Existence and Uniqueness of the Solution for a Two-Dimensional Elastic Frictional Contact Problem

2008 ◽  
Author(s):  
Baofeng Li ◽  
Yuhuan Cui ◽  
Yiming Chen
Keyword(s):  
Contact Problem ◽  
Existence And Uniqueness ◽  
Frictional Contact ◽  
Two Dimensional ◽  
Frictional Contact Problem ◽  
Uniqueness Of The Solution

Variational-hemivariational inverse problem for electro-elastic unilateral frictional contact problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Othmane Baiz ◽  
Hicham Benaissa ◽  
Zakaria Faiz ◽  
Driss El Moutawakil
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Contact Problem ◽  
Existence And Uniqueness ◽  
Frictional Contact ◽  
Hemivariational Inequalities ◽  
Frictional Contact Problem ◽  
Uniqueness Of A Solution

AbstractIn the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.

Numerical investigations into static and quasistatic problems of two-dimensional dry elastic frictional contact

2002 ◽  
Vol 80 (5) ◽  
pp. 505-524 ◽  
Author(s):  
M Schlesinger ◽  
L F McAven ◽  
Y Yao
Keyword(s):  
Contact Problem ◽  
Frictional Contact ◽  
Surface Deformation ◽  
Optimization Method ◽  
Tangential Displacement ◽  
Cauchy Stress ◽  
Two Dimensional ◽  
Loading Conditions ◽  
Accurate Analysis ◽  
Frictional Contact Problem

A numerical-modelling method is developed to investigate the stress of the static-equilibrium state of the two-dimensional frictional contact problem achieved through a quasistatic process of increasing loading. The problem of relative tangential displacement between particles on the two contact surfaces is addressed. This scheme relies on solving each of the two contact solids in turn and iterating back and forth. The solutions for the two elastic bodies are connected through the surface traction and surface deformation. The contact surface is approximated by a cubic spline, and friction is modelled using the classical Coulomb friction law. Variational inequalities and finite-element methods are used to implement this scheme and are solved by an optimization method. In addition, the distinction between Cauchy stress and Piola–Kirchoff stress is taken into account and discussed. A numerical investigation is conducted into the stress dependence on the loading conditions and geometries of the solids. The results from the numerical examples deviate from Hertz theory and previous reports. Stress is shown to be sensitive to the loading distribution and geometry of contact solids. Therefore, it suggests that an accurate analysis of the dry frictional contact problem requires a refined knowledge of the loading conditions and the total geometry of both solids. PACS Nos.: 03.40D, 46.30P, 62.20P

The Sliding Frictional Contact Problem in Two Dimensional Graded Materials Loaded by a Flat Stamp

2012 ◽  
Vol 463-464 ◽  
pp. 336-342 ◽  
Author(s):  
Romik Khajehtourian ◽  
Saeed Adibnazari ◽  
Samaneh Tashi
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Frictional Contact ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Graded Materials ◽  
Frictional Contact Problem ◽  
Macro Scale ◽  
Spatially Distributed ◽  
Comparison Of The Results

In this article, the sliding frictional contact problem for a half-plane which is graded in two dimensions is studied. The effect of medium properties gradient and coefficient of friction in contact mechanics of two dimensional (2D) graded materials which is loaded by a flat stamp have been investigated by developing two Finite Element (FE) models, in macro and micro scales. Discretizing the graded half- plane by quadrants for whose material properties are specified at the centroids by Mori-Tanaka method in both directions has been used to model the 2D FGM in macro scale. In micro scale, the ideal solid quadrant particles which are spatially distributed in a homogeneous matrix used to model the FGM structure. Also, boundary conditions and loading of both models are the same. The study is focused on determining the contact stress distributions on contact surface. The contact mechanic problem of 2D graded materials has been solved and the results are presented for various combinations of friction coefficient and material non-homogeneity constant parameters Analyses and comparison of the results showed that micro and macro scale results are in a very good agreement.

Hemivariational inequalities modeling electro-elastic unilateral frictional contact problem

2017 ◽  
Vol 23 (3) ◽  
pp. 329-347 ◽  
Author(s):  
Piotr Gamorski ◽  
Stanisław Migórski
Keyword(s):  
Contact Problem ◽  
Frictional Contact ◽  
Coupled System ◽  
Contact Friction ◽  
Hemivariational Inequalities ◽  
Unilateral Constraints ◽  
Frictional Contact Problem ◽  
Uniqueness Of The Solution ◽  
Pseudomonotone Mappings ◽  
Weak Solvability

We study a class of abstract hemivariational inequalities in a reflexive Banach space. For this class, using the theory of multivalued pseudomonotone mappings and a fixed-point argument, we provide a result on the existence and uniqueness of the solution. Next, we investigate a static frictional contact problem with unilateral constraints between a piezoelastic body and a conductive foundation. The contact, friction and electrical conductivity condition on the contact surface are described with the Clarke generalized subgradient multivalued boundary relations. We derive the variational formulation of the contact problem which is a coupled system of two hemivariational inequalities. Finally, for such system we apply our abstract result and prove its unique weak solvability.

scholarly journals On the Bean critical-state model in superconductivity

1996 ◽  
Vol 7 (3) ◽  
pp. 237-247 ◽  
Author(s):  
L. Prigozhin
Keyword(s):  
Variational Inequalities ◽  
Critical State ◽  
Existence And Uniqueness ◽  
Critical State Model ◽  
Type Ii ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Uniqueness Of The Solution ◽  
Type Ii Superconductivity ◽  
Special Case

We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.

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