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Radek Kucera - One of the best experts on this subject based on the ideXlab platform.
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approximation and numerical realization of 3d quasistatic contact problems with Coulomb Friction
Mathematics and Computers in Simulation, 2012Co-Authors: Jaroslav Haslinger, Radek Kucera, Oldřich Vlach, Charalambos C BaniotopoulosAbstract:AbstractThis paper deals with the full discretization of quasistatic 3D Signorini problems with local Coulomb Friction and a coefficient of Friction which may depend on the solution. After a time discretization we obtain a system of static contact problems with Coulomb Friction. Each of these problems is solved by the T-FETI domain decomposition method used in auxiliary contact problems with Tresca Friction. Numerical experiments show the efficiency of the proposed method.
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approximation and numerical realization of 3d contact problems with Coulomb Friction and a solution dependent coefficient of Friction
International Journal for Numerical Methods in Engineering, 2010Co-Authors: Tomas Ligurský, Jaroslav Haslinger, Radek KuceraAbstract:This paper analyzes 3D discrete contact problems with Coulomb Friction and a coefficient of Friction ℱ depending on the solution. The formulation of this problem is based on a fixed-point approach. Existence of at least one discrete solution is guaranteed for any continuous, non-negative and bounded function ℱ. The uniqueness result is established for ℱ small enough and Lipschitz continuous with a sufficiently small modulus of Lipschitz continuity. Results of several numerical experiments are shown. Copyright © 2009 John Wiley & Sons, Ltd.
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an algorithm for the numerical realization of 3d contact problems with Coulomb Friction
Journal of Computational and Applied Mathematics, 2004Co-Authors: Jaroslav Haslinger, Radek Kucera, Zdeněk DostalAbstract:This contribution deals with the numerical realization of static contact problems with Coulomb Friction for three-dimensional elastic bodies. We first introduce auxiliary contact problems with given Friction which define a mapping Φ associating with a given slip bound the normal contact stress in the equilibrium state. Solutions to contact problems with Coulomb Friction are defined as fixed points of Φ and are computed by using the method of successive approximations. The mathematical model of contact problems with given Friction leads to a variational inequality of the second kind. Its discretization is based on the so-called reciprocal variational formulation, i.e., the formulation in terms of the normal and tangential components of stresses on the contact boundary. Unlike the two-dimensional case, constraints imposed on the tangential components of contact stresses are quadratic. The main goal of this contribution is to show how to solve this problem by using existing fast algorithms for simple (box) constraints. Numerical experiments for several variants of our algorithm will be shown and compared.
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on a splitting type algorithm for the numerical realization of contact problems with Coulomb Friction
Computer Methods in Applied Mechanics and Engineering, 2002Co-Authors: Jaroslav Haslinger, Zdeněk Dostal, Radek KuceraAbstract:This paper presents and analyses an iterative process for the numerical realization of contact problems with Coulomb Friction which is based on the method of successive approximations combined with a splitting type approach. Numerical examples illustrate the efficiency of this method.
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Implementation of the fixed point method in contact problems with Coulomb Friction based on a dual splitting type technique
Journal of Computational and Applied Mathematics, 2002Co-Authors: Zdeněk Dostal, Jaroslav Haslinger, Radek KuceraAbstract:The paper deals with the numerical solution of the quasi-variational inequality describing the equilibrium of an elastic body in contact with a rigid foundation under Coulomb Friction. After a discretization of the problem by mixed finite elements, the duality approach is exploited to reduce the problem to a sequence of quadratic programming problems with box constraints, so that efficient recently proposed algorithms may be applied. A new variant of this method is presented. It combines fixed point with block Gauss-Seidel iterations. The method may be also considered as a new implementation of fixed point iterations for a sequence of problems with given Friction. Results of numerical experiments are given showing that the resulting algorithm may be much faster than the original fixed point method and its efficiency is comparable with the solution of Frictionless contact problems.
Jaroslav Haslinger - One of the best experts on this subject based on the ideXlab platform.
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shape optimization in contact problems with Coulomb Friction and a solution dependent Friction coefficient
Siam Journal on Control and Optimization, 2014Co-Authors: Petr Beremlijski, Jaroslav Haslinger, Jiři V Outrata, Robert PathoAbstract:The present paper deals with shape optimization in discretized two-dimensional (2D) contact problems with Coulomb Friction, where the coefficient of Friction is assumed to depend on the unknown solution. Discretization of the continuous state problem leads to a system of finite-dimensional implicit variational inequalities, parametrized by the so-called design variable, that determines the shape of the underlying domain. It is shown that if the coefficient of Friction is Lipschitz and sufficiently small in the $C^{0,1}$-norm, then the discrete state problems are uniquely solvable for all admissible values of the design variable (the admissible set is assumed to be compact), and the state variables are Lipschitzian functions of the design variable. This facilitates the numerical solution of the discretized shape optimization problem by the so-called implicit programming approach. Our main results concern sensitivity analysis, which is based on the well-developed generalized differential calculus of B. Mord...
