非局部摩擦在塑性加工中的应用

在几类金属塑性成形加工问题中,为了考虑金属材料表面微凸体在模具与工件之间的接触区上的非局部摩擦效应,采用Oden等提出的非局部摩擦模型,借助主应力法,建立了相应问题的单元体的积微分形式的力平衡方程,在简化的情况下,利用摄动法求得接触面上接触压力在非局部摩擦下的近似解,分析了影响接触压力非局部效应的各种因素。     

全长粘结式锚杆的非局部摩擦分析

本文对Oden等提出的非局部摩擦模型进行了修正,得到了修正后的非局部摩擦模型.并应用于全长粘结式锚杆问题.文中利用Mindlin问题的位移解导出的全长粘结式锚杆沿杆体表面所受的剪应力的弹性解,对全长粘结式锚杆进行非局部摩擦分析,得到了在修正后的非局部摩擦模型下的全长粘结式锚杆的侧剪应力.文中修正的非局部摩擦模型下的全长粘结式锚杆的剪应力分布规律与试验得到的结果以及局部摩擦模型(库仑模型)下的计算结果进行了对比,结果表明修正的非局部摩擦模型下的计算结果与实验更符合.因此在描述此锚杆剪应力时,非局部摩擦模型比局部摩擦模型(库仑模型)更接近的实际.     

三维摩擦接触问题的增量线性互补方法

借助罚因子建立了三维摩擦接触本构模型,接触条件被表示为类似于非关联流动的弹塑性本构关系的形式。采用增量描述,对Coulomb摩擦定律采用Taylor展开作线性近似,导出了接触问题的互补虚功方程,然后基于有限元离散建立了三维摩擦接触问题的增量线性互补方法。数值算例表明了本文方法的有效性。     

岩体灌浆锚杆的非局部摩擦分析

本文对Oden等提出的非局部摩擦模型进行了修正，得到了修正后的非局部摩擦模型，并应用于岩土工程问题。文中利用Mindlin问题的位移解导出了岩体灌浆锚杆沿杆体表面所受的剪应力的弹性解,对岩体灌浆锚杆进行非局部摩擦分析，在简化的情况下，得到了在修正后的非局部摩擦模型下的岩体灌浆锚杆侧剪应力的积分形式，再用Maple程序求解，将其所得的结果与局部摩擦(库仑摩擦)模型下的侧剪应力进行比较，结果表明是合理有效的。     

大变形中摩擦接触问题的数值模拟及应用

大变形的摩擦接触是复杂的非线性问题 ,本文介绍了一种处理摩擦接触问题的数值方法。采用接触单元技术模拟接触界面 ,基于弹塑性理论形式的非经典Coulomb摩擦定律及罚函数方法建立了摩擦接触的增量本构关系。结合大变形的增量分析格式给出了积分摩擦接触本构方程的回映方法。这种处理摩擦接触问题的方法计算简单、使用方便。给出的计算实例及应用实例说明了方法的精度与稳定性     

含摩擦与碰撞平面多刚体系统动力学线性互补算法

基于接触力学理论和线性互补问题的算法, 给出了一种含接触、碰撞以及库伦干摩擦, 同时具有理想定常约束(铰链约束) 和非定常约束(驱动约束) 的平面多刚体系统动力学的建模与数值计算方法. 将系统中的每个物体视为刚体, 但考虑物体接触点的局部变形, 将物体间的法向接触力表示成嵌入量与嵌入速度的非线性函数,其切向摩擦力采用库伦干摩擦模型. 利用摩擦余量和接触点的切向加速度等概念, 给出了摩擦定律的互补关系式; 并利用事件驱动法, 将接触点的黏滞-滑移状态切换的判断及黏滞状态下摩擦力的计算问题转化成线性互补问题的求解. 利用第一类拉格朗日方程和鲍姆加藤约束稳定化方法建立了系统的动力学方程, 由此可降低约束的漂移, 并可求解该系统的运动、法向接触力和切向摩擦力, 还可以求解理想铰链约束力和驱动约束力. 最后以一个类似夯机的平面多刚体系统为例, 分析了其动力学特性, 并说明了相关算法的有效性.      

