变曲率连续滚滑接触安定性的数值方法研究

针对接触表面变曲率的特点,引入局部坐标系,构造出局部坐标下残余应力应变场的分布状态,建立了变曲率连续啮合过程中安定状态残余应力的计算方法。该数值方法将弹塑性问题分解为弹性问题和特征应变决定的残余问题,并采用增量映射方法求解特征应变决定的残余问题,可直接得到接触安定状态下的接触残余应力,并随之进行安定极限的判定。采用该数值方法计算了不同曲率处接触点的安定极限,给出了安定极限与摩擦因数之间的关系,并与有关数值结果相比较,验证了该算法的有效性。     

三维结构安定分析的直接算法

基于线性随动强化理论和Von. Mises屈服准则,对蒙板结构直接安定分析法进行了扩展,建立了结构的三维安定直接分析法。根据投射原理,推导出结构发生塑性安定的存在条件,便于调整控制加载步长和载荷历程。采用逐次增量加载方式,确定出背应力的偏移范围,克服了原始直接分析法不能获得安定极限的缺陷,并得到安定极限条件下结构中残余应力与应变的分布状况。该数值方法将弹塑性问题分解为弹性问题和特征应变决定的残余问题,节约计算时间,提高计算效率,将该算法应用于相关算例,并与有关数值结果相比较,验证了该算法的有效性。     

珩磨缸套与活塞环表面弹塑性接触分析

缸套-活塞环表面接触分析，能够对船用发动机设计决策提供重要支持.由于缸套珩磨网纹表面具有双高斯分布特征，基于高斯分布假设建立的统计接触力学模型无法反映缸套-活塞环表面的真实接触状态.本文中基于边界元理论，采用快速傅里叶变换和共轭梯度法，开发了粗糙接触弹塑性接触数值仿真分析方法，并对缸套珩磨网纹表面与活塞环接触状态进行了仿真计算，获得了表面真实接触压力、接触面积、弹塑性变形和应力等接触特性参数，研究了不同载荷作用下珩磨网纹表面接触演变规律，为活塞环缸套摩擦学设计奠定了基础.     

非稳态纯滚动接触弹塑性分析

建立了二维弹塑性非稳态循环纯滚动接触有限元模型.材料本构采用一种较好的循环塑性模型,并通过材料用户子程序在通用有限元软件ABAQUS中自定义该本构模型.通过在弹塑性无限半空间表面上重复移动随时间按简谐规律变化的赫兹法向载荷来模拟非稳态循环纯滚动接触过程.通过数值模拟,得到接触表面附近的残余累积变形、应变和残余应力.不同的最大赫兹接触压力对残余应力和残余应变影响较大.在简谐变化的法向接触载荷作用下接触表面的变形呈波浪形,随着滚动次数的增加,该波状表面沿载荷移动相反方向逐渐移动,但移动速率要衰减.波状表面波谷处的残余应力、应变和变形大于波峰处.随滚动次数的增加,残余应力增大但很快趋于稳定,残余应变也增大但增大速率衰减.     

关于幂强化材料旋转圆盘的分折以及安定性的讨论

本文利用四阶 Runge—Kutta 法计算了幂强化材料旋转圆盘的应力(?)和残余应力(?)并计算了应力强度(?)和残余应力强度(?)讨论了满足(?)的安定性问题以及确定安定载荷(ω)的方法。     

动载荷下弹塑性随动强化结构的安定问题

本文讨论了弹塑性随动强化结构的动力安定问题,其加载面在应力空间中是任意形状的凸曲面。文中给出了相应的安定定理,指出如果能找到任何一个与时间无关的和虚设残余应力而使结构安定,则该结构将一定是动力安定的。此外,本文还给出了塑性功和塑性应变的上界估计式,并以在交变载荷作用下的Mises随动强化材料的简支圆板为例,对定理的应用进行了说明。     

弹塑性疲劳微弯裂纹尖端塑性区问题

主要研究疲劳载荷作用下弹塑性裂纹弯曲延伸扩展问题.通过分析论证,比较精确地研究了疲劳载荷作用下弯曲延伸裂纹尖端塑性区域边界上交变应力的分布状况.综合考虑了疲劳作用应力,塑性区域交变应力,利用二阶摄动方法,研究计算了弯曲延伸裂纹尖端塑性区域的范围,并预测了疲劳载荷作用下弹塑性裂纹扩展路径.     

含缺陷轴对称体的安定与极限分析

利用静力安全定理得到了计算轴对称体安定与极限载荷的统一格式，采用温度参数法构造安定分析所需的残余应力场，为了克服对工程实际问题进行安定分析时解题规模与计算精度的矛盾，针对轴对称体的特点，采用两种线性化方案对屈服面进行线性化处理，即直接内接法和在降维应力偏量空间中对屈服面的线性化处理，使安定分析转化为一线性规划问题，在简化过程中合理选择线性化方案以便使应力校核点接近精确的屈服面；为了减小计算量，在求     

基于正交基无单元Galerkin法和非线性规划的安定分析方法

基于安定分析的下限定理,用正交基无单元Galerkin法建立了交交载荷作用下理想弹塑性结构安定分析的下限计算格式.在给定载荷域的载荷角点所对应的载荷作用下,采用正交基无单元Galerkin法计算相应的虚拟弹性应力场.并且利用结构在正交基无单元Galerkin法弹塑性增量分析中平衡迭代结果计算得到自平衡应力场基矢量,然后由这些基矢量的线性组合模拟自平街应力场.安定分析问题最终被归结为一系列未知变量较少的非线性数学规划子问题,通过复合形法求解.算例表明该方法的计算结果是令人满意的,并且对初始复合形顶点和用于构造自平衡应力场基矢量的载荷增量是非常不敏感的.     

