Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established.

Frictional contact algorithm study on the numerical simulation of large deformations in deep soft rock tunnels

There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method to tackle the nonlinear eontact and large deformation problem in A Software on Large Deformation Analysis for Soft Rock Engineering at Great Depth was presented. In the software, based on Lagrange multiplier method and Coulomb friction law, kinematic constraints on contact boundaries were introduced in functional function, and the finite element equations was established for two incremental large deformation analyses models, polar decomposition model and additive decomposition model. For every incremental loading step, by searching for the contact points in the potential contact interfaces （the excavation boundaries）, the Lagrange multipliers, i.e., contact forces are cal- culated iteratively by Gauss-Seidel method, and justified through satisfy the inequalities of static constraint on contact boundaries. With the software, large deformation and frictional contact of a transport roadway were analyzed numerically by the two models. The numerical examples demonstrated the efficiency of the method used in the software.

FRICTIONAL CONTACT MULTIPOLE-BEM AND 3-D ANALYSIS OF SCREWPAIRS

The 3-D traction field in the pressure screw-pair of a 3 500 heavy and mediumplate mill press down system is successfully calculated by applying the 3-D frictional contactmultipole-BEM and the corresponding program that has been developed. The computing results show themedium diameter orientation is unreliable, especially under the interference of an outer forcecouple. Under such working conditions, the circumferential traction distribution on the screw teethis extremely uneven, which is the main reason for the destruction and short life time ofscrew-pairs. When utilizing the same precision (the relative tolerance is 10X10^(-5)), themultipole-BEM uses almost the same CPU time as used by the FEM, but the needed computer memory sizeis only one eightieth of that needed by the FEM (10 MB vs. 800 MB). The multipole-BEM is well suitedfor computing large-scale engineering problems.

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.

Numerical Analysis of Rolling-sliding Contact with the Frictional Heat in Rail

Thermal damage caused by frictional heat of rolling-sliding contact is one of the most important failure forms of wheel and rail. Many studies of wheel-rail frictional heating have been devoted to the temperature field, but few literatures focus on wheel-rail thermal stress caused by frictional heating. However, the wheel-rail creepage is one of important influencing factors of the thermal stress In this paper, a thermo-mechanical coupling model of wheel-rail rolling-sliding contact is developed using thermo-elasto-plastic finite element method. The effect of the wheel-rail elastic creepage on the distribution of heat flux is investigated using the numerical model in which the temperature-dependent material properties are taken into consideration. The moving wheel-rail contact force and the frictional heating are used to simulate the wheel rolling on the rail. The effect of the creepage on the temperature rise, thermal strain, residual stress and residual strain under wheel-rail sliding-rolling contact are investigated. The investigation results show that the thermally affected zone exists mainly in a very thin layer of material near the rail contact surface during the rolling-sliding contact. Both the temperature and thermal strain of rail increase with increasing creepage. The residual stresses induced by the frictional heat in the surface layer of rail appear to be tensile. When the creepage is large, the frictional heat has a significant influence on the residual stresses and residual strains of rail. This paper develops a thermo-meehanical coupling model of wheel-rail rolling-sliding contact, and the obtained results can help to understand the mechanism of wheel/rail frictional thermal fatigue.

Nonlinear Dynamics Seismic Response of Container Crane Based on Contact Friction Theory

To evaluate the dynamic behavior of a container crane under seismic loads accurately,the contact state between the wheels and the rails or the ground that significantly affect the seismic response of the structure must be considered elaborately.This paper has proposed a modeling method based on the theory of contact and friction for simulating the nonlinear seismic response of large and flexible structure of a jumbo movable container crane,including the contact problem regarding the wheels attached to the bottom of its legs and the rails on which they ride.These models are used to perform extensive dynamic time-history analysis in order to find out their nonlinear dynamic behavior under various excitation modes.It is found that the presented numerical modeling method simulates the nonlinear seismic response of a container crane quite well.Notably,it can verify and expand our understanding of the seismic behaviors by evaluating response performance for the large seaport cranes.

BLOCK PIVOT METHODS FOR SOLVING FRICTIONAL CONTACT PROBLEMS

Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number of steps when the friction coefficient is ''relative small''. Unlike most mathematical programming methods for contact problems, the block pivot methods permit multiple exchanges of basic and nonbasic variables.

