用有限元素法分析弹性固体接触问题

(一)用增量迭代法处理非线性位移一载荷关系图1为一个典型的平面弹性固体接触问题.假定应力-应变关系及应变-位移关系均为线性关系,于是用物体变形前的几何形状列出平衡方程.但是,由于接触物体之间的接触状况在加载过程中有变化,位移与载荷不能保持线性关系. ...     

基于约束函数法的热力耦合有限元分析

分析了滑移接触条件下热力耦合现象,建立了热力耦合的有限元分析连续模型,提出了系统动力学平衡方程和热力学平衡方程。对系统中物体间的接触条件进行了分析,得到了物体间接触条件的数学表达式,在此基础上,用约束函数表示接触约束条件。应用变分原理对约束函数进行变分,与系统平衡方程组成非线性方程组对热力耦合问题进行求解。实例表明,用约束函数法求解热力耦合问题,收敛性较好,算法稳定,计算结果能反映实际。     

滚动体几何相似条件在轴承边界元法中的应用

滚动轴承作为多物体接触系统,具有高度的非线性。为了求解滚动轴承的三维载荷分布,考虑所有滚动体的形状和边界条件相同,利用几何相似条件通过初始位置滚动体的离散模型,得到其他滚动体的离散数据。将所有滚动体看作是一个物体,轴承系统可以用3个物体无摩擦接触边界元法进行模拟计算。考虑全部滚动体作为一个整体的特殊性,叙述了边界积分方程和耦合的矩阵方程的建立,编制了基于滚动体几何相似条件的轴承边界元法Fortran源程序。利用该程序对轧机四列圆锥滚子轴承进行数值模拟,得到轴承的接触压力和载荷,滚动体接触宽度和接触滚动体个数,并说明了方法的有效性。     

用白光进行散斑图的信息处理

引言近几年来散斑法获得很大发展。这种方法具有非接触测量、不需要破坏被测物体、对被测物体材料没有特殊要求、测量灵敏度高和设备简单等优点。用散斑法能测量平面变形和三维问题,测量物体内部应变,研究静、动态应力分 ...     

接触问题的简化方法

本文基于一种合理的物理抽象，给出了一种计算接触问题的简化方法．其实质是在接触物体之间填加低弹模的虚构材料，以此来消除接触问题的边界非线性，将工程中广泛存在的接触问题转化为一般性的力学问题。这样可使问题得以简化，降低计算成本。简单的验算表明方法是可靠的．     

用拉格朗日函数分析不同模量静不定桁架内力

在外载荷作用下的不同模量静不定桁架平衡问题,是任意有限多个自变量的多元函数在任意有限多个约束条件下的极值问题,对采用拉格朗日乘数法求解此类极值问题进行了数学证明．通过求解不同模量静不定桁架极限载荷的几个算例,阐述拉格朗日乘数法在计算不同模量静不定桁架极限载荷中的应用．研究结果表明：采用拉格朗日乘数法求解不同模量静不定桁架极限载荷的通用性较强,用拉格朗日乘数法求解不同模量静不定桁架极限载荷的方法不但克服了常规方法需利用几何关系建立协调方程的缺陷,且具有力学概念清晰直观、计算过程简便、便于工程设计人员在实际中掌握和应用．     

数字全息计量技术及其在微小位移测量中的应用

数字全息是用数字的方式记录和处理全息图像，避免了传统全息照相的化学处理，既简化了处理过程，更便于用数字图像处理的方式来改进图像质量和提取信息。数字全息干涉计量技术是一种全场、非接触的光学测量方法，该方法测量精度高，光路简单，对防振要求低，实验条件容易满足，特别适合微小物体的微小位移或变形的精确测量。本文运用数字全息干涉计量法测定了两端固支梁的微小离面位移；经实验验证数字全息计量术能精确测量物体0．01微米量级位移或变形；而且该方法可靠性好、成本低；是非接触的无损测量。数字全息计量技术的这些特点使得该技术在小物体的微小变形测量上具有特别的优越性，因而在MEMS结构及MEMS材料参数(如弹性模量、泊松比、热变形系数等)的测定中有广阔的应用前景。     

多点碰撞动力学的规范求解

物体间的碰撞是工程技术中一个重要研究课题．大多数的研究工作都是集中在多刚体系统碰撞动力学问题的研究．在多刚体系统中，两个刚体之间是用一个铰连接的．但是，还存在另一类型的碰撞系统，在这类碰撞系统中，相碰的物体间没有铰存在．物体可能是自由的，也可能是被其周围环境约束的，但在物体之间没有铰的联系，这种碰撞问题称作为“分离式碰撞问题”，物体间的相互联系和相互作用仅仅在碰撞过程中存在．本文对这类“分离式碰撞问题”进行了研究，并且给出了一组解决这类问题的通用公式．这些公式可以方便地编程和计算，从而实现了多物体间的多点碰撞的动力学求解     

