应用三维光弹性分析轧辊的接触应力

对有限长，外载荷又集中作用的轧辊，当其母线接触压靠性，接触面上的应力分布是不均匀的。于是，根据弹性力学理论推导的无限长辊子相互压靠的接触应力“赫芝”解法无法得到充分应用。由于这个原因。该文提出了一个辊子接触应力非均匀分布模型假设，它是在横向满足半椭圆分布，而纵向为未可知的曲线分布，根据这个假设应用三维光弹性的应力切片法及有限元数值计算概念。导出了这类辊子接触应力的混合计算方法。作为一个应用实例，该文讨论了宝钢1420双平整轧机轧辊的接触问题，该轧机有六个辊子组成，上下三三对称，其中最外层为支承辊，中间是中间辊，下层是工作辊，工作辊与轧件接触，钢厂在板形控制研究中，十分需了解各辊子之间的接触应力，应用该文分析方法。可以得到接触面上理想的三向接触应力值。为厂方的板形控制工艺改进提供了极有用的参数。     

基于FEM-DEM的三体摩擦界面中接触行为与应力的多尺度分析

为了研究三体摩擦界面中第一体变形与第三体状态的相互影响，利用耦合有限元法和离散元法的多尺度法模拟了平行板剪切颗粒第三体的过程。整个模型分为两个区域：有限元区域（上板）和离散元区域（第三体和下板），上板在一定的外载荷压应力下挤压颗粒第三体，下板以恒定的速度剪切颗粒第三体。为实现两个子区域间的相互联系，建立了子区域间应力应变的传递机制。实现了三体摩擦界面的多尺度分析，模拟了平行板剪切颗粒第三体的过程。模拟结果表明：当外载荷压应力低于10MPa时，颗粒间的碰撞增多使得第三体内量纲归一化平均应力增大，宏观摩擦系数也随之增大；在剪切过程中，第三体内部颗粒间的接触随接触角度的分布呈现出一定的规律性，0~90°各区间内的强接触较多，尤其在54°~72°之间；颗粒接触随接触力大小的分布也具有一定的规律性，接触力与第三体颗粒平均接触力的比值在0~0.6之间内的接触较多，随后接触力越大，接触数越少。同时，第一体内压应力分布与第三体内力链的分布相对应，力链越强则与其接触的第一体的压应力越大。     

基于分子动力学-格林函数法的微凸体接触数值分析

表面接触是摩擦的先决条件,其真实接触面积、压应力大小、空间分布等一直是接触力学关注的核心问题.采用分子动力学-格林函数法(GFMD)模拟粗糙面的接触过程,验证了其在大规模接触分析中的高效及准确性,同时探讨了由微球体组成的粗糙面的接触力学特性,并分析了分子尺度下的结果和传统力学模型计算结果的差异.结果表明,单个微凸体接触结果和分子动力学-格林函数法模拟所得非常接近,误差在5%以内.数值模拟发现,在微凸体高度符合高斯分布的情况下,接触面积和接触力成线性关系;在相同接触面积下,微凸体模型得出的接触力偏高,是上限值.微凸体模型没有考虑微凸体间的相互影响,实际是高估了弹性体的刚度;实际接触过程中微凸体相互影响,微凸体对临域形变影响尤其大,使接触区域更加离散.GFMD模型可以准确计算数十亿量级别分子、原子接触过程中真实接触面积及分布,为后续摩擦、滑移等分析提供可靠的参考.     

考虑等效曲率的超二次曲面单元非线性接触模型

基于连续函数包络的超二次曲面单元可有效地描述自然界和工业生产中的非球体颗粒形态, 并通过非线性迭代方法精确计算单元间的接触力. 对于具有复杂几何形态的超二次曲面单元, 线性接触模型不能准确地计算不同接触模式下的作用力. 考虑超二次曲面单元相互作用时不同颗粒形状及表面曲率的影响, 本文发展了相应的非线性黏弹性接触模型. 该模型将不同接触模式下的法向刚度和黏滞力统一表述为单元间局部接触点处等效曲率半径的函数; 切向接触作用则借鉴基于Mohr-Coulomb摩擦定律的球体单元非线性接触模型的计算方法. 为检验超二次曲面单元接触模型的可靠性, 对球形颗粒间的法向碰撞、椭球体颗粒间的斜冲击过程、圆柱体的静态堆积和椭球体的动态卸料过程进行离散元模拟, 并与有限元数值结果及试验结果进行对比验证. 计算表明, 考虑接触点处等效曲率半径的超二次曲面非线性接触模型可准确地计算单元间的接触碰撞作用, 并合理地反映非球形颗粒体系的运动规律. 在此基础上进一步分析了不同长宽比和表面尖锐度对卸料过程中颗粒流动特性的影响, 为非球形颗粒材料的流动特性分析提供了一种有效的离散元方法.      