A NEW METHOD FOR SOLUTION OF 3D ELASTIC-PLASTIC FRICTIONAL CONTACT PROBLEMS

The solution of 3 D elastic-plastic frictional contact problems belongs to the un specified boundary problems where the interaction between two kinds of nonlinearities should occur. Considering the difficulties for the solution of 3 D frictional contact problems, the key part is the determination of the tangential slip states at the contact points, and a great amount of computing work is needed for a high accuracy result. A new method based on a combination of programming and iteration methods, which are respectively known as two main kinds of methods for contact analysis, was put forward to deal with 3 D elastic-plastic contact problems. Numerical results demonstrate the efficiency of the algorithm illustrated here.

Propagation of harmonic waves through micro gap with consideration of frictional contact

Transmission of elastic waves through a micro gap between two solids with consideration of frictional contact is investigated. By using the Fourier analysis technique and the corrective solution method, the nonlinear boundary problem is reduced to a set of algebraic equations. Numerical results exhibit the locations and extents of separation, slip, and stick zones, the interface tractions, and the energy partition. The effects of gap width, frictional coefficients, and the incident angle on the wave transmission are discussed in detail. The results show that higher harmonics are generated due to the local contact/slip at the interface.

F0RMULATION OF BOUNDARY ELEMENT-LINEAR COMPLEMENTARY EQUATION FOR THE FRICTIONAL ELASTIC CONTACT PROBLEMS

Boundary element-linear complementary equations are formulated to solve elastic contact problems with Coulomb frictions.It is also a new attempt to solve free boundary problems in solid mechanics by means of boundary element-mathematical programming techniques.

CONTACT FRICTION ANALYSIS AND STRESS OSCILLATION SUPPRESSION WITH A SIMPLE INTERFACE ELEMENT

A simple interface element for analyzing contact friction problems is developed. Taking nodal displacements and contact stresses as unknowns, this element can simulate frictional slippage, decoupling and re-bonding of two bodies initially mating or having gaps at a common interface. The method is based on the Finite Element Method and load incremental theory. The geometric and static constraint conditions on contact surfaces are treated as additional conditions and are included in stiffness equations. This simple element has the advantages of easy implementation into standard finite element programs and fast speed for convergence as well as high accuracy for stress distribution in interface. Undesirable stress oscillations are also investigated whenever large stress gradients exist over the contact surfaces. Exact integration or the conventional Gauss integration scheme used to evaluate the interpolation function matrix of the interface element is found to be the source of the oscillations. Eigenmode analysis demonstrates that the stress behavior of an interface element can be improved by using the Newton-Cotes integration scheme. Finally, the test example of a strip footing problem is presented.

BOUNDARY ELEMENT-COMPLIANCE MATRIX METHOD FOR 3D ELASTIC FRICTIONAL CONTACT ANALYSIS

Boundary element compliance matrix (BEM) method to deal with 3D elastic frictional contact problem was presented, and its calculation method and convergence criteria were discussed. It has the advantages of both boundary element method and compliance matrix methods: small number of inputting data, simple and convenient model, precise solution, short calculating time and requirements for a small quantity of computer memory. In comparison to the other BEM with friction problems, we obtain more precise solution and less iteration times. The effect of friction coefficient on contact area. contace state, and relative displacement, normal and tangential stress was analyzed by two examples. And because of the quickness of calculation of program and efficient method, we visualize the result in virtual reality (VR) environment. We grant the real time of VR and provide more immersion to users who ware the VR device.

Analysis of composite material interface crack face contact and friction effects using a new node-pairs contact algorithm

A new node-pairs contact algorithm is proposed to deal with a composite material or bi-material interface crack face contact and friction problem （e.g., resistant coating and thermal barrier coatings） subjected to complicated load conditions. To decrease the calculation scale and calculation errors, the local Lagrange multipliers are solved only on a pair of contact nodes using the Jacobi iteration method, and the constraint modification of the tangential multipliers are required. After the calculation of the present node-pairs Lagrange multiplier, it is turned to next contact node-pairs until all node-pairs have finished. Compared with an ordinary contact algorithm, the new local node-pairs contact algorithm is allowed a more precise element on the contact face without the stiffness matrix singularity. The stress intensity factors （SIFs） and the contact region of an infinite plate central crack are calculated and show good agreement with those in the literature. The contact zone near the crack tip as well as its influence on singularity of stress fields are studied. Furthermore, the frictional contacts are also considered and found to have a significant influence on the SIFs. The normalized mode-II stress intensity factors KII for the friction coefficient decrease by 16% when f changes from 1 to 0.

