scholarly journals Analysis of a Unilateral Contact Problem with Normal Compliance

2014 ◽  
Vol 52 (1) ◽  
Author(s):  
Arezki Touzaline ◽  
Rachid Guettaf
Keyword(s):  
Contact Problem ◽  
Order Differential Equation ◽  
Uniqueness Result ◽  
Unilateral Contact ◽  
Normal Compliance ◽  
Mechanical Problem ◽  
First Order ◽  
Coulomb’S Friction ◽  
The Coefficient Of Friction ◽  
Nonlinear Elastic

AbstractThe paper deals with the study of a quasistatic unilateral contact problem between a nonlinear elastic body and a foundation. The contact is modelled with a normal compliance condition associated to unilateral constraint and the Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove an existence and uniqueness result in the case where the coefficient of friction is bounded by a certain constant. The technique of the proof is based on arguments of time-dependent variational inequalities, differential equations and fixed-point theorem.

scholarly journals Analysis of a frictionless contact problem for elastic-viscoplastic materials

2012 ◽  
Vol 17 (1) ◽  
pp. 99-117
Author(s):  
Mohamed Selmani ◽  
Lynda Selmani
Keyword(s):  
Contact Problem ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Order Differential Equation ◽  
Nonlinear Evolution ◽  
Monotone Operators ◽  
Uniqueness Result ◽  
Nonlinear Evolution Equations ◽  
Frictionless Contact ◽  
First Order

We consider a dynamic frictionless contact problem for elastic-viscoplastic materials with damage. The contact is modelled with normal compliance condition. The adhesion of the contact surfaces is considered and is modelled with a surface variable, the bonding field whose evolution is described by a first order differential equation. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed-point arguments.

A QUASISTATIC UNILATERAL CONTACT PROBLEM WITH FRICTION FOR NONLINEAR ELASTIC MATERIALS

2007 ◽  
Vol 12 (4) ◽  
pp. 497-514 ◽  
Author(s):  
Arezki Touzaline ◽  
Djamel Eddine Teniou
Keyword(s):  
Friction Coefficient ◽  
Contact Problem ◽  
Dry Friction ◽  
Unilateral Contact ◽  
Elastic Materials ◽  
Existence Of A Solution ◽  
Coulomb’S Law ◽  
Nonlinear Elastic ◽  
Coulomb's Law

The aim of this paper is to prove the existence of a solution to the quasistatic unilateral contact problem with a modified version of Coulomb's law of dry friction for nonlinear elastic materials. We derive a variational incremental problem which admits a solution if the friction coefficient is sufficiently small and then by passing to the limit with respect to time we obtain the existence of a solution.

On the Contact Problem of an Inflated Spherical Nonlinear Membrane

1973 ◽  
Vol 40 (1) ◽  
pp. 209-214 ◽  
Author(s):  
W. W. Feng ◽  
W.-H. Yang
Keyword(s):  
Contact Problem ◽  
Contact Region ◽  
Material Behavior ◽  
Elastic Membrane ◽  
Rigid Plate ◽  
Constraint Condition ◽  
Governing Equations ◽  
First Order ◽  
Stress Strain Relation ◽  
Nonlinear Elastic

The contact problem of an inflated spherical nonlinear elastic membrane between two large rigid plates is formulated in terms of three first-order ordinary differential equations for the region where the spherical membrane is not in contact with the rigid plates. The constraint condition introduced by the rigid plate on part of the spherical membrane reduces the number of governing equations to two for the contact region. A general stress-strain relation for the spherical membrane is used in the formulation. The results presented in this paper assume that the material behavior of the spherical membrane is that described by the Mooney model. Nonlinear spring characteristics and the instability phenomena of the inflated membrane are discussed.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

A piezoelectric contact problem with slip dependent friction and damage

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abderrezak Kasri
Keyword(s):  
Weak Solution ◽  
Contact Problem ◽  
Dry Friction ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Normal Compliance ◽  
Electrically Conductive ◽  
Coulomb’S Law ◽  
Electrical Condition ◽  
Coulomb's Law

Abstract The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb’s law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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