具有曲面接触斑弹性体滚动接触理论及其数值方法

该文基于了Kalker三维弹性体非Hertz滚动接触理论模型,考虑滚动接触物体具有曲面接触斑,利用有限元法,推导出物体柔度系数,即力与位移之间的关系,将理论模型转化为数学上的非线性规划问题。结合拉格朗日乘子法,求解非线性方程组,从而得到接触斑力学行为。该模型是考虑曲面接触斑三维弹性体滚动接触理论模型,考虑了滚动接触物体的真实几何尺寸和接触区外边界因素对滚动接触行为的影响。为解决任何几何形状弹性体滚动接触问题提供了方法。该文主要对二维问题的数值模拟,所得数据结果较为合理。并结合商业有限元软件计算结果对静态问题进行对比验证,两种模型的分析结果吻合的较好。该文的模型和数值方法进一步完善后将适用于任意曲面接触斑滚动接触问题的求解。     

基于MLS-NMM的摩擦接触问题研究

摩擦接触问题的求解是将基于移动最小二乘插值的数值流形法（MLS-NMM）应用到裂纹扩展的必经之路。该文通过结合罚-线性互补方式的施加接触边界条件,并使用拉格朗日乘子法施加本质边界条件,得出一套基于MLS_NMM的摩擦接触问题的求解体系。该方法无需节点与边界重合,则可域外布点和均匀布点,来提高插值精度和降低布点难度,尤其是接触边界处。采用罚-线性互补的方式施加接触条件,使计算格式统一而简洁,利于编程实现。通过算例表明,该方法能准确地模拟接触面的张开、黏结和滑动状态,证明该方法对求解接触摩擦问题是可行的、有效的。     

高分子复合材料接触力学的有限元研究

采用有限元方法，并结合边界元方法，研究了高分子复合材料的力学问题，用可能接触区接触节点对方法，比例加载方法和库仑摩擦定律来模拟该问题。在受载过程中，随载的增加而逐渐改变接触边界条件。由于边界条件的不定性，导致了该问题的非线性，故了数学规划方法求解高度不定性的弹性接触方程组，进而求得接触区的接触位移和接触压力。     

摩擦接触热传导有限元研究

用接触力学计算方法中的缩聚技术，通过能量传递建立接触表面温度和热流边界条件，得到建立在接触边界的热接触有限元方程组。固体接触力学中的各类有限元数值方法因而可用于时变热传导问题，对于精确确定由摩擦功转化而来的表面温升不容忽视时的温度场分布、温度梯度及其对结构强度、材料相变的影响提供了一种新的方法。当材料是热的不良导体，例如高分子粘弹性材料时，尤有重要意义。通过对聚乙烯材料和不锈钢摩擦接触的计算，说明     

基于分形的三维粗糙表面弹塑性接触力学模型与试验验证

基于分形几何理论,利用双变量的Weierstrass-Mandelbrot函数模拟三维分形粗糙表面,建立了三维分形粗糙表面弹塑性接触模型。推导出各等级微凸体发生弹性、弹塑性以及完全塑性变形的存在条件。确定了粗糙表面上各等级微凸体的面积分布密度函数,获得了总接触载荷和真实接触面积之间的关系式。计算结果表明:单个微凸体的临界接触面积与其尺寸相关,随着微凸体等级的增大,微凸体的高度和峰顶曲率半径减小。微凸体的变形顺序为弹性变形、弹塑性变形和完全塑性变形,与经典的赫兹模型保持一致。粗糙表面的力学性能仅与最小等级及后续的6个等级微凸体相关,其余微凸体基本上对整个粗糙表面的力学性能影响很小。最后对粗糙表面的接触力学性能进行了试验测试,验证了该模型的合理性与正确性。     

纸张在弹性胶辊夹持下接触区域的数值分析

在准静态、无摩擦的条件下,应用级数形式的应力函数对复印机中纸张在弹性胶辊夹持下的接触问题进行了分析。模型源于复印机中的进纸单元,根据弹性理论,分别使用施密特正交化方法与无网格配点法对问题进行了求解,得到了接触区域的应力应变分布以及胶辊与纸张的表面速度比,为提高复印机胶辊的可靠性提供了参考。     

考虑异质材料的线接触性能建模与分析

提出了一种考虑材料非均匀特性的线接触弹性场数值建模方法。该方法基于数值化等效夹杂方法（NEIM）,以矩形异质材料作为基本单元,并在此基础上,结合镜像法,可求解得到线接触载荷作用下的材料弹性场。利用对比验证、参数化分析及算例验证的方法,将本文方法计算结果与有限元法（FEM）和传统等效夹杂方法（EIM）计算结果进行对比,并分析研究了异质材料分布参数对材料线接触性能的影响。结果表明:本文方法相较FEM和传统EIM具有优越性,可处理和简化涂层问题及任意分布的异质材料线接触问题。不同位置异质材料将引起基体最大von Mises应力的增大或减小;异质材料的尺寸以及异质材料和基体之间的材料差异将影响基体应力集中程度。      

