接触问题的自适应无网格伽辽金方法

针对接触问题提出了基于应变能梯度的自适应无网格伽辽金方法。通过对自适应无网格伽辽金方法的原理讨论,给出了基于背景网格的误差估计方法,并对自适应求解流程进行了阐述。研究了无网格节点加密技术和自适应搜索半径等关键技术。编程求解了圆柱体接触问题,并与理论解和均匀密化数值解进行比较,给出了接触计算中合理的参数范围,对真实粗糙表面接触问题进行了计算,计算结果表明,在相当计算精度下,自适应加密计算耗时仅为同等整体加密计算的18.6%。     

二维无网格伽辽金-有限元耦合方法的研究

论述无网格伽辽金方法（element-free Galerkin method,EFG）的基本原理－－移动最小二乘原理（moving leastsquare,MLS）和EFG方法的位移近似函数，给出变分方程及离散方程。对无网格伽辽金－有限元耦合（EFG－FE coupling）方法进行详细阐述。编制相应程序，通过算例表明拉格朗日乘子对强制边界条件的作用及无网格伽辽金方法在权函数参数变化时的收敛特性，论证无网格伽辽金－有限元耦合的有效性。     

Analysis of rectangular stiffened plates under uniform lateral load based on FSDT and element-free Galerkin method

This paper presents an element-free Galerkin (EFG) method for the static analysis of concentrically and eccentrically stiffened plates based on first-order shear deformable theory (FSDT). The stiffened plates are regarded as composite structures of plates and beams. Imposing displacement compatible conditions between the plate and the stiffener, the displacement fields of the stiffener can be expressed in terms of the mid-surface displacement of the plate. The strain energy of the plate and stiffener can be superimposed to obtain the stiffness matrix of the stiffed plate. Because there are no elements used in the meshless model of the plate, the stiffeners need not to be placed along the meshes, as is done in the finite element methods. The stiffeners can be placed at any location, and will not lead to the re-meshing of the plate. The validity of the EFG method is demonstrated by considering several concentrically and eccentrically stiffened plate problems. The present results show good agreement with the existing analytical and finite element solutions. The influences of support size (denoted by a scaling factor d_max) and order of the complete basis functions (N_c) on the numerical accuracy are also investigated. It is found that larger support size and higher order of basis function will furnish better convergence results.     

Adaptive multiscale method for two-dimensional nanoscale adhesive contacts

There are two separate traditional approaches to model contact problems: continuum and atomistic theory. Continuum theory is successfully used in many domains, but when the scale of the model comes to nanometer, continuum approximation meets challenges. Atomistic theory can catch the detailed behaviors of an individual atom by using molecular dynamics (MD) or quantum mechanics, although accurately, it is usually time-consuming. A multiscale method coupled MD and finite element (FE) is presented. To mesh the FE region automatically, an adaptive method based on the strain energy gradient is introduced to the multiscale method to constitute an adaptive multiscale method. Utilizing the proposed method, adhesive contacts between a rigid cylinder and an elastic substrate are studied, and the results are compared with full MD simulations. The process of FE meshes refinement shows that adaptive multiscale method can make FE mesh generation more flexible. Comparison of the displacements of boundary atoms in the overlap region with the results from full MD simulations indicates that adaptive multiscale method can transfer displacements effectively. Displacements of atoms and FE nodes on the center line of the multiscale model agree well with that of atoms in full MD simulations, which shows the continuity in the overlap region. Furthermore, the Von Mises stress contours and contact force distributions in the contact region are almost same as full MD simulations. The method presented combines multiscale method and adaptive technique, and can provide a more effective way to multiscale method and to the investigation on nanoscale contact problems.     

自适应无网格伽辽金方法的研究

对基于位移或应变梯度的二阶导数和基于应变能密度的自适应无网格方法进行了研究。利用无网格方法结点排布灵活、结点添加删除方便等特点,给出两种自适应无网格伽辽金方法的原理、计算流程和程序实现。采用基于应变能密度的自适应方法,提出基于背景网格的误差估计和一种由结点组成的四边形局部结点加密技术,计算了悬臂梁拉伸和带小圆孔平板拉伸的算例。结果表明,自适应无网格伽辽金方法可以在较少结点数的情况下获得较准确的结果,具有一定的适用性。     

The Effect of Scale-Dependent Hardness on Elasto-Plastic Asperity Contact between Rough Surfaces

Statistical methods are used to model elasto-plastic contact between two rough surfaces using a recent finite element model of elasto-plastic hemispherical contact and also recent advances in strain gradient modeling. The elasto-plastic hemispherical contact model used to model individual asperities accounts for a varying hardness effect due to deformation of the contact geometry that has been documented by other works. The strain gradient model accounts for changes in hardness due to scaling effects. The contact between surfaces with hypothetical material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. A model is also constructed to consider a variable asperity contact radius to evaluate if the strain gradient model will affect it differently. The models produce predictions for contact area, contact force, and surface separation. The strain gradient effects decrease the real area of contact and increase the average contact load in comparison to the model without these effects. The strain gradient model seems to have a larger influence on the predictions of contact load and area than does considering a variable asperity contact radius for the cases considered in this work.     