Modeling and Calculation of Impact Friction Caused by Corner Contact in Gear Transmission

Corner contact in gear pair causes vibration and noise,which has attracted many attentions.However,teeth errors and deformation make it difficulty to determine the point situated at corner contact and study the mechanism of teeth impact friction in the current researches.Based on the mechanism of corner contact,the process of corner contact is divided into two stages of impact and scratch,and the calculation model including gear equivalent error-combined deformation is established along the line of action.According to the distributive law,gear equivalent error is synthesized by base pitch error,normal backlash and tooth profile modification on the line of action.The combined tooth compliance of the first point lying in corner contact before the normal path is inversed along the line of action,on basis of the theory of engagement and the curve of tooth synthetic complianceload-history.Combined secondarily the equivalent error with the combined deflection,the position standard of the point situated at corner contact is probed.Then the impact positions and forces,from the beginning to the end during corner contact before the normal path,are calculated accurately.Due to the above results,the lash model during corner contact is founded,and the impact force and frictional coefficient are quantified.A numerical example is performed and the averaged impact friction coefficient based on the presented calculation method is validated.This research obtains the results which could be referenced to understand the complex mechanism of teeth impact friction and quantitative calculation of the friction force and coefficient,and to gear exact design for tribology.

Modeling for thermal contact resistance of frictional interface under high temperature and high pressure

According to the thermodynamic characteristics in the work interface of the plastic forming of metals, a set of TCR (thermal contact resistance) experimental system under the conditions of high temperature and high pressure has been designed. The interrelations between the thermal contact resistance (TCR) and its influence factors such as contact pressure etc, are obtained. A modified coefficient E is introduced to consider the relative slide in the contact interface. Then the interfacial TCR calculating model, which suits to the special conditions of `high temperature+plastic rheology’ and frictional contact such as continuous roll casting process, is established.

Solving frictional contact problems by two aggregate-function-based algorithms

Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.

Influence of Friction Interface Contact on Ultrasonic Motor Efficiency Under Static Conditions

The friction interface matching plays a deterministic role in the motor efficiency,and the microcosmic contact status of friction interface should be investigated to improve the ultrasonic motor performance.The main purpose is to improve the effective output power of ultrasonic motor.Hence,one studies the contact condition of the friction interface of the ultrasonic motor,analyzes the micro condition of contact interface through finite element analysis,optimizes unreasonable structures,and compares the two different-structure ultrasonic motors through experiments.The results reflect the necessity of optimization.After optimization,the stator and rotor deform after pre-pressure and the contact interface of them full contact theoretically.When reaching heat balance the effective output of the motor is 37%,and the average effective output efficiency is 2.384 times higher than that of the unoptimized.It can be seen that the total consumption of the ultrasonic motor system decreases significantly.Therefore,when using in certain system the consumption taken from the system will decreases largely,especially in the system with a strict consumption control.

The Effects of Contact Interface on the Friction Characteristics of Self-assembly Monolayers

The effects of different contact interfaces on the friction characteristics of OTS self-assembled monolayers were investigated by a universal micro-tribometer in different sliding velocities. The results indicate that there exist lower friction coefficients between OTS SAMs and Ti, Ni and Cu films deposited on GCr15 steel balls than those between OTS SAMs and GCr15 steel ball. The friction coefficient between OTS SAMs and Ti film is the largest, and the friction coefficient between OTS SAMs and Cu film is the least in these three films, which depends on the intrinsic characteristics of the materials. The friction coefficients between OTS SAMs and GCr15 steel ball and three nanometer films increase with the sliding velocity increasing, which can be explained by the relaxation characteristics of OTS molecules.

Frictional contact problem for elastic-viscoplastic materials with thermal effect

A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca＇s friction law with heat exchange. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear first order evolution inequalities, the equations with monotone operators, and the fixed point arguments. Finally, the continuous dependence of the solution on the friction yield limit is studied.