从苍蝇与物面的触粘看尺度效应

苍蝇与光滑硬物体接触时，靠腿上纤毛与物体表面产生吸附作用，在JKR接触理论下，得出考虑表面能作用时的粘附力表达式，结果表明芬蝇与物面的触粘和脱脱离界定了其纤毛的尺度范围，该尺度范围与扫描电镜观察的结果相一致。     

几何规划的最速下降法

本文把无约束极值问题中的最速下降法应用到几何规划的集约迭代中,从而控制和加快了收敛速度。用该法计算了两杆桁架和平面腹板梁的优化设计问题取得满意的结果。     

On the general contact problem of an inflated nonlinear plane membrane

The nonaxisymmetric contact problem between an inflated membrane and a rigid indentor is considered. The membrane is assumed to be an initially thin plane sheet. The shape and the boundary of the contact region and the configuration of the deformed membrane under both inflation and indentation are found by employing the minimum potential energy principle subjected to an inequality constraint condition. A slack variable that converts the inequality constraint to an equality constraint condition is introduced. The coordinate functions that describe the deformed configurations of the membrane are assumed to be represented by a series of geometric admissible functions with unknown coefficients. The unknown coefficients that minimize the total potential energy are determined by Fletcher and Powell's[1] iterative descent method for finding the minimum of a function of multivariables.     

The equilibrium state of a structure subject to frictional contact

A structure in frictional contact subject to static loads has not, in general, a unique static equilibrium state. This is because the state, displacements and contact forces, depend on the load history of the structure.In cases where the exact load history is not known it would be of interest to find a state that is in some sense likely and define this as the equilibrium state. In this paper, it is assumed that the state with the smallest potential energy is the most likely one. The implication of this definition of likely state is analysed and shows that the resulting problem basically can be seen as a generalization of the frictionless contact problem to structures where no frictionless state is possible, i.e. structures where non-zero friction forces are necessary to satisfy force equilibrium.The results of several numerical experiments are given. The structures in the experiments are trusses and structures modelled by the finite element method. Both a sequential quadratic programming method and an enumeration method are used to solve the likely-state problem.     

A REDUCED QUADRATIC PROGRAMMING METHOD FOR ELASTIC CONTACT PROBLEMS

基于势能原理以节点位移为设计变量、以接触条件为约束方程构建了无摩擦弹性接触问题的二次规划数学模型,在此基础之上利用力平衡线性约束方程的特解和由基础解向量构成的奇异模态矩阵,提出一种新的基于奇异坐标变换的自由度缩减方法,大大降低了二次规划的规模,并使得二次规划模型不再含显性等式约束;根据弹性接触力学体系的特点,通过人为假定接触自由度位移模式,提出了一种简单高效的奇异模态矩阵的计算方法。通过两圆柱接触、轴孔间隙配合接触两个数值算例的对比分析,验证了对于弹性接触问题的求解,缩减二次规划方法有效克服了传统方法计算量大、对求解参数设置敏感、收敛困难的问题。     

On the unilateral contact problem of structures with a non quadratic strain energy density

The analysis of structures with “unilateral contact” boundary conditions is considered. The stress-strain relations are nonlinear and they are derived from a non quadratic strain energy density by “subdifferentiation”. It is proved that for the inequality constrained boundary value problem the “principles” of virtual and of complementary virtual work hold in an inequality form constituting a variational inequality. The theorems of minimum potential and complementary energy are proved to be valid to account for this type of boundary conditions. These theorems are used to formulate the analysis as a nonlinear programming problem. A numerical example of a structure having the “unilateral contact” boundary condition illustrates the theory.     

刚性圆形压头作用下热电材料半平面的无摩擦接触问题

热电材料可以将热能转化为电能,反之亦然,这一优良的性质将有助于研发更具成本效益的设备和器件。本文研究了刚性圆形压头作用在热电材料半平面的无摩擦接触问题。假定压头为电导体、热导体,且压头压入深度及与材料的接触区域宽度未知。首先求解电场和温度场,利用傅里叶变换得到了电势函数、温度、电流密度和能量通量的解析表达式。然后求解弹性场,利用积分变换和边界条件,将该热弹性接触问题转化为第一类奇异积分方程并数值求解。数值结果讨论了压头半径和热电载荷对法向接触应力、电流强度因子和能量通量强度因子的影响。结果表明,对于圆压头,热电材料的法向电流密度、法向能量通量在接触边缘表现出奇异性,而表面法向接触应力在接触边缘为零。本文建立的研究模型有助于更深层次的了解热电材料的接触行为。     

Mass redistribution method for finite element contact problems in elastodynamics

This paper is devoted to a new method dealing with the semi-discretized finite element unilateral contact problem in elastodynamics. This problem is ill-posed mainly because the nodes on the contact surface have their own inertia. We introduce a method based on an equivalent redistribution of the mass matrix such that there is no inertia on the contact boundary. This leads to a mathematically well-posed and energy conserving problem. Finally, some numerical tests are presented.     

