应用非线性有限元法对某止水橡皮进行仿真计算

应用有限元分析软件对某具有超弹性、不可压缩性和大变形性质的伸缩式止水橡皮进行应力应变仿真分析计算。考虑到材料非线性、几何非线性和边界非线性等问题。通过对超弹性橡皮材料的大变形性质作定性的分析。和对止水橡皮在安装过程中的变形分析。计算支臂翼头在受到刚性夹板央紧作用下的应力分布、橡皮与钢夹之间的接触应力分布。从而分析止水橡皮的止水性能。     

Solvability of Static Contact Problems with Coulomb Friction for Orthotropic Material

We calculate an exact upper bound for the magnitude of the coefficient of friction that ensures the existence of a solution to a static contact problem with Coulomb friction. The approach is based on a general existence result that is valid under the assumption that the coefficient of friction is bounded by a certain constant depending on the constants in two special trace type estimates for a half space domain. We calculate these constants for orthotropic material and two space dimensions with the help of a representation for a partial Fourier transform of the solution to the corresponding system of elasticity equations. The result is compared to the formula for general anisotropic material. The new bound for orthotropic material is significantly larger than the old one for general material, if the material is close to an isotropic material with Poisson ration greater than zero. For some cases the new bound can be even larger than one.      

On the Analytical Approach to Galin’s Stick-Slip Problem. A Survey

Galin’s classical work (PMM J Appl Math Mech 9:413–424, 1945) on the contact of a rigid flat-ended indenter with an elastic half-plane with partial slip was the first successful attempt to take into account friction in the problem of normal contact. As Galin was unable to find an exact solution of the formulated problem, the problem of contact with partial slip of a rigid punch with an elastic half-plane was challenged by many researchers. At the same time Galin’s seminal work stimulated development of solutions for other contact problems with friction that feature different punch geometries and different material responses. This paper presents an overview of the developments in the area of elastic contact with partial slip. In the spirit of Galin’s work the focus is placed on contributions with substantial analytical merit.      

Neo-Hookean fiber-reinforced composites in finite elasticity

The response of a transversely isotropic fiber-reinforced composite made out of two incompressible neo-Hookean phases undergoing finite deformations is considered. An expression for the effective energy-density function of the composite in terms of the properties of the phases and their spatial distribution is developed. For the out-of-plane shear and extension modes this expression is based on an exact solution for the class of composite cylinder assemblages. To account for the in-plane shear mode we incorporate an exact result that was recently obtained for a special class of transversely isotropic composites. In the limit of small deformation elasticity the expression for the effective behavior agrees with the well-known Hashin-Shtrikman bounds. The predictions of the proposed constitutive model are compared with corresponding numerical simulation of a composite with a hexagonal unit cell. It is demonstrated that the proposed model accurately captures the overall response of the periodic composite under any general loading modes.     

Finite element computation of torsional plastic waves in a thin-walled tube

Summary  A finite element technique is presented for the analysis of one-dimensional torsional plastic waves in a thin-walled tube. Three different nonlinear consitutive relations deduced from elementary mechanical models are used to describe the shear stress–strain characteristics of the tube material at high rates of strain. The resulting incremental equations of torsional motion for the tube are solved by applying a direct numerical integration technique in conjunction with the constitutive relations. The finite element solutions for torsional plastic waves in a long copper tube subjected to an imposed angular velocity at one end are given, and a comparison with available experimental results to assess the accuracy of the constitutive relations considered is conducted. It is demonstrated that the strain-rate dependent solutions show a better agreement with the experimental results than the strain-rate independent solutions. The limitations of the constitutive equations are discussed, and some modifications are suggested. Received 9 February 1999; accepted for publication 28 March 2000     

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.     

Shakedown in elastic contact problems with Coulomb friction

Elastic systems with frictional interfaces subjected to periodic loading are sometimes predicted to ‘shake down’ in the sense that frictional slip ceases after the first few loading cycles. The similarities in behaviour between such systems and monolithic bodies with elastic–plastic constitutive behaviour have prompted various authors to speculate that Melan’s theorem might apply to them – i.e., that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down.In this paper, we prove this result for ‘complete’ contact problems in the discrete formulation (i) for systems with no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions and (ii) for certain two-dimensional problems in which the friction coefficient at each node is less than a certain critical value. We also present counter-examples for all systems that do not fall into these categories, thus giving a definitive statement of the conditions under which Melan’s theorem can be used to predict whether such a system will shake down.     

WONDER BEYOND EXPECTATION: NOETHER’S THEOREM IN MECHANICS

诺特(Noether) 定理建立了对称性与守恒定律之间的联系,是现代物理学与力学的基石之一。文中介绍了诺特定理提出的起因、定理的内涵及相关逸闻,说明了固体力学中J 积分、艾西比(Eshelby) 张量与诺特定理的关系。     

Theory of large-strain torsion of prismatic bodies with moment stresses

The problem of the torsion and tension-compression of a prismatic bar with a stress-free lateral surface is studied using three-dimensional elasticity theory for materials with moment stresses. A substitution is found that allows one to separate one variable in the nonlinear equilibrium equations for a Cosserat continuum and boundary conditions on the lateral surface. This substitution reduces the original spatial problem of the equilibrium of a micropolar body to a two-dimensional nonlinear boundary-value problem for a plane region shaped like the cross section of the prismatic bar. Variational formulations of the two-dimensional problem for the section are given that differ in the sets of varied functions and the constraints imposed on their boundary values. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 167–175, July–August, 2006.     