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approximation and numerical realization of 3d quasistatic contact problems with Coulomb Friction
Mathematics and Computers in Simulation, 2012Co-Authors: Jaroslav Haslinger, Radek Kucera, Oldřich Vlach, Charalambos C BaniotopoulosAbstract:AbstractThis paper deals with the full discretization of quasistatic 3D Signorini problems with local Coulomb Friction and a coefficient of Friction which may depend on the solution. After a time discretization we obtain a system of static contact problems with Coulomb Friction. Each of these problems is solved by the T-FETI domain decomposition method used in auxiliary contact problems with Tresca Friction. Numerical experiments show the efficiency of the proposed method.
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approximation and numerical realization of 3d contact problems with Coulomb Friction and a solution dependent coefficient of Friction
International Journal for Numerical Methods in Engineering, 2010Co-Authors: Tomas Ligurský, Jaroslav Haslinger, Radek KuceraAbstract:This paper analyzes 3D discrete contact problems with Coulomb Friction and a coefficient of Friction ℱ depending on the solution. The formulation of this problem is based on a fixed-point approach. Existence of at least one discrete solution is guaranteed for any continuous, non-negative and bounded function ℱ. The uniqueness result is established for ℱ small enough and Lipschitz continuous with a sufficiently small modulus of Lipschitz continuity. Results of several numerical experiments are shown. Copyright © 2009 John Wiley & Sons, Ltd.
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an algorithm for the numerical realization of 3d contact problems with Coulomb Friction
Journal of Computational and Applied Mathematics, 2004Co-Authors: Jaroslav Haslinger, Radek Kucera, Zdeněk DostalAbstract:This contribution deals with the numerical realization of static contact problems with Coulomb Friction for three-dimensional elastic bodies. We first introduce auxiliary contact problems with given Friction which define a mapping Φ associating with a given slip bound the normal contact stress in the equilibrium state. Solutions to contact problems with Coulomb Friction are defined as fixed points of Φ and are computed by using the method of successive approximations. The mathematical model of contact problems with given Friction leads to a variational inequality of the second kind. Its discretization is based on the so-called reciprocal variational formulation, i.e., the formulation in terms of the normal and tangential components of stresses on the contact boundary. Unlike the two-dimensional case, constraints imposed on the tangential components of contact stresses are quadratic. The main goal of this contribution is to show how to solve this problem by using existing fast algorithms for simple (box) constraints. Numerical experiments for several variants of our algorithm will be shown and compared.
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on a splitting type algorithm for the numerical realization of contact problems with Coulomb Friction
Computer Methods in Applied Mechanics and Engineering, 2002Co-Authors: Jaroslav Haslinger, Zdeněk Dostal, Radek KuceraAbstract:This paper presents and analyses an iterative process for the numerical realization of contact problems with Coulomb Friction which is based on the method of successive approximations combined with a splitting type approach. Numerical examples illustrate the efficiency of this method.
Alina Besanconvoda - One of the best experts on this subject based on the ideXlab platform.
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describing function approximation of a two relay system configuration with application to Coulomb Friction identification
Control Engineering Practice, 2002Co-Authors: Alina Besanconvoda, P BlahaAbstract:Abstract The paper shows the use of describing function approximation for identifying a relay nonlinearity of the plant. For this purpose, the system configuration contains an inherent relay (plant nonlinearity) and another relay introduced in the loop, to control the system. The frequency behaviour of this two-relay system configuration is reported—the inherent relay models Coulomb Friction while the other relay controls the system's output and produces limit cycles. The harmonic balance method yields an algorithm for estimation of Coulomb Friction tested on illustrative examples, both in simulation and on a physical plant.
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brief analysis of a two relay system configuration with application to Coulomb Friction identification
Automatica, 1999Co-Authors: Alina Besanconvoda, Gildas BesanconAbstract:This paper presents an analysis of a class of two-relay feedback systems, motivated by the idea of estimating a relay-type nonlinearity on the feedback path of a plant by adding another relay. The time response of the resulting system is first analyzed, and stability conditions for possible limit cycles are then proposed using Poincare's method. On this basis, a simple procedure for estimating the unknown value (e.g. Coulomb Friction) of the relay on a plant feedback, by a closed-loop experiment, is finally presented and illustrated on both simulated and real-time examples.
Andrea Puglisi - One of the best experts on this subject based on the ideXlab platform.