铆接界面端三维奇异性应力场的研究

针对铆接结构的特点,应用特征函数扩展技术分析柱坐标下接触界面端的应力奇异性问题。建立了柱坐标下圆柱体端面接触边缘附近的三维渐近位移场和应力场渐近表达式,并根据铆钉/被铆接件接触界面端的位移和应力边界条件,建立一个非线性特征方程组。据此方程组可求解界面端邻域的应力奇异性指数、位移和应力角分布函数的数值解。通过与有限元方法计算结果相对比,验证了该方法的有效性。分析了平头、沉头以及半圆头铆钉构成的铆接结构的应力奇异性问题,考察了铆钉材料、几何形式和摩擦系数对接触界面端应力奇异性指数和应力场角分布的影响。     

结合面切向接触刚度的概率统计模型

该文考虑结合面上微凸体接触为椭圆形接触, 运用弹性力学空间半无限体受载荷变形理论, 并根据椭圆形接触面上压力分布的Hertz理论, 推导出椭圆形接触面的长、短半轴计算式和单个微凸体接触时的切向接触刚度表达式. 建立了结合面上微凸体椭圆形接触面的长、短半轴呈二维正态分布、高度呈正态分布情况下的宏观切向接触刚度模型, 得到了相应的宏观切向接触刚度表达式. 通过数值计算给出了切向接触刚度随结合面的法向载荷、切向载荷、椭圆微凸体的离心率、微凸体分布的相关系数、微凸体测量高度和微凸体分布的标准方差等各影响因素的变化情况, 增大法向载荷可以提高结合面的切向接触刚度, 而切向载荷的增大会导致切向接触刚度的 减小.     

混合润滑状态下结合面的法向接触刚度研究

针对润滑条件下机械结合面的接触特性受油膜影响的问题,基于结合面接触刚度由油膜接触刚度和固体表面接触刚度组成的思想,建立混合润滑状态下结合面的法向接触刚度模型。采用三维的Weierstrass-Mandelbrot函数获得具有分形特征的粗糙表面,并基于统计学方法建立干摩擦条件下结合面的法向接触刚度模型,考虑了微凸体的完全弹性变形、弹塑性变形以及完全塑性变形过程。在此基础上,求解了油膜的等效厚度并建立油膜的接触刚度模型。结果表明:结合面的法向接触刚度随法向载荷的增加而增加,且混合润滑状态下结合面的接触刚度大于干摩擦条件下结合面的接触刚度;该模型避免了油膜厚度测量难的问题,为机械结构的润滑状态预测提供了帮助。     

Frictional contact analysis of composite materials

In this paper, the highly non-linear frictional contact problems of composite materials are analysed. A proportional loading, the potential contact zone method and finite element analysis are used to solve the problems. A tree-like searching method is used to obtain the solution of the parametric linear complementary problem, which may overcome the anisotropic properties of contact equations caused by composite materials. In the frictional contact analysis of composite materials, the distributions of normal contact pressures, tangential contact stresses and relative tangential displacements are presented for different contact material systems and different coefficients of friction. The results show that the solutions in the paper have good agreement with Hertzian solutions. The influence of different contact material systems and different coefficients of friction on the contact stresses and displacements is large. As a numerical example, ball-indentation tests of composite materials are modelled by the three-dimensional finite element method.     

摩擦接触裂纹问题的扩展有限元法

扩展有限元法(XFEM)是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法。扩展有限元法分析闭合型裂纹时,必须考虑裂纹面间的接触问题。已有文献均采用迭代法求解裂纹面的接触问题。该文建立了闭合型摩擦裂纹问题的扩展有限元线性互补模型,将裂纹面非线性摩擦接触转化为一个线性互补问题求解,不需要迭代求解。算例分析说明了该方法的正确性和有效性,同时表明扩展有限元法结合线性互补法求解接触问题具有较好的前景。     

Contact behaviors of a rigid punch and a homogeneous half-space coated with a graded layer

A contact model between a homogeneous half-space with a linearly graded layer and a rigid punch is proposed and studied in the present paper. The governing equation, which describes the relation of the displacements and the normal tractions at the contact interface, is obtained by means of Fourier transform and a transfer matrix method. Appropriate collocation methods are used in order to solve the equation numerically. Singular behaviors at the edge of a flat punch are revealed. Compared to the case with a graded surface varying according to an exponential law, stress concentration is relatively weaker in the case with the graded surface varying according to a linear law. Furthermore, stress distributions in cases of a flat or cylindrical punch are given for different varying graded laws, thickness of graded layer, ratios of stiffness, and frictional coefficients. All the results are helpful for the design of strong and wear resistance coating surfaces.     

Berechnung der Temperaturfelder in Bremssystemen

This paper presents an iterative method for the investigation of the quasi-stationary temperature field of frictional hot spot moving on the infinite half-space. The nonlinear differential equation of heat transfer has been transformed to a nonlinear integral equation. It was assumed that the thermal conductivity coefficient and the specific heat strongly depend on the actual temperature. In the case of a graphite half-space the dependence of contact temperature on the contact pressure as well as on the velocity has been presented. The temperature distribution, taking into consideration the thermal sensitivity of physical parameters, has been illustrated perpendicularly to the surface of half-space. The results can allow the thermal analysis of brake systems.     

