弹性摩擦接触问题边界元缩聚法分析

利用边界元法对带摩擦弹性接触问题进行了分析，根据接触问题局部非线性的特点，将缩聚法的思想用于接触问题分析。给出了一种带摩擦弹性接触问题的缩聚迭代格式，提高了迭代求解的效率。采用隐含对称条件处理对称结构，通过两个数值算例，说明了该方法的可行性和有效性     

三维真实粗糙表面弹性接触的全域数值解

本文提出了三维真实粗糙表面弹性接触问题的全域数值求解方法。这种方法采用网格规则划分和局部柔度矩阵存储解决了计算机存储问题;采用求解域收缩和逐次低松弛迭代解决了接触方程求解问题。运用这种方法可以获得真实粗糙表面弹性接触时全接触域内的压力分布与总载荷、接触图象及其实接触面积、接触变形与接触刚度等参数。计算结果与实测结果符合得较好。     

用边界元法解无摩擦接触问题

用互易定理导出了弹性静力学问题的边界积分方程,并由弹性接触的协调条件和力平衡条件获得了接触的补充方程,从而将弹性接触问题化为一组线性代数方程求解。接触区的计算采用了逐步逼近法。计算结果与理论值的对照说明这种方法数方法可给出满意的计算结果。     

几何非线性问题的无网格法分析

用局部Petrov-Galerkin方法求解几何非线性问题,这是一种真正的无网格方法。这种方法采用移动最小二乘近似函数作为试函数;只包含巾心在所考虑点处的规则局部区域上以及局部边界上的积分;所得系统矩阵是一个带状稀疏矩阵。该方法可以容易推广到求解非线性问题以及非均匀介质力学问题。在涉及几何非线性问题的数值方法中,通常都采用增量和迭代分析的方法。本文从虚功原理出发,用移动最小二乘近似函数的权函数替代虚位移,并在整个分析过程中所有变量的表达格式都是采用全拉格朗日格式。数值算例表明,无网格局部Petrov-Galerkin方法在求解几何非线性问题时仍具有很好的精度。     

三维边界元法解摩擦型弹性接触问题

基于工程需要,将三维边界元法用于解摩擦型弹性接触问题。在考虑摩擦作用的情况下,于接触区建立局部坐标系,引入边界接触条件,并使用等参单元离散边界,使单元形状与物体边界更好地贴合,最后针对接触问题的非线性特性,讨论了它的增量迭代求解过程。算例表明,在此提出的数值方法是精确有效的。     

关于一个静不定杆系变形协调条件的讨论

研究了一个静不定杆系的内力求解问题。由于静不定杆系内力的矩阵与位移的矩阵是互为转置矩阵,所以可方便求得静不定杆系的变形协调条件。针对该静不定杆系的内力求解问题,指出有关文献给出的该静不定杆系的变形协调条件是错误的。     

解弹性接触问题的二次规划法

本文研究弹性体接触问题,这个问题属于小变形几何非线性问题,它的非线性是由于接触点的接触状态所引起的. 本文提出的二次规划法适用于求解此类非线性问题。首先从理论上研究涉及两个物体的弹性接触问题,把这种问题从数学上归纳为一个标准的二次规划的公式,并导出这类问题解的必要和充分条件。籍助于有限元素法来产生所研究物体的弹性特性数据,并运用二次规划算法来得到具有复杂几何形状问题的数值解.文中介绍了数值例子及其与试验结果的比较,表明该方法是可靠而实用的,且有很高的精度。     

三维边界元法解摩擦型弹性接触问题

基于工程需要,将三维边界元法用于解摩擦型弹性接触问题。在考虑摩擦作用的情况下,于接触区立局部坐标系,引入边界接触条件,并使用等参单元离散边界,使单元形状态与物体边更好地贴合,阳后针对接触问题的非线性特性,了它的增量迭代求解过程。算例表明,在此提出了的数值方法是精确的有效的。     

用边界元法分析接触问题

本文提出用边界元法求解弹性接触问题。边界元法以Ｋｅｖｉｎ函数作为场方程的基本解，具有解析和离散相合的特点，因而大大提高了解的精度。边界元法只需对弹性体的边界离散化。待求末知量只是边界上各离散点的未知数，将这界剖分为一系列单元，按常数元、线性元或二次元的模式，建立代数方程组，这个方程组就确定地边界上全部末知量。弹性接触问题属于小变形几何非线性问题，而这种晨线性恰恰是由于接触边界上边界元的接触条件引起     

