New results on the stability of quasi-static paths of a single particle system with Coulomb friction and persistent contact
نویسنده
چکیده
In this paper we announce some new mathematical results on the stability of quasistatic paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle.A quasi-static path is said to be stable at some value of the load parameter if, for some finite interval of the load parameter thereafter, the dynamic solutions behave continuously with respect to the size of the initial perturbations (as in Lyapunov stability) and to the smallness of the rate of application of the external forces, ε (as in singular perturbation problems). In this paper we prove sufficient conditions for stability of quasi-static paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle. The present system has the additional difficulty of its non-smoothness: the friction law is a multivalued operator and the dynamic evolutions of this system may have discontinuous accelerations.
منابع مشابه
Development of a New Dynamic Friction Model for Analytical Modeling of Elliptical Vibration Assisted Turning Process
A new dynamic friction model for modeling of elliptical vibration assisted turning (EVAT) was developed in this research. The periodic change of the friction force direction is known to be one of the most important causes of this phenomenon. In modeling of machining processes (including the EVAT process), static Coulomb friction model was employed by most of the researchers. Because of the peri...
متن کاملDevelopment of a New Dynamic Friction Model for Analytical Modeling of Elliptical Vibration Assisted Turning Process
A new dynamic friction model for modeling of elliptical vibration assisted turning (EVAT) was developed in this research. The periodic change of the friction force direction is known to be one of the most important causes of this phenomenon. In modeling of machining processes (including the EVAT process), static Coulomb friction model was employed by most of the researchers. Because of the peri...
متن کاملQuasi-static contact problem with finitely many degrees of freedom and dry friction
A quasi-static contact problem is considered for a non-linear elastic system with finitely many degrees of freedom. Coulomb’s law is used to model friction and the friction coefficient may be anisotropic and may vary along the surface of the rigid obstacle. Existence is established following a time-incremental minimization problem. Friction is artificially decreased to resolve the discontinuity...
متن کاملArc-length Method for Frictional Contact with a Criterion of Maximum Dissipation of Energy
An arc-length equilibrium path-following method is proposed for two-dimensional quasi-static frictional contact problems. We consider the Coulomb friction law as well as geometrical nonlinearity. Incorporating a criterion of maximum dissipation of energy, we propose a formulation as a mathematical program with complementarity constraints (MPCC) in order to avoid unloading solutions in which mos...
متن کاملEvaluating the Soil Bearing Capacity Coefficients by Means of a Finite Element Program Based on Elasto - Plastic Mohr - Coulomb Behavior
A finite element program based on elastic –plastic model of Mohr-Coulomb criterion was used to evaluate the bearing capacity coefficients of soil under shallow strip flexible footing . The results were compared with others’ analytical results and it was found that the present study could offer quite consistent and rather precise values for the bearing capacity coefficients . 

The effect ...
متن کامل