Singularity Analysis and Boundary Integral Equation Method for Frictional Crack Problems in Two-Dimensional Elasticity

This study investigates the stress singularities in the neighborhood of the tip of a sliding crack with Coulomb-type frictional contact surfaces, and applies the boundary integral equation method to solve some frictional crack problems in plane elasticity. A universal approach to the determination of the complex order of stress singularity is established analytically by using the series expansion of the complex stress functions. When the cracks are open, or when no friction exists between the upper and lower crack faces, our results agree with those given by Williams. When displacement and traction are prescribed on the upper and lower crack surfaces (or vice versa), our result agrees with those by Muskhelishvili. For the case of a closed crack with frictional contact, the only nonzero stress intensity factor is that for pure shear or sliding mode. By using the boundary integral equation method, we derive analytically that the stress intensity factor due to the interaction of two colinear frictional cracks under far field biaxial compression can be expressed in terms of E(k) and K(k) (the complete elliptic integrals of the first and second kinds), where k=[1-(a/b)2]1/2 with 2a the distance between the two inner crack tips and b- a the length of the cracks. For the case of an infinite periodic colinear crack array under remote biaxial compression, the mode II stress intensity factor is found to be proportional to [2b tan(π a/2b)]1/2 where 2a and 2b are the crack length and period of the crack array. This revised version was published online in July 2006 with corrections to the Cover Date.     

Using Krylov subspace and spectral methods for solving complementarity problems in many‐body contact dynamics simulation

Many‐body dynamics problems are expected to handle millions of unknowns when, for instance, investigating the three‐dimensional flow of granular material. Unfortunately, the size of the problems tractable by existing numerical solution techniques is severely limited on convergence grounds. This is typically the case when the equations of motion embed a differential variational inequality problem that captures contact and possibly frictional interactions between rigid and/or flexible bodies. As the size of the physical system increases, the speed and/or the quality of the numerical solution decreases. This paper describes three methods – the gradient projected minimum residual method, the preconditioned spectral projected gradient with fallback method, and the modified proportioning with reduced gradient projection method – that demonstrate better scalability than the projected Jacobi and Gauss–Seidel methods commonly used to solve contact problems that draw on a differential‐variational‐inequality‐based modeling approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical analysis of elastic contact problems using the boundary integral equation method. Part 2: Results

This paper gives solutions to various frictionless and frictional contact problems using the boundary integral formulation developed in Part 1. A range of problems is considered in order to demonstrate the applicability of the approach. In most cases equal size linear elements are found to give best results. In the case of frictional problems the arrangement of strick-slip zones is affected by the node locations and a relatively large number of elements may be required to produce satisfactory results. In all cases, the boundary integral equation method yields numerical solutions that are in very good agreement with the analytical solutions to which they are compared.     

Contact with friction between beams in 3‐D space

In this paper a formulation to deal with friction between straight beams undergoing large displacements in 3‐D space is proposed. The detection of the contact point and the computation of the amount of sliding are carried out using a completely symmetric treatment between the two contacting beams. Starting from the virtual work equation the consistent linearization of the frictional contact contribution is computed and the complete equation set is arranged in matrix form suitable for FE implementation. Some numerical examples are added to show the effectiveness of the method. Copyright © 2000 John Wiley & Sons, Ltd.     

Effect of frictional anisotropy on the quasistatic motion of a deformable solid sliding on a planar surface

In this paper, the motion of a deformable body sliding on a half-plane is considered. The solid undergoes large displacements but small strains. An orthotropic friction model described by an elliptic cone is considered. This model allows to describe the sliding-direction dependence of the frictional behavior observed in experience. The algorithm used to solve the problem is based on a weak variational statement of the frictional contact law. The Uzawa algorithm is used to solve the discrete problem. The corresponding algorithm is robust and can deal with large sliding increments. The study shows that frictional properties can influence significantly the trajectory of a deformable body sliding on a frictional surface. Supported by the Australian Research Council     

Fast FE–BEM algorithms for orthotropic frictional contact

This paper presents a new and efficient methodology for solving 3D frictional contact problems considering an orthotropic friction law. The contact methodology is based on a proposed augmented Lagrangian formulation for orthotropic frictional contact problems, and a new discrete contact operator, which allows to reduce the number of unknowns in a Newton‐like algorithm that accelerates the attainment of the solution. A fast Uzawa scheme is also proposed on the basis of the Steffensen's method. Both algorithms prove to be very robust and efficient to solve orthotropic frictional contact problems. The proposed formalism has the advantage of being very compact and valid for both the FEM and the BEM. Numerical results are given to demonstrate the validity of the formulation and algorithms proposed. Copyright © 2013 John Wiley & Sons, Ltd.