The present paper is concerned with the unilateral contact model and the Coulomb friction law in linear elastostatics. We consider a mixed formulation in which the unknowns are the displacement field and the normal and tangential constraints on the contact area. The chosen finite element method involves continuous elements of degree one and continuous piecewise affine multipliers on the contact...

Virtual decomposition control is applied to control a KUKA 361 six-joint industrial robot performing hybrid tasks with a rigid unilateral constraint. In order to accommodate motion/force control, the required velocity is re-designed by introducing filtered contact forces in full control dimensions, which makes the controlled robot behave as hybrid controlled for a known contact geometry and imp...

A finite element approximation to the solution of a one-dimensional linear thermoelastic problem with unilateral contact of the Signorini type and heat flux is proposed. An error bound is derived and some numerical experiments are performed.

For the static contact problem with limited interpenetration with the obstacle the existence of solutions is proved. The frictionless case is studied at first, then the problem with Coulomb friction is investigated as well. The body has nowhere a Dirichlet boundary value condition prescribed. In both cases, if the prescribed bound of the interpenetratiom tends to 0, the solutions tend to a solu...

Two mathematical models are developed within the theoretical framework of large strain elasticity for the determination of upper and lower bounds on the total strain energy of a finitely deformed hyperelastic body in unilateral contact with a rigid surface or with an elastic substrate. The model problems take the form of two continuous optimization problems with inequality constraints, the solu...

We study the dual mixed finite element approximation of unilateral contact problems. Based on the dual mixed variational formulation with three unknowns (stress, displacement and the displacement on the contact boundary), the a priori error estimates have been established for both conforming and nonconforming finite element approximations. A Uzawa type iterative algorithm is developed to solve ...

In this paper, we consider the unilateral frictional contact problem of a hyperelastic body in the case of large displacements and small strains. In order to retain the linear elasticity framework, we decompose the deformation into a large global rotation and a small elastic displacement. This co-rotational approach is combined with a primal-dual active set strategy to tackle the contact proble...

This paper is concerned with the unilateral contact problem in linear elasticity. We define two a posteriori error estimators of residual type to evaluate the accuracy of the mixed finite element approximation of the contact problem. Upper and lower bounds of the discretization error are proved for both estimators and several computations are performed to illustrate the theoretical results. Mat...

The aim of this work is to study a class of nonsmooth dynamic contact problem which model several surface interactions, including relaxed unilateral contact conditions, adhesion and Coulomb friction laws, between two viscoelastic bodies of Kelvin-Voigt type. An abstract formulation which generalizes these problems is considered and the existence of a solution is proved by using Ky Fan’s fixed p...

In this paper we present an algorithm which allows qualitative and quantitative analysis of the general force closure property of a grasp when ngertip contact forces are limited by unilateral friction constraints. It is applied to grasp synthesis during re-grasping sequences. Contact points for moving ngers which result in structurally stable grasps are calculated. The proposed method is suitab...