非光滑优化的双层规划模型及内点算法

对于包含接触约束的非光滑结构优化问题,其非光滑性体现在状态函数并不是处处可微的,针对含有应力约束及接触约束的非光滑结构优化问题,建立了一种双层规划模型,避免了求解时非光滑性所带来的问题,同时提出了一种迭代算法,用对偶内点二次规划进行分析,线性规划进行优化,算例表明这种方法十分有效。     

离散元法在求解三维冲击动力学问题中的应用

提出了三维连结型离散模型,建立了可实现连结型模型(用于连续介质)-接触型模型(用于非连续介质)转化的三维离散元计算程序,用来模拟连续介质转变为非连续介质的力学过程．利用该计算程序对冲击载荷下混凝土块体内(连续体情况下)的应力波传播过程进行了数值模拟．将计算结果的数值与LS-DYNA程序计算的结果进行比较,验证了该计算程序的计算精度．在此基础上,模拟了混凝土块体的动态破坏(连续介质向非连续介质转化)过程．其计算结果可用动画显示,得到的破坏形式与由实验得到的破坏形式相近．两个算例说明该离散元模型及其计算程序是模拟计算伴随有连续介质向非连续介质转变的动态破坏问题的有力工具．     

非连续变形计算力学模型的粘弹性分析方法Ⅱ:算例分析

应用作者提出的非连续变形计算力学模型粘弹性分析方法对具体的多体系统在动力外荷载作用下的响应进行了数值模拟，探讨了系统中物体的粘性阻尼对整个系统的变形、应力和接触应力等的影响。与通用软件ABAQUS的计算结果进行了比较研究，两种方法所得到的结果基本一致，但所发展的方法克服了ABAQUS中接触应力分段均匀分布的缺陷，因而所得到的接触应力较为合理，同时也说明了所提出的方法为由刚体、弹性体和粘弹性体所构成的复杂多体系统的数值分析提供了有力的工具。     

考虑等效曲率的超二次曲面单元非线性接触模型

基于连续函数包络的超二次曲面单元可有效地描述自然界和工业生产中的非球体颗粒形态,并通过非线性迭代方法精确计算单元间的接触力.对于具有复杂几何形态的超二次曲面单元,线性接触模型不能准确地计算不同接触模式下的作用力.考虑超二次曲面单元相互作用时不同颗粒形状及表面曲率的影响,本文发展了相应的非线性黏弹性接触模型.该模型将不同接触模式下的法向刚度和黏滞力统一表述为单元间局部接触点处等效曲率半径的函数;切向接触作用则借鉴基于Mohr-Coulomb摩擦定律的球体单元非线性接触模型的计算方法.为检验超二次曲面单元接触模型的可靠性,对球形颗粒间的法向碰撞、椭球体颗粒间的斜冲击过程、圆柱体的静态堆积和椭球体的动态卸料过程进行离散元模拟,并与有限元数值结果及试验结果进行对比验证.计算表明,考虑接触点处等效曲率半径的超二次曲面非线性接触模型可准确地计算单元间的接触碰撞作用,并合理地反映非球形颗粒体系的运动规律.在此基础上进一步分析了不同长宽比和表面尖锐度对卸料过程中颗粒流动特性的影响,为非球形颗粒材料的流动特性分析提供了一种有效的离散元方法.     