内时弹塑性分析的一种新算法及其实验验证

本文提出了一种内时塑性理论的弹塑性本构矩阵,发展了内时切线刚度有限元算法。与文[1]相比,该法所需迭代次数显著减少,且无需采用加速因子。作为验证与应用的例子,分析了35CrNi3MoV钢自增强厚壁圆筒(内径22mm,外径55mm)在单调或脉动循环载荷下的弹塑性应变场和残余应力场。与实验的比较是在自增强压力分别为7245,7055,6789个大气压力下进行的。比较结果表明计算得到的残余应力值与文[2]中用Sachs镗孔法测得的残余应力值、计算得到的内压-外壁应变关系与实验结果等都吻合的较好。计算预言了脉动循环载荷下自增强残余应力的松弛现象。本文发展的非线性问题的算法具有数值稳定性好,收敛性好等优点,在实际中可能具有较大的应用价值。     

Contact interaction of an elastic punch and an elastic half-space with initial (residual) stresses

The contact interaction of an elastic punch of arbitrary cross-section and an elastic semi-space with initial (residual) stresses is studied. A general method to solve the problem is proposed. It allows solving contact problems for bodies with initial (residual) stresses when the solution of the corresponding elastic problem is known __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 28–40, December 2007.     

New stress intensity factor solutions of a periodic array of cracks in residual stress field

Many important applications of crack mechanics involve self-equilibrating residual or thermal stress fields. For these types of problems, the traditional fracture mechanics approach based on the superposition principle has ignored the effect of crack surface contact when the crack-tip propagates into the residual compressive region. Contact between the crack faces and the wedging action are responsible for subsequent crack-tip reopening, which often leads to a much larger mode I stress intensity factor. In this study, an analytical approach is used to study the effect of crack face contact for a period array of collinear cracks embedded in several typical residual stress fields. It is found that the nonlinear contact between crack surfaces dominates the cracking behavior in residual/thermal stress fields, which is responsible for crack coalescence.     

PROGRAM-PATTERN MULTIPOLE BOUNDARY ELEMENT METHOD FOR FRICTIONAL CONTACT

A mathematical program is proposed for the highly nonlinear problem involving frictional contact. A program-pattern using the fast multipole boundary element method (FMBEM) is given for 3-D elastic contact with friction to replace the Monte Carlo method. A newoptimized generalized minimal residual (GMRES) algorithm is presented. Numerical examples demonstrate the validity of the program-pattern optimization model for node-to-surface contact with friction. The GMRES algorithm greatly improves the computational efficiency.     

Plane contact problem for a half-space with boundary imperfections

In this paper the new micrmodelling approach to the contact problem for a half-space with boundary imperfections is proposed. The approach is based on a periodic distribution of micro-undulations along the space boundary and leads to the 2-D mathematical macro-model of the contact problem. The general idea of the modelling takes into account certain concepts used in the investigation of periodic composite materials (see e.g. Wozniak, 1993) . The resulting model constitutes a generalization of the known Winkler-type model (see e.g. Shtayerman, 1949) . The numerical solution to the special problem shows the boundary imperfections effect on the contact of bodies.     

Contact Problem for an Elastic Ring Punch and a Half-Space with Initial (Residual) Stresses*

International Applied Mechanics - The problem of contact interaction without friction between an elastic cylindrical ring punch and an elastic half-space with initial (residual) stresses under...     

Contact vibration analysis of the functionally graded material coated half-space under a rigid spherical punch

This paper studies the contact vibration problem of an elastic half-space coated with functionally graded materials (FGMs) subject to a rigid spherical punch. A static force superimposing a dynamic time-harmonic force acts on the rigid spherical punch. Firstly, we give the static contact problem of FGMs by a least-square fitting approach. Next, the dynamic contact pressure is solved by employing the perturbation method. Lastly, the dynamic contact stiffness with different dynamic contact displacement conditions is derived for the FGM coated half-space. The effects of the gradient index, coating thickness, internal friction, and punch radius on the dynamic contact stiffness factor are discussed in detail.     

Mindlin??s Problem for a Halfspace Indented by a Flexible Plate

The paper deals with a contact problem for an isotropic elastic halfspace indented by a flexible circular plate and simultaneously subjected to a Mindlin-type axial force. The approach adopted is to solve the contact problem for the flexible circular plate and the elastic halfspace; this serves as the auxiliary solution to examine, via the Maxwell-Betti reciprocal theorem, the influence of the internal Mindlin force. The contact between the flexible plate and the elastic halfspace is solved using a variational approach. The net displacement of the flexible circular plate and the internal Mindlin force can be evaluated in analytical form. The result has applications to the in situ evaluation of the deformability characteristics of geologic media.