Residual-based a posteriori error estimation for contact problems approximated by Nitsche's method

International audienc

Adaptive FE-BE Coupling for Strongly Nonlinear Transmission Problems with Coulomb Friction

We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction, where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation on the exterior domain. The problem is reduced to a boundary/domain variational inequality, a discretized saddle point formulation of which is then solved using the Uzawa algorithm and adaptive mesh refinements based on a gradient recovery scheme. The Galerkin approximations are shown to converge to the unique solution of the variational problem in a suitable product of L^p- and L^2-Sobolev spaces.Comment: 27 pages, 3 figure

Adaptive FE-BE coupling for strongly nonlinear transmission problems with friction II

This article discusses the well-posedness and error analysis of the coupling of finite and boundary elements for transmission or contact problems in nonlinear elasticity. It concerns W^{1,p}-monotone Hencky materials with an unbounded stress-strain relation, as they arise in the modelling of ice sheets, non-Newtonian fluids or porous media. For 1<p<2 the bilinear form of the boundary element method fails to be continuous in natural function spaces associated to the nonlinear operator. We propose a functional analytic framework for the numerical analysis and obtain a priori and a posteriori error estimates for Galerkin approximations to the resulting boundary/domain variational inequality. The a posteriori estimate complements recent estimates obtained for mixed finite element formulations of friction problems in linear elasticity.Comment: 20 pages, corrected typos and improved expositio

Optimal control design for robust fuzzy friction compensation in a robot joint

This paper presents a methodology for the compensation of nonlinear friction in a robot joint structure based on a fuzzy local modeling technique. To enhance the tracking performance of the robot joint, a dynamic model is derived from the local physical properties of friction. The model is the basis of a precompensator taking into account the dynamics of the overall corrected system by means of a minor loop. The proposed structure does not claim to faithfully reproduce complex phenomena driven by friction. However, the linearity of the local models simplifies the design and implementation of the observer, and its estimation capabilities are improved by the nonlinear integral gain. The controller can then be robustly synthesized using linear matrix inequalities to cancel the effects of inexact friction compensation. Experimental tests conducted on a robot joint with a high level of friction demonstrate the effectiveness of the proposed fuzzy observer-based control strategy for tracking system trajectories when operating in zero-velocity regions and during motion reversals

Adaptive numerical simulation of contact problems : Resolving local effects at the contact boundary in space and time

This thesis is concerned with the space discretization of static and the space and time discretization of dynamic contact problems. In particular, we derive a new efficient and reliable residual-type a posteriori error estimator for static contact problems and a new space-time connecting discretization scheme for dynamic contact problems in linear elasticity. The methods enable the efficient resolution of local effects at the contact boundary in space and time. Firstly, we prove efficiency and reliability of the new residual-type a posteriori error estimator for the case of simplicial meshes. Several numerical examples in the two- and three-dimensional case show the performance of the residual-type a posteriori error estimator for simplicial and even for non-simplicial meshes. Secondly, for the discretization in time, we present a new method which allows to implicitly compute the local impact times of each node without decreasing the time step size. As it turns out this method gives rise to a generalization of the Newmark scheme which takes into account the local impact times without additional computational effort

Space-time adaptive finite elements for nonlocal parabolic variational inequalities

This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic variational inequalities associated to the fractional Laplacian we obtain a priori and a posteriori error estimates and study the resulting space-time adaptive mesh-refinement procedures. Particular emphasis is placed on mixed formulations, which include the contact forces as a Lagrange multiplier. Corresponding results are presented for elliptic problems. Our numerical experiments for $2$-dimensional model problems confirm the theoretical results: They indicate the efficiency of the a posteriori error estimates and illustrate the convergence properties of space-time adaptive, as well as uniform and graded discretizations.Comment: 47 pages, 20 figure