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A smooth model of the resultant friction force on a plane contact area

Kudra G., Awrejcewicz J.

Journal of Theoretical and Applied Mechanics

2016

Vol. 54 nr 3

909--919

A class of smooth approximations of the total friction force occurring on a plane finite contact surface is presented. It is assumed that the classical Coulomb friction law is valid on any infinitesimal element of the contact region. The models describe the stick phase, the fully developed sliding and the transition between these two modes. They take into account different values of static and dynamic friction coefficients. The models are applied in simulation of a dynamical system performing translational and rotational stick-slip oscillations, and then they are verified by comparison with the corresponding results in which an event-driven discontinuous model of friction is used.

On plane contact problem of an elastic periodically layered composite with boundary normal to layering

Perkowski D. M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2007

Vol. 6, nr 1

205-218

This paper deals with some plane contact problem of an elastic laminated halfplane with boundary normal to layering. The considered problem is solved within the framework of the homogenized model with microlocal parameters given by Woźniak [6], Matysiak and Woźniak [7]. The body is assumed to be composed of two-layered, periodically repeated laminae. The perfect mechanical bonding between the layers is assumed. Moreover, the boundary condition for normal stresses on boundary normal to layering is approximated by using approach given by Perkowski et al. [8], Matysiak and Perkowski [9]. This approach allows to reduce the described problem to well-known dual integral equations and it can be solved exactly. Thus, the problem is solved by using analytical methods. The results of numerical analyses shown the distribution of contact pressure and stress distributions are presented in the form of figures.