一步推导出两个柔性机器人系统发生碰撞的动力学方程。该方程中碰撞冲量和广义速度增量是解耦的,且适合于计算机程式求解。求解方程能得到因碰撞而产生的系统广义速度突变量和在碰撞点处的碰撞冲量。给出柔性机器人与其工作环境发生碰撞的算例,验证了所提出方法的有效性。     

Caustic imaging of gallium droplets using mirror electron microscopy

We discuss a new interpretation of mirror electron microscopy (MEM) images, whereby electric field distortions caused by surface topography and/or potential variations are sufficiently large to create caustics in the image contrast. Using a ray-based trajectory method, we consider how a family of rays overlaps to create caustics in the vicinity of the imaging plane of the magnetic objective lens. Such image caustics contain useful information on the surface topography and/or potential, and can be directly related to surface features. Specifically we show how a through-focus series of MEM images can be used to extract the contact angle of a Ga droplet on a GaAs (001) surface.     

基于广义模糊随机强度的模糊可靠性计算理论

同时考虑广义应力和广义强度的模糊性和随机性,在对影响模糊数大小的两个最主要的特征因素进行分析的基础上,建立了用广义模糊随机强度表示模糊失效准则时模糊安全状态隶属函数的计算理论,提出结构模糊可靠度的计算方法,用算例验证了其有效性与合理性。提出的确定模糊安全状态隶属函数的方法,充分利用了模糊数所包含的信息,计算结果合理。     

基于组合近似模型的轻量化设计方法

针对传统结构优化设计方法效率低、计算量大等缺陷,提出一种基于组合近似模型的轻量化设计方法。以某型号内燃叉车的两级门架结构为例,通过熵权TOPSIS综合贡献度分析方法筛选出对门架性能影响最大的上下翼缘及腹板厚度作为轻量化的设计变量,采用最优拉丁超立方设计方法进行样本点采集,得到包含设计变量和性能响应的100个样本点,分别构建外门架质量、最大应力、最大变形的组合近似模型,结合二次序列规划算法展开轻量化设计,结果表明：外门架经过优化后,质量减小13.36%,最大应力减小4.65%。     

Solution of analytical-variational method on bi-material interface crack and its comparison with experiment

An analytical method is developed to describe the fields of stress and displacement in a bi material strip with an edge interfacial crack. All of the basic governing equations, boundary conditions on crack surfaces, and conditions of continuity along the interface are satisfied by the eigen-function expansion method. The other boundary conditions will be satisfied by the generalized variational principle. Good convergence of generalized stress intensity factors is obtained, and the values of crack opening displacement and energy release rate obtained by this method are close to the experimental results. Some problems regarding oscillatory singularity, contact zone and energy release rate are discussed. Finally, the effects of modulus, thickness and crack length to mode mixity are presented.     

基于全局动态应力解空间谱单元插值的关键时间点识别

针对结构动态响应优化中动态分析的复杂性与高耗时性问题,提出了基于全局动态应力解空间谱单元插值的关键点识别方法,找到结构动态响应下最危险的时刻。首先利用模态叠加法,获得结构的模态应力分布,并计算全局动态应力解空间,然后利用谱单元离散动态应力绝对极大值点曲线,采用Lagrange插值并调用区域细分全局优化求解器,找到全局动态应力的极大值与极小值,即关键时间点。将该方法应用到124杆平面桁架和均布力与集中力共同作用的结构关键时间点识别问题中,识别结果说明了该方法的可行性和有效性。     

基于T-S模糊模型的非线性系统广义预测控制

针对离散非线性系统,提出一种基于T-S模糊模型的广义预测控制方法。该方法将采样点的T-S模糊模型转化为采样点线性模型与非线性误差叠加的线性形式,通过迭代修正非线性误差,使具有非线性误差的线性模型预测控制律逐渐逼近采样点T-S模糊模型预测控制律。同时,该预测控制方法也能适用于当系统受输入输出约束时的控制。仿真结果验证了所提出的TS模糊模型广义预测方法有效。     

基于广义延拓逼近法的凸轮轮廓反求设计

在高精度的凸轮轮廓反求设计中,利用凸轮轮廓非圆曲面的离散测量点,采用一种新的方法--广义延拓逼近法,构造出凸轮非圆曲面的广义延拓逼近模型,来实现高精度凸轮轮廓的反求设计.为验证设计效果,分别运用三次样条插值法和最小二乘拟合法对凸轮非圆曲面数据进行逼近计算.结果对比表明,采用广义延拓逼近法数学模型处理凸轮非圆曲面的离散数据时,如果在延拓域边界点上满足插值条件,可以实现区域内部的最佳拟合.此外,在插值次数相同的条件下,广义延拓逼近法具有更高的设计精度.