正交各向异性弹塑性摩擦接触问题的数值求解

采用正交各向异性摩擦定律对三维弹塑性摩擦接触问题进行分析,基于参变量变分原理,经过有限元离散,将问题化为线性互补问题模型,之后给出一个求解互补问题的非内点光滑化算法．对三维接触问题,滑动方向的确定一直是个难点,为此,该文采用作者提出的组合规划法和迭代法对各向异性摩擦本构模型进行分析,数值结果说明了模型与算法的正确性。     

INVESTIGATIONS ON THE MECHANICAL CHARACTERISTICS OF NANOBEAMS BASED ON THE NONLOCAL STRAIN GRADIENT THEORY1)

基于非局部应变梯度理论,建立了一种具有尺度效应的高阶剪切变形纳米梁的力学模型. 其中,考虑了应变场和一阶应变梯度场下的非局部效应. 采用哈密顿原理推导了纳米梁的控制方程和边界条件,并给出了简支边界条件下静弯曲、自由振动和线性屈曲问题的纳维级数解. 数值结果表明,非局部效应对梁的刚度产生软化作用,应变梯度效应对纳米梁的刚度产生硬化作用,梁的刚度整体呈现软化还是硬化效应依赖于非局部参数与材料特征尺度的比值. 梁的厚度与材料特征尺度越接近,非局部应变梯度理论与经典弹性理论所预测结果之间的差异越显著.     

非局部应变梯度理论下纳米梁的力学特性研究

基于非局部应变梯度理论,建立了一种具有尺度效应的高阶剪切变形纳米梁的力学模型.其中,考虑了应变场和一阶应变梯度场下的非局部效应.采用哈密顿原理推导了纳米梁的控制方程和边界条件,并给出了简支边界条件下静弯曲、自由振动和线性屈曲问题的纳维级数解.数值结果表明,非局部效应对梁的刚度产生软化作用,应变梯度效应对纳米梁的刚度产生硬化作用,梁的刚度整体呈现软化还是硬化效应依赖于非局部参数与材料特征尺度的比值.梁的厚度与材料特征尺度越接近,非局部应变梯度理论与经典弹性理论所预测结果之间的差异越显著.     

微结构非局部效应的多重性模型及在微梁弯曲中的应用

基于Eringen非局部弹性理论,直接利用逐次逼近法推导了非局部应力场的精确表达,该精确的非局部应力可具体表示为一个无穷级数的形式. 然后以微梁的横向弯曲和纯弯曲变形为例,建立平衡方程并求解及分析了挠度受非局部效应的影响. 结果表明：根据所取非局部小尺度参数大小的不同,非局部微梁的弯曲挠度可低于也可以高于经典力学下的挠度,非局部效应的增大可提高亦可降低结构的抗弯刚度. 本文结果证明了Wang以及Lim等人分别提出的两种相反的非局部模型的各自正确性. 同时首次发现,弯曲挠度随着非局部效应的增大而上下波动且存在若干跳跃点,挠度是非局部小尺度参数的非单调函数,研究同时给出了一种确定材料非局部常数的建议途径.     

Force Action of a Body with a Permeable Boundary on a Wall in a Fluid

The ideal fluid flow due to fluid penetration through the boundary of an infinitely long solid cylinder in contact with a solid wall is determined. A formula is derived according to which the force exerted by a finite-length part of the cylinder on the wall is directed into the wall and can thus have an arbitrarily large absolute value. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 82–84, January–February, 2006.     