螺纹连接件承载能力分析

本文将螺纹牙扣之间的接触受力状态表示为二次规划的型式,解二次规划直接得出接触载荷和接触状态:通过弹性或弹塑性有限无分析产生二次规划的系数矩阵和螺纹连接件的接触应力状态;对于材料非线性的处理,将刚度矩阵的修改缩聚到小的局部塑性区,并通过二次方程来求解过渡无素的加权系数;进行二次规划和弹塑性有限无分析的交替迭代,确定螺纹连接件的承载能力;从实际工程问题的计算和实验的验论表明,该方法效率高,精度好,具有工程应用价值。图6数1参8     

二维多体机械系统多区域接触问题的研究

传统上，人们大多研究物体局部区域或简单结构间的接触问题及其详细力学性态；本文将接触问题放入机械系统中进行研究，不仅考虑物体间的接触，更关注机械系统中各物体的总体弹性变形与物体接触边界间的耦合影响。本文应用势能最小原理，建立了一类描述机械系统中多区域接触问题的力学模型，用一组代数方程组描述接触体间点的约束关系，获得一组包含力学模型和约束方程的代数方程组。用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ法求解之，可获得     

Analysis of clearance fit pin joints

The analysis of clearance fit joints falls within the realm of mixed boundary problems with moving boundaries. In this paper, this problem is solved by a simple continuum method of analysis applying an inverse technique; the region of contact is specified and the corresponding causative load is evaluated. Illustrations are given for a rigid clearance fit pin in a large elastic plate with smooth zero-shear interface between pin and plate, under biaxial plate stress at infinity and due to load transfer through pin.     

A novel finite-element method for use in classical elastic plate problems

We present a novel finite-element method for solving problems in the bending of elastic plates. The basic matrix for an element has mixed force and displacement variables. The coefficients of the matrix are derived without recourse to extremum principles, by the application of conventional structural theory to a set of simple sub-problems or loading cases. Inter-connection of elements by their mid-side nodes is easy, and force or displacement boundary conditions may be imposed directly and easily. The method gives good results, and all force and displacement quantities, including boundary reactions, are readily accessible. The rectangular element here presented is one of a family developed by Woodhead.     

A semi-analytical approach for the geometrically nonlinear analysis of trapezoidal plates

This paper presents a semi-analytical approach for the geometrically nonlinear analysis of skew and trapezoidal plates subjected to out-of-plane loads. The thin elastic plate theory with nonlinear von Kármán strains is used for the nonlinear large deflection analysis of the plate. The solution of the governing nonlinear partial differential equations with variable coefficients is reduced to an iterative solution of nonlinear ordinary differential equations using the multi-term extended Kantorovich method. The geometry of the trapezoidal plate is mapped into a rectangular computational domain. Parallelogram (skew) plates are considered as a particular case of the general trapezoidal ones. The capabilities and convergence of the method are numerically examined through comparison with other semi-analytical and numerical methods and with finite element analyses. The applicability of the approach to the nonlinear large deflection analysis of skew and trapezoidal plates is demonstrated through various numerical examples. The numerical study focuses on combinations of geometry, loading and boundary conditions that are beyond the applicability of other semi-analytical methods.     

Optimization of a structure with contact conditions using equivalent loads

Engineering structures consist of various components, and the components interact with each other through contact. Engineers tend to consider the interaction in analysis and design. Interactions of the components have nonlinearity because of the friction force and boundary conditions. Nonlinear analysis has been developed to accommodate the contact condition. However, structural optimization using nonlinear analysis is fairly expensive, and sensitivity information is difficult to calculate. Therefore, an efficient optimization method using nonlinear analysis is needed to consider the contact condition in design. Nonlinear Response Optimization using Equivalent Loads (NROEL) has been proposed for nonlinear response structural optimization. The method was originally developed for optimization problems considering geometric/material nonlinearities. The method is modified to consider the contact nonlinearity in this research. Equivalent loads are defined as the loads for linear analysis, which generate the same response field as that of nonlinear analysis. A nonlinear response optimization problem is converted to linear response optimization with equivalent loads. The modified NROEL is verified through three examples with contact conditions. Three structural examples using the finite element method are demonstrated. They are shape optimization with stress constraints, size optimization with stress/displacement constraints and topology optimization. Reasonable results are obtained in the optimization process.     