颗粒流动力学及其离散模型评述

颗粒流是由众多颗粒组成的具有内在相互作用的非经典介质流动. 自然界常见颗粒流 都是密集流, 颗粒间接触形成力链, 诸多力链相互交接构成支撑整个颗粒流重量和外载荷的 网络, 其局部构型及强度在外载荷下演化, 是颗粒流摩擦特性和接触应力的来源.本文 介绍球形颗粒间无粘连作用时的Hertz法向接触理论和Mindlin-Deresiewicz切向接触 理论. Campbell依据是否生成较为稳定的力链把颗粒流分为弹性流和惯性流两大 类, 其中弹性-准静态流和惯性-碰撞流分别对应准静态流和快速流, 作为两种极端流动情况通常处理成连续体, 分 别采用摩擦塑性模型和动理论予以描述, 但是表征接触力链的颗粒弹性参数并不出现这两个 模型和理论框架中, 如何进一步考虑颗粒弹性参数将非常困难. 目前离散动力学方法逐渐 成为复现其复杂颗粒流动现象、提取实验不可能获得的内部流动信息进而综合起来探索颗粒 流问题的一种有效工具, 其真实性强于连续介质理论的描述. 软球模型对颗粒间接触力简化 处理, 忽略了切向接触力对法向接触力及其加载历史的依赖, 带来了法向和切向刚度系数 如何标度等更艰难的物理问题, 但由于计算强度小而广泛应用于工程问题中. 硬球模型不考虑 颗粒接触变形, 因而不能描述颗粒流内在接触应变等物理机理, 仅适用于快速颗粒流, 这不 仅仅是由于两体碰撞的限制. 因此基于颗粒接触力学的离散颗粒动力学模型是崭新的模型, 适用于准静态流到快速流整个颗粒流态的模拟, 可以细致考虑接触形变及接触力的细节, 建立更为合理的颗粒流本构关系, 进而有力的促进颗粒流这一非经典 介质流动的研究.     

多体系统碰撞动力学中接触力模型的研究进展

接触碰撞行为作为大自然与多体系统中的常见现象, 其接触力模型对于多体系统的碰撞行为机理研究与性能预测至关重要. 静态弹塑性接触模型与考虑能量耗散的连续接触力模型是研究接触碰撞行为的两类不同方法, 在多体系统碰撞动力学中存在诸多共性与差异. 本文分别从上述两类接触模型的发展历程入手, 详细介绍了两类模型的区别与联系. 首先, 根据阻尼项分母中是否含有初始碰撞速度将连续接触力模型分为黏性接触力模型与迟滞接触力模型, 讨论了能量指数与Hertz接触刚度之间的关系, 阐述了现有连续接触力模型在计算弹塑性材料接触碰撞行为时存在的问题. 其次, 着重介绍了分段连续的准静态弹塑性接触力模型(可连续从完全弹性转换到完全塑性接触阶段), 分析了利用此类弹塑性接触力模型计算碰撞行为的技术特点. 同时, 以恢复系数为桥梁和借助线性化的弹塑性接触刚度, 避免了Hertz刚度对弹塑性接触刚度的计算误差, 根据碰撞前后多体系统的能量与动能守恒推导了弹塑性接触模型等效的迟滞阻尼因子. 探索了连续接触力模型与准静态弹塑性接触力模型之间的内在联系, 数值计算结果定量说明了人为阻尼项代表的能量耗散与弹塑性接触力模型中加卸载路径代表的能量耗散具有等效性. 另外, 为了避免阻尼项分母中初始碰撞速度在计算颗粒物质动态性能时导致的数值奇异问题, 通过求解等效的线性单自由度欠阻尼非受迫振动方程获得了阻尼项分母中不含初始碰撞速度的连续接触力模型, 并以一维球链为例, 证明了该模型相比EDEM软件使用的连续接触力模型具有更高的精度. 最后, 本文分析了当前多体系统碰撞动力学的研究现状, 并简要展望了多体系统碰撞动力学中接触力模型的发展趋势与面临的挑战.      