A nonlinear numerical analysis for metal-forming process using the rigid-(visco)plastic element-free Galerkin method

A new approach for isothermal metal-forming process, which is based on the element-free Galerkin (EFG) method for incompressible rigid-(visco)plastic material models, is put forward. The meshless analysis of the non-steady plastic deformation processes with arbitrarily shaped dies is realized. A nail-shaped part-forming process based on the meshless method is analyzed numerically. The flow patterns and the effective strain and effective strain rate obtained by the EFG and finite element methods (FEM) are studied. Obviously, the EFG simulation results are in good agreement with FEM results. It shows that the model and key techniques are effective and accurate. Meanwhile, the influence of the node number on analytical accuracy is remarkable during EFG simulation. The more the node number is, the more accurate the analysis result is. The volume loss decreases with increase of the node number.     

An accurate solution of a hemisphere contact against a rigid flat under varying elastic moduli and yield strengths and comparison with previous model

The contact behavior of hemisphere pressed by a rigid flat is analyzed based on the finite element method under the condition of independent varying elastic moduli (E) and yield strengths (Y). The contact behavior is related to the ratio of E/Y. The mean contact pressure (p*) first increases and then decreases with the increasing interference, and this trend is more obvious for the contact of materials with the comparatively small ratio of E/Y. The end of the elastoplastic range or the inception of the fully plastic range is determined according to the interference corresponding to the peak value of the p*. The contact load and area in elastoplastic and fully plastic ranges are determined by the interference and the ratio of E/Y. Then, a new contact model to accurately predict the contact load and area for a wide range of E and Y is proposed, and compared with the previous models. The correctness of the current model is verified by the experimental measurement results recorded in previous literature.

     

Energy, Adhesion, and the Elastic Foundation

A theory for elastic contact adhesion between a rigid sphere and an elastic foundation is developed. The theory derives relationships between the contact deformation and the externally applied force. The derivation is based on elastic contact between a sphere and a thin linear-elastic foundation in which the strain energies are balanced by the work of indentation and the change in surface energy. Contacting regimes where there is either compressive strain energy or only tensile strain energy (pull-off regime) are both treated. The model is non-dimensionalized and an order of magnitude analysis is performed in order to develop simplified closed form solutions; the simplified model is then evaluated and compared to the full solution. This theory finds that the adhesion force is significantly larger for an elastic foundation in which the surface elements act independently as compared to more traditional solutions for elastic solids. The theory gives an adhesion force of $ F_{\text{adh}} \cong 7\pi R\Updelta \gamma . $      

粗糙表面热弹塑性接触自适应无网格分析

为了在较真实地模拟接触状态的同时节省计算耗费,采用自适应无网格法求解粗糙表面热弹塑性接触问题。计算中考虑了屈服强度温度相关因素,将基于应变能梯度的自适应无网格法与线性规划-增量初应力法相结合,构建了热弹塑性接触自适应无网格分析模型,并给出相应的程序流程。通过粗糙表面与弹塑性平面热弹塑性接触算例进行验证,分别对两种不同工程材料考虑切向摩擦力、材料应变硬化和材料屈服强度温度相关等情况进行了讨论。结果表明,采用自适应无网格法能有效求解粗糙表面热弹塑性接触问题,在保证计算精度与整体加密相当的情况下,自适应加密的计算耗费约为整体加密计算耗费的10%。     

Enriched finite element method for three-dimensional viscoelastic interface crack problems

The enriched finite element method is developed for three-dimensional problems of an interface crack between elastic and viscoelastic (including dissimilar viscoelastic) materials. According to the displacement fields of elastic interface crack, the displacement fields of viscoelastic interface crack are derived through the correspondence principle. By incorporating the displacement expressions into the displacement model of regular element, the incremental formulations of enriched element are derived. The stress intensity factors and strain energy release rates can be solved based on the enriched degree of freedoms. A 3-D through interface crack at the center of jointed dissimilar viscoelastic plate subjected to remote tension and a quarter-circular viscoelastic interface corner crack subjected to uniform thermal loading was investigated using the enriched finite element method. It is shown that the present solutions are consistent with the analytical solutions, which indicates the present method is correct and efficient.

     

刚塑性成形模拟中有限元和无网格迦辽金法的自动耦合算法

利用有限元法分析金属的刚塑性问题时,在变形的高梯度区域单元容易严重畸变,这极大地降低了分析精度.在刚塑性有限元方法的框架中,文中根据计算增量步的网格质量,提出金属刚塑性有限元和无网格迦辽金法的自动耦合算法,在单元严重畸变的区域转换为无网格迦辽金法进行计算.数值实例表明:算法在很大程度上既保持了有限元法的计算效率,又能够...     

Elastoplastic contact mechanics model of rough surface based on fractal theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ϕ, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.     