一种新型安全车轮的非线性有限元分析

建立了新型安全车轮的几何模型,说明了车轮构成及基本原理。基于车轮的几何非线性、材料非线性及车轮与地面接触的非线性,建立了车轮的三维非线性有限元模型,用ANSYS软件的非线性分析技术对车轮进行了有限元分析。建模时充分考虑了橡胶材料的超弹性,材料模型采用Mooney-Rivlin橡胶材料。分析了车轮在静态接触、侧倾和侧偏受载3种工况下载荷与变形量的关系,并对车轮应力分布、轮胎接地印迹和接地压力进行了研究,为模拟与分析轮胎行驶性能和车轮的结构设计与优化提供了相关依据。     

Identification of micro-vibro-impacts at boundary condition of a nonlinear beam

Under high amplitude vibrations, contact interfaces experience micro-vibro-impacts and frictional slips. These nonlinear mechanisms can introduce response nonlinearity and energy dissipation into the structures containing them. Beams are widely used in engineering structures and almost in every application they are subjected to boundary conditions. Boundary conditions may contain nonlinear contact interfaces. Therefore, modeling accurately the micro-vibro-impacts and frictional slips developing at the boundary condition of a beam is important in structural dynamics. Ignoring this may result in major discrepancies between experimental observations and theoretical calculations. In this paper identification of micro-vibro-impacts and frictional slips at boundary condition of a nonlinear beam is considered. The structure, being modeled as an Euler-Bernoulli beam, is analyzed using nonlinear normal modes. A reduced-order model governing the dynamic response of the beam near its first resonant point is resulted from the analysis. Identification of the nonlinear boundary condition parameters can be performed by means of the reduced order model and using experimental results.     

Deterministic mixed lubrication modelling using roughness measurements in gear applications

The presence of surface roughness on the teeth of hardened and ground power transmission gears is an unavoidable consequence of their manufacture. The paper discusses the effect of surface roughness when the elastohydrodynamic lubricant film thickness developed between the gear tooth surfaces is small compared to the heights of the roughness features. The ratio of these quantities, called the Λ value, may be well below unity in typical applications. For such thin film conditions the moving roughness features cause the elastohydrodynamic contact between the gears to be highly transient in nature. Surface roughness features on the working surfaces of the gears move past each other during meshing and these asperity encounters are associated with extreme pressure perturbations, or with film breakdown and isolated asperity boundary lubrication events. The paper reviews approaches used to study this problem and describes a coupled approach to solving the elastic and hydrodynamic equations. This allows numerical solutions to be obtained for these extreme conditions so that transient contact events associated with mixed lubrication can be predicted in a unified numerical solution scheme. Typical results obtained from such an analysis are presented including surface fatigue modelling and contact strain energy calculations.     

Numerical modeling an elastohydrodynamic contact of shaped rollers with allowance for misalignment of their axes

A method of numerically solving an elastohydrodynamic (EHD) contact of shaped rollers with allowance for misalignment of their axes in a plane perpendicular to the rolling direction is advanced. The mode of EHD lubrication is typical of such friction assemblies as roller bearings and gearings, in which the contacting elastic bodies are separated by a lubricant film and deformed under the action of an external load. Results of numerical modeling demonstrate the significant effect of the misalignment angle on the distribution of pressure and thickness of the lubricant film in the EHD contact and can be used further to analyze friction in a contact area and the stress tensor in a subsurface layer. The mathematical model of the EHD contact is described through nonlinear integro-differential equations and inequalities. The computational algorithm is based on Newton’s method.     

Response of frictional receding contact problems to cyclic loading

Dundurs [Properties of elastic bodies in contact. In: de Pater AD, Kalker JJ, editors. The mechanics of the contact between deformable bodies. Delft: Delft University Press; 1975. p. 54–66] has shown that if the contact area in a frictionless elastic system under load is equal to or smaller than that before loading (i.e. the contact is receding), the extent of the contact area is load-independent and the stress field varies linearly with load. Similar results apply to problems with Coulomb friction as long as the loading is monotonic, but otherwise non-linearities and variation in the contact area occur. In this paper, we examine this effect for the simple case of an elastic block pressed against a frictional rigid plane. During unloading there is continuous variation of both contact and slip/stick boundaries. For the important case where the loading contains a mean and a periodic component, the system approaches a steady periodic state relatively slowly and in this final state there is continuous variation of the contact area, with the minimum (i.e. the maximum amount of separation) occurring at the minimum applied load.