Transient thermoelastic contact problem of two sliding half-planes

A transient contact problem with frictional heating for two sliding halfplanes is considered. One of the half-planes is slightly rounded to give a hertzian initial pressure distribution; the other is a rigid non-conductor. It is shown that if the ratio of initial width of contact to the width in the steady state is less than some critical value, the contact area shrinks smoothly until the steady state is reached. Otherwise the pressure distribution develops a wavy perturbation and eventually bifurcates. Results are compared with previous approximate solutions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25738/1/0000295.pd

Some History-Dependent Problems for Dissimilar Cylinders With Finite Friction

This paper is concerned with the problem of contact between two dissimilar elastic cylinders. The cylinders are pressed together by a compressive force, P, and loaded by a tangential force, H, which is transmitted in the form of a distribution of frictional tractions at the interface. We assume that Coulomb’s law of friction holds at the interface. We develop a numerical algorithm which is sufficiently general to deal with an arbitrary history of normal and tangential loading, P(t), H(t) and which retains the full description of the coupling between the normal and tangential tractions. The proposed algorithm gives good numerical accuracy in comparison with previous analytical and numerical solutions of a variety of problems for normal and tangential loading of two contacting cylinders with friction. It is also found to be very efficient in the use of computer time. Results for some previously unsolved problems involving the full coupling between normal and tangential contact tractions indicate that such coupling can have a significant effect on the solution, particularly in regard to the extent of slip and stick zones within the contact area.</jats:p

A Generalization of the Upper Bound Method With Particular Reference to the Problem of a Ploughing Indenter

An algorithm based on a combination of the upper bound method and finite element repesentation has been developed. The algorithm is applied to the problem of a rigid indenter ploughing through a rigid/perfectly-plastic material. Numerical examples are given and the results are compared with previous approximate solutions. Limitations of the upper bound method are discussed.</jats:p

On partial contact of a thin-walled circular cylinder and a rigid half-space

A long circular cylinder with radius R and thickness t transmits a longitudinal eccentrically applied force to a rigid half-space. We study the influence of the eccentricity of the load and the ratio R/t on the stress state of the cylinder using the theory of thin shells in bending. The elastic displacements are presented in the form of a Fourier expansion, the coefficients of which are found by the variational formulation of the problem combined with the penalty approach for a numerical implementation of contact conditions. Results are applied to certain problems of buckling of a circular bar and compared with previous approximate solutions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25911/1/0000474.pd

Transient Contact of Two Sliding Half-Planes With Wear

We study the transient contact of two sliding bodies with a simple geometry. The model employs the Archard law of wear in which the rate of material removal is proportional to pressure and speed of sliding. The problem is formulated in terms of two governing equations with unknown pressure and heat flux at the interface. The equations are solved numerically, using appropriately chosen Green’s functions. We start with a single area of contact. As a result of frictional heating and thermal expansion, the contact area shrinks, which leads to further localization of pressure and temperature. The role of wear is twofold. By removing protruding portions of the two bodies, wear tends to smoothen out pressure and temperature. On the other hand, it causes the contact area to grow sufficiently large to become unstable and bifurcate. Areas carrying load are eventually removed by wear, and the contact moves elsewhere. The system develops a cyclic behavior in which contact and non-contact areas interchange.</jats:p