A QUASISTATIC FRICTIONAL CONTACT PROBLEM WITH NORMAL DAMPED RESPONSE FOR THERMO-ELECTRO-ELASTIC-VISCOPLASTIC BODIES

2021 ◽  
Vol 10 (12) ◽  
pp. 3549-3568
Author(s):  
A. Hamidat ◽  
A. Aissaoui
Keyword(s):  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Contraction Mapping ◽  
Original Problem ◽  
Frictional Contact ◽  
Unique Fixed Point ◽  
Mathematical Problem ◽  
Response Condition ◽  
Electric Potential Field ◽  
Normal Damped Response

We consider a mathematical problem for quasistatic contact between a thermo-electro--elastic-viscoplastic body and an obstacle. The contact is modeled by a general normal damped response condition with friction law and heat exchange. We present a variational formulation of the problem and prove the existence and uniqueness of the weak solution. The proof is based on the formulation of four intermediate problems for the displacement field, the electric potential field and the temperature field, respectively. We prove the unique solvability of the intermediate problems, then we construct a contraction mapping whose unique fixed point is the solution of the original problem.

scholarly journals A CLASS OF QUASISTATIC CONTACT PROBLEMS FOR VISCOELASTIC MATERIALS WITH NONLOCAL COULOMB FRICTION AND TIME-DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 491-508 ◽  
Author(s):  
Si-sheng Yao ◽  
Nan-jing Huang
Keyword(s):  
Mathematical Model ◽  
Variational Inequality ◽  
Time Delay ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Contact Problems ◽  
Existence And Uniqueness Theorem ◽  
Differential Variational Inequality

In this paper, a mathematical model which describes the explicit time dependent quasistatic frictional contact problems is introduced and studied. The material behavior is described with a nonlinear viscoelastic constitutive law with time-delay and the frictional contact is modeled with nonlocal Coulomb boundary conditions. A variational formulation of the mathematical model is given, which is called a quasistatic integro-differential variational inequality. Using the Banach's fixed point theorem, an existence and uniqueness theorem of the solution for the quasistatic integro-differential variational inequality is proved under some suitable assumptions. As an application, an existence and uniqueness theorem of the solution for the dual variational formulation is also given.

scholarly journals VARIATIONAL ANALYSIS OF A FRICTIONAL CONTACT PROBLEM WITH WEAR AND DAMAGE

2021 ◽  
Vol 26 (2) ◽  
pp. 170-187
Author(s):  
Mohammed Salah Mesai Aoun ◽  
Mohamed Selmani ◽  
Abdelaziz Azeb Ahmed
Keyword(s):  
Long Memory ◽  
Dry Friction ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Variational Analysis ◽  
Friction And Wear ◽  
Frictional Contact ◽  
Constitutive Law ◽  
Quasistatic Problem ◽  
Elliptic Variational Inequalities

We study a quasistatic problem describing the contact with friction and wear between a piezoelectric body and a moving foundation. The material is modeled by an electro-viscoelastic constitutive law with long memory and damage. The wear of the contact surface due to friction is taken into account and is described by the differential Archard condition. The contact is modeled with the normal compliance condition and the associated law of dry friction. We present a variational formulation of the problem and establish, under a smallness assumption on the data, the existence and uniqueness of the weak solution. The proof is based on arguments of parabolic evolutionary inequations, elliptic variational inequalities and Banach fixed point.

scholarly journals A New Class of History–Dependent Evolutionary Variational–Hemivariational Inequalities with Unilateral Constraints

2020 ◽  
Author(s):  
Stanisław Migórski ◽  
Biao Zeng
Keyword(s):  
Frictional Contact ◽  
Hemivariational Inequalities ◽  
Normal Velocity ◽  
Unilateral Constraints ◽  
Response Condition ◽  
New Class ◽  
Fixed Point Principle ◽  
Selected Functions ◽  
Normal Damped Response ◽  
Weak Solvability

Abstract In this paper we study a new abstract evolutionary variational–hemivariational inequality which involves unilateral constraints and history–dependent operators. First, we prove the existence and uniqueness of solution by using a mixed equilibrium formulation with suitable selected functions together with a fixed-point principle for history–dependent operators. Then, we apply the abstract result to show the unique weak solvability to a dynamic viscoelastic frictional contact problem. The contact law involves a unilateral Signorini-type condition for the normal velocity combined with the nonmonotone normal damped response condition while the friction condition is a version of the Coulomb law of dry friction in which the friction bound depends on the accumulated slip.

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.

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.

scholarly journals Bernoulli Collocation Polynomials Algorithm for Calculus of Variational Problems

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Mohammed Abdelhadi Sarhan
Keyword(s):  
Approximate Method ◽  
Original Problem ◽  
Mathematical Problem ◽  
Bernoulli Polynomials ◽  
Variational Problems ◽  
Calculus Of Variation ◽  
Collocation Technique ◽  
Basic Functions

<p>This paper presents an approximate method that depends on the Bernoulli Polynomials as basic functions. The method is concerned with collocation technique for solving problems in calculus of variation. Some interesting properties of Bernoulli polynomials are used to reduce the original problem to mathematical problem. Some illustrative examples are described to show the applicability of the proposed method.</p>

scholarly journals On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

2021 ◽  
Author(s):  
Mohammad Hussein Mohammad Rashid
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Random Operator ◽  
Random Solution ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Mappings

Abstract In this paper we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in $\tau$-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show that the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

scholarly journals On singular systems of nonlinear equations involving 3n-Caputo derivatives

2020 ◽  
Vol 23 (2) ◽  
pp. 179-192
Author(s):  
Amele Taïeb
Keyword(s):  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Singular Systems ◽  
Nonlinear Differential Equations ◽  
Contraction Mapping Principle ◽  
Systems Of Nonlinear Equations ◽  
Fractional Systems ◽  
Caputo Derivatives ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We study singular fractional systems of nonlinear differential equations involving 3n-Caputo derivatives. We investigate existence and uniqueness results using the contraction mapping principle. We also discuss the existence of at least one solution by means of Schauder fixed point theorem. Moreover, we define and discuss the Ulam–Hyers stability and the generalized Ulam–Hyers stability of solutions for such systems. To illustrate the main results, we present some examples.

scholarly journals A New Existence and Uniqueness Theorem for Continuous Games

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Seamus D Hogan
Keyword(s):  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Jacobian Matrix ◽  
Iterative Sequence ◽  
Response Functions ◽  
Unique Equilibrium ◽  
Contraction Mapping Theorem ◽  
Best Response ◽  
General Sufficient Condition ◽  
General Game

This paper derives a general sufficient condition for existence and uniqueness in continuous games using a variant of the contraction mapping theorem applied to mappings from a subset of the real line on to itself. We first prove this contraction mapping variant, and then show how the existence of a unique equilibrium in the general game can be shown by proving the existence of a unique equilibrium in an iterative sequence of games involving such mappings. Finally, we show how a general condition for this to occur is that a matrix derived from the Jacobian matrix of best-response functions has positive leading principal minors, and how this condition generalises some existing uniqueness theorems for particular games. In particular, we show how the same conditions used in those theorems to show uniqueness, also guarantee existence in games with unbounded strategy spaces.

Sign in / Sign up

Export Citation Format

Share Document