Discrete Contact Problems with Coulomb Friction
نویسنده
چکیده
The paper deals with a discrete model of a two-dimensional Signorini problem with Coulomb friction and a coefficient of friction F depending on the spatial variable. It is shown that a solution exists for any F and is unique if F is sufficiently small. We also prove that this unique solution is a Lipschitz continuous function of F . Numerical realization is done by the piecewise smooth Newton method which is tested on an elementary example with a known solution.
منابع مشابه
Qualitative analysis of 3D elastostatic contact problems with orthotropic Coulomb friction and solution-dependent coefficients of friction
This paper analyzes a discrete form of 3D contact problems with local orthotropic Coulomb friction and coefficients of friction which may depend on the solution itself. The analysis is based on the fixed-point reformulation of the original problem. Conditions guaranteeing the existence and uniqueness of discrete solutions are established. Finally, numerical results of a model example are presen...
متن کاملSolving Frictional Contact Problems with Multigrid Efficiency
The construction of fast and reliable solvers for contact problems with friction is even nowadays a challenging task. It is well known that contact problems with Coulomb friction have the weak form of a quasi-variational inequality [KO88, HHNL88, NJH80]. For small coefficients of friction, a solution can be obtained by means of a fixed point iteration in the boundary stresses [NJH80]. This fixe...
متن کاملNumerically and parallel scalable TFETI algorithms for quasistatic contact
This paper deals with the solution of the discretized quasistatic 3D Signorini problems with local Coulomb friction. After a time discretization we obtain a system of static contact problems with Coulomb friction. Each of these problems is decomposed by the TFETI domain decomposition method used in auxiliary contact problemswith Tresca friction. The algebraic formulation of these problems in 3D...
متن کاملSolution Existence and Non-Uniqueness of Coulomb Friction
The existence and (non-)uniqueness of rigid multibody problems with impact, contact and friction is discussed by means of the renowned Painlevé paradox. Different approaches to solve such contact problems, their pros and cons and their connections are discussed.
متن کاملOn non-unique solutions of contact problems with the Coulomb friction
Our contribution deals with contact problems of linear elasticity with the Coulomb friction in two space dimensions. The finite element approximation leads to an algebraic problem whose projective primaldual formulation is given as an equation described by a piecewise differentiable function. The solution can be computed iteratively by the semi-smooth Newton method [1]. However, there are known...
متن کامل