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granular brownian motion with dry Friction
EPL, 2013Co-Authors: Andrea Gnoli, Andrea Puglisi, Hugo TouchetteAbstract:The interplay between Coulomb Friction and random excitations is studied experimentally by means of a rotating probe in contact with a stationary granular gas. The granular material is independently fluidized by a vertical shaker, acting as a “heat bath” for the Brownian-like motion of the probe. Two ball bearings supporting the probe exert nonlinear Coulomb Friction upon it. The experimental velocity distribution of the probe, autocorrelation function, and power spectra are compared with the predictions of a linear Boltzmann equation with Friction, which is known to simplify in two opposite limits: at high collision frequency, it is mapped to a Fokker-Planck equation with nonlinear Friction, whereas at low collision frequency, it is described by a sequence of independent random kicks followed by Friction-induced relaxations. Comparison between theory and experiment in these two limits shows good agreement. Deviations are observed at very small velocities, where the real bearings are not well modeled by Coulomb Friction.
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ratchet effect driven by Coulomb Friction the asymmetric rayleigh piston
Physical Review E, 2013Co-Authors: Alessandro Sarracino, Andrea Gnoli, Andrea PuglisiAbstract:The effect of Coulomb Friction is studied in the framework of collisional ratchets. It turns out that the average drift of these devices can be expressed as the combination of a term related to the lack of equipartition between the probe and the surrounding bath, and a term featuring the average Frictional force. We illustrate this general result in the asymmetric Rayleigh piston, showing how Coulomb Friction can induce a ratchet effect in a Brownian particle in contact with an equilibrium bath. An explicit analytical expression for the average velocity of the piston is obtained in the rare collision limit. Numerical simulations support the analytical findings.
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brownian ratchet in a thermal bath driven by Coulomb Friction
Physical Review Letters, 2013Co-Authors: Andrea Gnoli, Alberto Petri, Fergal Dalton, Giorgio Pontuale, Giacomo Gradenigo, Alessandro Sarracino, Andrea PuglisiAbstract:The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtained under statistical nonequilibrium conditions. Here we propose a new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb Friction due to solid-on-solid contacts. Numerical simulations and analytical calculations demonstrate a net drift induced by Friction. If the thermal bath is replaced by a granular gas, the well-known granular ratchet effect also intervenes, becoming dominant at high collision rates. For our chosen wheel shape the granular effect acts in the opposite direction with respect to the Friction-induced torque, resulting in the inversion of the ratchet direction as the collision rate increases. We have realized a new granular ratchet experiment where both these ratchet effects are observed, as well as the predicted inversion at their crossover. Our discovery paves the way to the realization of micro and submicrometer Brownian motors in an equilibrium fluid, based purely upon nanoFriction.
Christian Schoof - One of the best experts on this subject based on the ideXlab platform.
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a hydrologically coupled higher order flow band model of ice dynamics with a Coulomb Friction sliding law
Journal of Geophysical Research, 2010Co-Authors: Gwenn E Flowers, S Pimentel, Christian SchoofAbstract:[1] The influence of hydrologic transience and heterogeneity on basal motion is an often-neglected aspect of numerical ice-flow models. We present a flow-band model of glacier dynamics with a Coulomb Friction sliding law that is coupled to a model of the basal drainage system by means of subglacial water pressure. The ice-flow model contains “higher-order” stress gradients from the Stokes flow approximation originally conceived by Blatter (1995). The resulting system of nonlinear equations is solved using a modified Picard iteration that is shown to improve the rate of convergence. A parameterization of lateral shearing is included to account for the effects of three-dimensional geometry. We find that lateral drag has a discernible effect on glacier speed even when glacier width exceeds glacier length. Variations in flow-band width are shown to have a greater influence on flow line speed than either different valley cross-sectional shapes or the presence or absence of glacier sliding along valley walls. Modeled profiles of subglacial water pressure depart significantly from pressures prescribed as a uniform fraction of overburden, thus producing profiles of glacier sliding that are distinctly different from those that would be described by a sliding law controlled by overburden pressures. Simulations of hydraulically driven glacier acceleration highlight the value of including a representation of basal hydrology in models aiming for improved predictive capability of glacier dynamics.
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Coulomb Friction and other sliding laws in a higher order glacier flow model
Mathematical Models and Methods in Applied Sciences, 2010Co-Authors: Christian SchoofAbstract:We consider a widely used higher-order glacier flow model with a variety of parametrizations of wall slip, including Coulomb Friction, regularized Coulomb Friction laws and a power law. Mathematically, the Coulomb Friction problem is found to be analogous to a classical Friction problem in elasticity theory. We specifically analyze the case in which slip is possible everywhere at the boundary, in which case the weak formulation becomes a semi-coercive convex minimization problem which has a solution only if a solvability condition representing force and torque balance is satisfied. Going beyond previous work, we study the uniqueness of solutions in depth, finding that non-unique solutions are possible under very specialized circumstances. Further, in an extension of work by Campos, Oden and Kikuchi, we show that solutions to the regularized Coulomb Friction and power law problems converge to the Coulomb Friction problem in appropriate parametric limits, provided the latter is unique, and briefly discuss the implications of possible non-unique solutions for a priori error estimation in numerical approximations.