Modeling and analysis of sliding joints with clearances in flexible multibody systems

The modeling of the sliding joint with clearance between a flexible beam and a rigid hole is investigated in this paper. The flexible beam is discretized using the three-dimensional curved Euler–Bernoulli beam element of the Absolute Nodal Coordinate Formulation, while the motion of the rigid hole is described by the Cartesian coordinates. Moreover, the cross sections of both the flexible beam and the rigid hole are assumed to be circular. The existing joints with clearances are mainly rigid joints with small clearances, and the contact detection algorithm adopted can solve only one pair of potential contact points within one section. In order to model the contact problem in the sliding joint with clearance, a new contact detection method based on the intersection of the rigid hole’s cross section and the flexible beam is proposed, which yields a two-dimensional contact detection problem. Based on the common-normal concept, the ellipse–circle contact detection problem within the hole’s cross section can be solved. The potential contact point on the hole’s cross section will be determined, and the closest point projection on the beam’s neutral axis can be defined further. The proposed contact detection method can deal with the sliding joint with large clearance and the multiple-point contact problem within one section. In addition, the penalty method is adopted to model the frictionless contact between the flexible beam and the rigid hole. Finally, two numerical examples about sliding joints with clearances, one with an initially curved beam under gravity and the other with a straight beam under zero gravity, are presented to demonstrate the influence of the clearance of sliding joint on the dynamic performance of flexible multibody systems.     

含黏弹性夹芯FG-GRC后屈曲梁的低速冲击响应

研究了含黏弹性夹芯的功能梯度石墨烯增强复合材料(functionally graded graphene reinforced composite, FG-GRC)后屈曲梁在低速跌落冲击下的跳跃振荡行为.采用修正Halpin-Tsai细观模型预测FG-GRC的材料宏观属性.使用赫兹点接触模型确定冲击器和梁之间的接触力.提出了考虑轴向预应力的复合材料层本构关系和阻尼层的Kelvin型黏弹性本构.通过一种广义高阶剪切变形锯齿梁模型建立夹芯梁的非线性位移场. 基于Hamilton 能量变分原理, 推导了动力学控制方程组. 通过两步分析,首先获得弹性后屈曲平衡路径作为冲击问题的初始状态. 随后, 结合四阶龙格库塔法,拓展了两步摄动-伽辽金法计算接触力的时程曲线以及后屈曲梁的位移时程曲线.研究了后屈曲梁在单次和两次撞击下双稳态大幅振荡过程的动力学特征.讨论了轴向载荷、冲击速度、黏弹性阻尼特性、冲击器材料等因素对于碰撞接触力以及后屈曲梁动力响应的影响规律.结果表明, 接触力仅对冲击速度较为敏感,一定的结构碰撞参数设计可以在接触力变化不大的情况下,使得后屈曲梁由单势能阱运动转变为双阱大幅振荡.      

摩擦约束塑性力学变分不等原理的半反推法

带摩擦约束的弹塑性接触问题,由于摩擦约束条件是一种判别性的条件,它的变分问题的逆问题的研究比较困难。本文对弹塑性接触力学中的变分不等问题的逆问题进行了研究,改进了半反推法并将其应用到弹塑性变分不等原理的研究中,导出了摩擦约束弹塑性增量广义变分不等原理中的能量泛函,消除了用拉氏乘子法可能产生的临界变分现象,在证明中,巧妙地处理了增量表示的接触摩擦边界条件,避免了使用非线性泛函分析和凸分析,简化了证明。     

一种基于面-面局部搜索的接触算法

接触-碰撞算法是影响动态接触问题数值分析精度的重要因素,发展健壮、精确的局部搜索算法对提高数值模拟精度具有重要意义。为解决点-面接触搜索算法存在的盲区问题,提出了一种基于面-面的局部搜索算法,并发展了相应的接触力计算方法。新的接触算法以面心坐标与特征长度表征接触片,进行预搜索快速排除不会发生接触的潜在接触对;利用主从接触片的投影与侵入深度关系确定接触片间的接触状态;利用等参逆变换解析给出接触点,避免了方程组的迭代求解。典型算例与工程实例计算表明,本文算法消除了接触搜索的盲区,具有很好的健壮性与计算精度。