On a Paradox in the Motion of a Rigid Particle along a Wall in a Fluid

The results of an experimental investigation of spherical particles with different surface roughnesses rolling under their own weight down an inclined pipe wall in a Newtonian fluid at low Reynolds numbers, both with (friction should be taken into account) and without contact with the wall, are presented. It is shown that a fixed particle moves differently in different fluids with similar viscosities and densities. This fact, as well as the possibility of particle motion without contact with the wall, cannot be explained within the framework of the usual hydrodynamic theories. An example is the dependence of the particle motion on the static pressure.     

Simulation by a source of a thin jet from a body

An exact analytic solution is found to the following plane hydrodynamic problem. An unbounded flow of an ideal incompressible fluid flows around a plate BB' placed at right angles to the velocity vector of the flow at infinity. The pressure on the free boundary P is equal to the pressure in the flow. From an opening in the center of the plate, a jet with flow rate Q from a cavity with pressure P₀ encounters the flow head-on. As a result of the solution, it is found that for fixed width of the opening the values of Q allowed by the scheme are limited. In the limiting case Q = 0 Chaplygin's flow is obtained with stagnation region at the front [1], and in the limiting case Q = Q_max a jet out of a cavity with pressure P₀ into a cavity with pressure P. As Q varies in this interval, the total drag, regarded as the drag of the plate and the chamber from which the jet emerges, takes a minimal value at a certain point. If the width of the opening tends to the length of the slab, the problem of the collision of two jets is obtained; if the width of the opening tends to zero (Q o), the problem of jet flow past a slab with a source is obtained. It is shown that the replacement of the jet by the source gives a good approximation in both the sense of the force characteristics and in the sense of the behavior of the free streamlines.Translated from Izvestiya Akademii Nauk SSSR, Hekhanika Shidkosti i Gaza, No. 5, pp. 47–54, September–October, 1979.We thank L. I. Sedov for his interest in the work and G. Yu. Stepanov for proposing the method of solution and for a helpful discussion.     

Unsteady-state filtration of a liquid in a fractured-porous stratum to a well with a hemispherical end-face

A study is made of the motion of a liquid toward a well with a hemispherical end-face with unsteady-state spherical-radial filtration in a fractured-porous stratum consisting of hemispherical regions with different values of the permeability of the system of cracks, superposed one on another. A Laplace transform is used to find exact solutions to the problem of the lowering of the stratum pressure as a function of time and distance as well as of the output of a well working with a constant end-face pressure. The article discusses partial cases corresponding to the exploitation of closed and bounded open fractured-porous strata by a central well with a hemispherical end-face. On the basis of numerical calculations, the effect of the parameters of fractured-porous strata on the change in the indices of the process of their exploitation is established. It is established that, with the exploitation of fractured-porous strata, the process of the lowering of the end-face pressure of the well and its output become stabilized with sufficiently large values of the time.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 115–123, November–December, 1973.     

Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack

Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and its numerical results coincide with those in references. Thus the method proposed here is verified. The project supported by National Natural Science Foundation of China     

Interaction of a cylinder with a free surface and a jet

The problem of the asymmetric flow around a cylinder of a nonviscous jet is considered and, in particular, of flow with one free boundary. The problem of the choice of circulation is posed, based on a generalization of the Zhukovskii-Chaplygin postulate. Several possibilities are considered and the principle of the minimum of the maximum velocity on a contour is proposed, which qualitatively and quantitatively truly reflects certain aspects of the interaction of the cylinder with the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 50–58, September–October, 1977.     

Impact of a body with a plane bottom on a thin liquid layer at a small angle

The problem of the impact of a body with a plane bottom (of the type of a box) on a thin liquid layer at a small angle is solved in the two-dimensional formulation. The nonlinear shallow water equations are used, together with the method of matched asymptotic expansions. It is found that at certain values of the input parameters of the problem the liquid pressure diminishes near the lower end of the body and becomes smaller than the atmospheric pressure, which results in liquid separation from the box bottom. The numerical results show that all input parameters of the problem have a considerable effect on the nature of body motion. The liquid separation effect on body motion is analyzed.