连接结构接触界面非线性力学建模研究

连接界面上存在的跨尺度、多物理场和非线性行为是引起结构复杂非线性动力学的主要原因。由于连接界面力学行为的复杂性,以及对连接界面进行直接试验观测的困难,连接界面的力学建模一直是非常具有挑战性的科学问题。本文首先从分析结合面的跨尺度物理机理入手,将名义的光滑平面视作凹凸不平的粗糙面,考虑单个微凸体的黏滑摩擦行为,建立接触载荷与变形的非线性关系,然后采用GW(Greenwood和Williamson, GW)模型数理统计方法建立整个粗糙界面的跨尺度力学模型,并与公开文献中试验结果进行对比。然后考虑连接界面典型非线性特征,提出一种改进的Iwan唯象模型,利用精细有限元方法获得非线性特征结果,采用系统辨识理论建立连接结构的降阶力学模型,并利用有限元结果进行模型验证。结果表明,本文提出的粗糙界面跨尺度模型在法向载荷较小时与试验结果吻合较好,改进的Iwan模型能够较好描述连接界面非线性特征,并与有限元结果吻合较好。      

Linear and Nonlinear Algorithms for Stress Separation in Photoelasticity

An experimental-numerical hybrid method for the stress separation in photoelasticity is proposed in this study. In the proposed method, boundary conditions for a local finite element model, that is, tractions along boundaries are inversely determined from photoelastic fringes. Two algorithms are proposed for determining the boundary condition. One is a linear algorithm in which the tractions are obtained by the method of linear least-squares from both principal stress difference and principal direction. Another is the nonlinear algorithm in which the tractions are determined only from the principal stress difference. After determining the boundary conditions for the local finite element model, the stresses can be obtained by finite element direct analysis. The effectiveness is demonstrated by applying the proposed method to a perforated plate under tension and contact problems. Results show that the boundary conditions of the local finite element model can be determined from the photoelastic fringes and then the individual stresses can be obtained by the proposed method. Furthermore, the stresses can be evaluated even if the boundary condition is complicated such as at the contact surface. It is expected that the proposed method can be powerful tool for stress analysis.     

Three-dimensional problems of the hydrodynamic interaction between bodies in a viscous fluid in the vicinity of their contact

The study is devoted to the hydrodynamic interaction between bodies near their contact. The stresses produced in a narrow gap between the bodies in the vicinity of their contact determine the main part of forces acting on the bodies in motion. In many cases, the velocity and pressure fields in the vicinity of the contact can be determined and the main asymptotics for the hydrodynamic interaction force in the small spacing between the surfaces can be derived. An overview of the three-dimensional problems solved using this method is presented and for certain problems new formulations are given. The reliability of the results is confirmed by the comparison with available exact particular solutions and experimental data.     

Pseudo-random number generator based on discrete-space chaotic map

This paper describes an efficient method to predict the nonlinear steady-state response of a complex structure with multi-scattered friction contacts. The contact friction force is equivalent to additional stiffness and damping based on optimal approximation theory, and as a consequence, the computation is simplified greatly by the linearization for a nonlinear system. In order to obtain accurate pressure distribution on the contact interfaces, the dynamic contact normal pressure is obtained by the equivalent static analysis which is validated for most engineering cases. Considering the complex procedure to determine the transformation between two different contact states, the differential forms of friction force are given to solve the tangential force accurately under the complex movement of interfaces. The approaches developed in this paper are particularly suitable to solve the dynamic response of large-scale structures with local contact nonlinearities. The entire procedure to calculate the steady-state response of a finite element model with a large number of degrees of freedom is demonstrated taking the blades with underplatform dampers as an example. The method is proved to be accurate and efficient; in particular, it does not suffer convergence problem in the allowable range of precision error, which exhibits remarkable potential engineering application values.     

A three-parameter elastic foundation model for interface stresses in curved beams externally strengthened by a thin FRP plate

Externally bonding of fiber reinforced polymer (FRP) plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP–concrete interface are of great importance to the effectiveness of this type of strengthening because high stress concentration along the FRP–concrete interface can lead to the FRP debonding from the concrete beam. In this study, we develop an analytical solution of interface stresses in a curved structural beam bonded with a thin plate. A novel three-parameter elastic foundation model is used to describe the behavior of the adhesive layer. This adhesive layer model is an extension of the two-parameter elastic foundation commonly used in existing studies. It assumes that the shear stress in the adhesive layer is constant through the thickness, and the interface normal stresses along two concrete/adhesive and adhesive/FRP interfaces are different. Closed-form solutions are obtained for these two interfacial normal stresses, shear stress within the adhesive layer, and beam forces. The validation of these solutions is confirmed by finite element analysis.     