Transition from stick to slip in Hertzian contact with “Griffith” friction: The Cattaneo–Mindlin problem revisited

Classically, the transition from stick to slip is modelled with Amonton–Coulomb law, leading to the Cattaneo–Mindlin problem, which is amenable to quite general solutions using the idea of superposing normal contact pressure distributions – in particular superposing the full sliding component of shear with a corrective distribution in the stick region. However, faults model in geophysics and recent high-speed measurements of the real contact area and the strain fields in dry (nominally flat) rough interfaces at macroscopic but laboratory scale, all suggest that the transition from ‘static’ to ‘dynamic’ friction can be described, rather than by Coulomb law, by classical fracture mechanics singular solutions of shear cracks. Here, we introduce an ‘adhesive’ model for friction in a Hertzian spherical contact, maintaining the Hertzian solution for the normal pressures, but where the inception of slip is given by a Griffith condition. In the slip region, the standard Coulomb law continues to hold. This leads to a very simple solution for the Cattaneo–Mindlin problem, in which the “corrective” solution in the stick area is in fact similar to the mode II equivalent of a JKR singular solution for adhesive contact. The model departs from the standard Cattaneo–Mindlin solution, showing an increased size of the stick zone relative to the contact area, and a sudden transition to slip when the stick region reaches a critical size (the equivalent of the pull-off contact size of the JKR solution). The apparent static friction coefficient before sliding can be much higher than the sliding friction coefficient and, for a given friction fracture “energy”, the process results in size and normal load dependence of the apparent static friction coefficient. Some qualitative agreement with Fineberg's group experiments for friction exists, namely the stick–slip boundary quasi-static prediction may correspond to the arrest of their slip “precursors”, and the rapid collapse to global sliding when the precursors arrest front has reached about half the interface may correspond to the reach of the “critical” size for the stick zone.     

Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints

An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are treated as bilat- eral constraints by neglecting the impact between sliders and guides. Firstly, the normal forces acting on sliders, the driv- ing constraint forces （or moments） and the constraint forces of smooth revolute joints are all described by complementary conditions. The frictional contacts are characterized by a set- valued force law of Coulomb＇s dry friction. Combined with the theory of the horizontal linear complementarity problem （HLCP）, an event-driven scheme is used to detect the transi- tions of the contact situation between sliders and guides, and the stick-slip transitions of sliders, respectively. And then, all constraint forces in the system can be computed easily. Secondly, the dynamic equations of multibody systems are written at the acceleration-force level by the Lagrange multiplier technique, and the Baumgarte stabilization method is used to reduce the constraint drift. Finally, a numerical example is given to show some non-smooth dynamical behaviors of the studied system. The obtained results validate the feasibility of algorithm and the effect of constraint stabilization.     

Influence of friction and asymmetric freeplay on the limit cycle oscillation in aeroelastic system: An extended Hénon’s technique to temporal integration

Nonlinear effects such as friction and freeplay on the control surfaces can affect aeroelastic dynamics during flight. In particular, these nonlinearities can induce limit cycle oscillations (LCO), changing the system stability, and because of this it is essential to employ computational methods to predict this type of motion during the aircraft development cycle. In this context, the present article presents a matrix notation for describing the Hénon’s method used to reduce errors when considering piecewise linear nonlinearities in the numerical integration process. In addition, a new coordinate system is used to write the aeroelastic system of equations. The proposal defines a displacement vector with generalized and physical variables to simplify the computational implementation of the Hénon’s technique. Additionally, the article discusses the influence of asymmetric freeplay and friction on the LCO of an airfoil with control surface. The results show that the extended Hénon’s technique provides more accurate LCO predictions, that friction can change the frequency and amplitude of these motions, and the asymmetry of freeplay is important to determine the LCO behavior.     

三元可燃混合气体爆炸极限实验及预测方法

为了控制并预防原油的储存及输运过程中挥发气体造成的安全风险,在20 L球形爆炸容器内开展了由原油中挥发轻烃CH₄、C₃H₈和C₂H₄构成的三元可燃混合气体的爆炸极限实验,提出并验证了基于Le Chatelier定律及Chemkin模拟的一维层流预混火焰模型预测三元可燃混合气体爆炸极限的方法。结果表明,三元可燃混合气体爆炸极限始终位于3种纯组分的爆炸极限内,随着某一纯组分增加呈现出接近其爆炸极限的趋势。3种纯组分对爆炸上限的影响要强于对爆炸下限的影响,其中C₂H₄对三元可燃混合气体爆炸上限影响尤为显著。两种预测方法的预测结果均与实验规律性一致。Le Chatelier定律预测混合气体爆炸下限较准确,但对爆炸上限的预测随着C₂H₄的增加偏差增大,修正后偏差明显减小;Chemkin预测爆炸下限虽存在一定偏差,但在实验偏差的允许范围内,可作为一种预测三元可燃混合气体爆炸下限的新方法。     

Classical and sequential limit analysis revisited

Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic–plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity – in the absence of hardening and within a linearized geometrical framework –, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity – although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic–plastic coupling in the specific case considered.