EFG法在线弹性结构形状优化中的应用研究

出现在基于有限元形状优化过程中的网格畸变与扭曲问题,可通过引入无网格方法得到解决。本文首先建立了结构形状优化的数学模型,利用无网格Galerkin(EFG)法对形状优化的设计域进行了离散,采用罚函数法来施加边界条件,借助于直接微分法建立了一种离散型基于无网格Galerkin法的设计灵敏度分析算法,然后用1个具有解析解的实例对其进行了验证,所得结果显示两者是一致的。最后利用对所建立的算法完成了1个工程实例的形状优化设计,并对所得到的优化结果结合工程应用进行了讨论。     

Analysis of High-Speed Intershaft Cylindrical Roller Bearing with Flexible Rings

For high-precision mechanisms such as machine tools or gas-turbine engines, which operate at extreme conditions, it is particularly important to accurately predict the behavior of the included bearing. This prediction includes, among other things, its load distribution, stiffness, and power dissipation. Although shaft speeds tend to increase, rings and shaft walls are becoming thinner due to size and weight constraints. Thus, bearing behavior is no longer independent of the housing and ring stiffness. This paper focuses on the problem of elastic ring deformation and certain behaviors of high-speed intershaft cylindrical roller bearings such as heat dissipation, contact pressure, and risk of bearing failure due to scuffing. The paper presents an analytical method to account for the structural deformation of the rings based on Roark's formulas. The elastic deformation of thin cylindrical rings has been introduced in the set of displacement and load equations that describes the bearing equilibrium. A correlation with a high-speed intershaft cylindrical roller bearing application is made and the results are compared with those obtained with the finite element method for housing deformations. Heat dissipation, load distribution, contact pressure, and internal kinematics are discussed to evaluate co-rotating and contrarotating shaft design solutions.     

印刷滚体非牛顿流体弹流动压性能的有限元分析

印刷滚体间的接触是一个带有共性的主要技术问题,对于非牛顿性质的流体,本文介绍了一种研究这种软层接触问题的分析模型。应用加辽金加权残留方法和虚功原理分别得到了关于压力和变形的控制方程。用有限元方法求得了问题的数值解,与测试数据相比较,结果具有一定的一致性。     

晶粒尺寸对多晶铜接触力学特性的影响

为研究晶粒尺寸对材料接触力学特性的影响,考虑多晶铜基体弹塑性变形情况,基于分子动力学方法,在原子尺度下模拟了金刚石压头与不同晶粒尺寸的铜基体的接触与分离过程。研究结果表明：在不同晶粒尺寸下,多晶铜黏着接触过程中的最大黏着力基本保持不变,最大法向接触力随晶粒尺寸的减小表现出先增大后减小的趋势。纳米硬度和接触刚度分别与接触过程中的塑性能和弹性能的变化相关,且纳米硬度与接触刚度的变化总体成负相关。最后,采用公共近邻分析方法研究了多晶铜基体弹塑性变形过程,研究发现晶界数量对材料的纳米硬度有重要影响,并进一步影响其接触力学特性。     

金属塑性成形过程无网格伽辽金法数值模拟技术研究

将无网格伽辽金法与刚(粘)塑性流动理论相结合,对无网格伽辽金法在金属塑性成形过程数值模拟中的应用技术进行了研究,分别采用混合变换法和罚函数法实现速度边界条件和体积不变条件,提出了基于刚(粘)塑性力学流动理论的无网格伽辽金法,给出了金属塑性成形无网格伽辽金法数值模拟的关键算法,拓展了无网格方法在金属成形领域的应用范围。典型算例的数值计算结果表明了方法的可行性。     

微观随机粗糙表面接触有限元模型的构建与接触分析

基于相关文献提出粗糙表面模拟方法,通过软件工具在ANSYS中建立微观粗糙表面接触有限元模型,利用该模型分析载荷对弹塑性变形和接触面积的影响。结果表明:随着正压力的增大,粗糙表面上不断地有微凸峰与平面发生弹性接触变形,接触斑点(或接触斑点群)的数目逐渐增加,斑点中心区域的弹性变形很快达到最大,微凸峰负荷变形的同时也使斑点四周区域受到挤压;初始接触时,轮廓高度较大的微凸峰率先发生弹性变形,随着压力的增大,金属材料所受应力达到屈服极限同时粗糙表面的弹性变形和塑性变形的集中区域不断增加,真实接触面积不断增大;接触区数目的增多和接触区面积的增加都可以导致接触面上真实接触面积增加;随着压力的增大,真实接触面积的增大并不是由于接触区数目的增多,而是微观接触区面积的增大。     

A finite-element analysis of the indentation of an elastic-work hardening layered half-space by an elastic sphere

An elastic–plastic contact problem in elastic-work hardening layered half-space indented by an elastic sphere was solved numerically using the finite element method. The case of a surface layer stiffer than the substrate is considered, and general solutions for the subsurface stresses and deformation fields are presented for a relatively thin elastic layer. Differences between the elastic and elastic–plastic solutions for the contact pressure distribution have been investigated for various layer thicknesses. Crack initiation and decohesion of the layer was also discussed with reference to the growth of the plastic zone.