Analysis of rotating solids with cracks by the boundary element method

The use of the boundary element method for the solution of linear elastic fracture mechanics problems, without body forces, is quite extensive since the method is intrinsically well suited to the analysis of high stress gradients associated with crack problems. The crack-tip stresses for rotating bodies are similar to the stresses for stationary bodies and therefore all the advantages of the boundary element procedure can be encompassed in the extension of the method to the solution of rotating bodies with cracks. In the present analysis, the additional volume integral that arises from the treatment of inertial body forces is eliminated by using the well-known particular integral procedure. The matrix ill-conditioning that results from the need to model co-planar crack surfaces of non-symmetrical cracks is avoided by using the multi-region approach. The accuracy of the numerical solutions is improved by utilizing quarter-point elements with traction singular enhancement at the crack-tip. The procedure is then applied to the solution of arbitrary cracks in two- and three-dimensional rotating bodies.     

Fast evaluation of friction forces in traction-drive contacts including thermal effects

Summary  In automotive traction drives, power is transmitted by friction forces. The friction forces result from the shear stresses developed in lubricated and highly loaded contacts between rolling bodies. Due to the kinematics of a traction drive, shear velocities occur in both the rolling direction and perpendicular to it. Due to these shear velocities and by normal pressure, the lubricant is forced to build up shear stresses. The increase of the shear stresses may be modelled by a nonlinear viscous element. The describing differential equations are coupled by the equivalent shear stress, which defines the nonlinear behaviour of the element. A fast method is described to evaluate the coupled differential equations. By using a known analytical approximation for the equivalent shear stress, the differential equations are decoupled and can be solved analytically. In an iterative procedure the equivalent shear stress is updated, and the complete solution is found. The iterative method is extended to account for thermal effects in the contact. Received 17 June 1999; accepted for publication 26 October 1999     

薄壁细胞受微吸管与探针共同作用接触模型及数值模拟

建立了以典型的薄壁球型植物细胞为原型的细胞、微吸管及探针接触模型.模型的细胞壁采用封闭球形薄膜,其本构关系为体积不可压超弹性,膜球内充满有压流体以模拟细胞质.应用轴对称几何非线性方法得出了基本微分方程组,并应用龙格-库塔法进行了求解;同时,应用流固耦合有限元法进行了数值模拟以资比较.两种方法得出了较为一致的变形和应力分...     

Interface Forces in Laterally Impacted Steel Tubes

In engineering mechanisms, solid bodies frequently come to a contact with a variety of geometric and kinematic situations. There has been a trend to express the interaction of the contacted bodies in the form of equivalent interface forces. The interface force represents the level of load transferred from one body to another. In a static or quasi-static contact problem, the interface forces could be sensibly evaluated by integrating the normal and the shear stresses over the common interfaces. In a dynamic contact, the interface stresses and subsequently the interface forces happen to be more complicated. They are, furthermore, affected by other parameters such as inertia forces, stress waves propagation, the material strain rate dependency and damping. This paper reports interface forces recorded in a series of experimental impact tests on axially pre-compressed steel tubes along with those from the numerical simulations of the tests. To monitor the so called impact loads, two small steel rings as load cells have been built in the striker. Based on the experimental and numerical results, the concept of equivalent interface forces in the impacted tubes has been verified. It has been highlighted that the interface forces (or the impact loads) may vary on the striker or the specimen themselves, depending on the measuring locations. Effects of axial compressions on the interface forces picked up by the striker load cells, impact loads imparted to the specimen supports and on the impact duration have been discussed. It has been reported that the initial compression applied to the tubes does not remain constant during and after the impact event. The amount of variations also depends on the initial level of the tube compression.     

自适应无网格热弹塑性接触模型研究

提出一种自适应无网格热弹塑性接触求解模型,求解接触问题的线性规划-增量初应力法与基于应变能梯度的自适应无网格法相结合,给出了模型计算理论和算法实现.通过圆柱体与弹塑性平面热弹塑性接触算例对模型进行验证.对是否考虑材料应变硬化,是否考虑摩擦力和热输入,是否考虑材料屈服强度温度相关等情况的两种算例进行了讨论.结果表明,该模型能有效地求解考虑不同情况下的热弹塑性接触问题,在较真实地模拟接触状况的同时,具有较高的计算精度和计算效率.