University Sétif 1 FERHAT ABBAS Faculty of Sciences
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Auteur Hana Benarour |
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Titre : Mathematical Analysis Of A Quasistatic Frictionless Antiplane Contact Problem For Piezoelectric Materials Type de document : document électronique Auteurs : Hana Benarour, Auteur ; Laldja Benziane, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2026 Importance : 1 vol (33 f.) Format : 29 cm Note générale : Langues : Anglais (eng) Catégories : Mathématique Mots-clés : Anti-plan shear
Electro-elastic material
Frictionless contact
Weak solution
Banach space
Lax-MilgramRésumé :
In this thesis ,we consider a mathematical model describing the antiplane shear deformation of a piezoelectric cylinder in frictionless contact with a conductive foundation. The material is assumed to be electro-elastic, and homogeneous properties, and the process is modeled as quasistatic.
This work is divided into three chapters. First, we present preliminary results from functional analysis and partial differential equations, which lay the mathematical foundation for the subsequent analysis. Next, the second chapter focuses on the mathematical modeling of the antiplane shear deformation problem, electro-elastic homogeneity under quasistatic assumptions. Finally, the third chapter establishes derive a variational formulation of the models which ares given by a system coupling two variational equations for the displacement and the electric potential fields . By using the Banach space,Lax-Milgram theorem, we prove the existence and uniqueness of a weak solution to the problem.Note de contenu : Contents
Acknowledgements i
Notation iii
Introduction 1
1 MathematicalTools 4
1.1 FunctionSpaces . ...................................... 4
1.1.1 TheSpaces Cm(Ω) and Lp(Ω) . .......................... 5
1.1.2 Equivalentnormsonthespace H1(Ω) . ...................... 7
1.2 BilinearForminHilbertSpaces . ............................. 8
1.3 DiverseAdditions . ..................................... 8
1.4 Someinequalities . ..................................... 9
1.5 VariationalInequalitiesandEqualities . .......................... 10
1.5.1 EllipticVariationalInequalities . .......................... 10
1.5.2 LinearVariationalEqualities . ........................... 11
2 MathematicalModelingofAntiplaneShearDeformation 12
2.1 MathematicalModel . ................................... 12
2.2 AFunctionSpaceforAntiplaneProblems . ........................ 18
3 VariationalAnalysisoftheContactProblem 21
3.1 MechanicalFormulationoftheProblemandHypotheses . ................ 21
3.1.1 MechanicalFormulation . ............................. 22
3.1.2 Hypotheses . .................................... 22
3.1.3 Variationalformulation . .............................. 25
3.1.4 AnExistenceandUniquenessResult . ...................... 27
3.1.5 ProofofTheorem 3.3 . ............................... 28
Côte titre : MAM/0837 Mathematical Analysis Of A Quasistatic Frictionless Antiplane Contact Problem For Piezoelectric Materials [document électronique] / Hana Benarour, Auteur ; Laldja Benziane, Directeur de thèse . - [S.l.] : Sétif:UFS, 2026 . - 1 vol (33 f.) ; 29 cm.
Langues : Anglais (eng)
Catégories : Mathématique Mots-clés : Anti-plan shear
Electro-elastic material
Frictionless contact
Weak solution
Banach space
Lax-MilgramRésumé :
In this thesis ,we consider a mathematical model describing the antiplane shear deformation of a piezoelectric cylinder in frictionless contact with a conductive foundation. The material is assumed to be electro-elastic, and homogeneous properties, and the process is modeled as quasistatic.
This work is divided into three chapters. First, we present preliminary results from functional analysis and partial differential equations, which lay the mathematical foundation for the subsequent analysis. Next, the second chapter focuses on the mathematical modeling of the antiplane shear deformation problem, electro-elastic homogeneity under quasistatic assumptions. Finally, the third chapter establishes derive a variational formulation of the models which ares given by a system coupling two variational equations for the displacement and the electric potential fields . By using the Banach space,Lax-Milgram theorem, we prove the existence and uniqueness of a weak solution to the problem.Note de contenu : Contents
Acknowledgements i
Notation iii
Introduction 1
1 MathematicalTools 4
1.1 FunctionSpaces . ...................................... 4
1.1.1 TheSpaces Cm(Ω) and Lp(Ω) . .......................... 5
1.1.2 Equivalentnormsonthespace H1(Ω) . ...................... 7
1.2 BilinearForminHilbertSpaces . ............................. 8
1.3 DiverseAdditions . ..................................... 8
1.4 Someinequalities . ..................................... 9
1.5 VariationalInequalitiesandEqualities . .......................... 10
1.5.1 EllipticVariationalInequalities . .......................... 10
1.5.2 LinearVariationalEqualities . ........................... 11
2 MathematicalModelingofAntiplaneShearDeformation 12
2.1 MathematicalModel . ................................... 12
2.2 AFunctionSpaceforAntiplaneProblems . ........................ 18
3 VariationalAnalysisoftheContactProblem 21
3.1 MechanicalFormulationoftheProblemandHypotheses . ................ 21
3.1.1 MechanicalFormulation . ............................. 22
3.1.2 Hypotheses . .................................... 22
3.1.3 Variationalformulation . .............................. 25
3.1.4 AnExistenceandUniquenessResult . ...................... 27
3.1.5 ProofofTheorem 3.3 . ............................... 28
Côte titre : MAM/0837 Exemplaires
Code-barres Cote Support Localisation Section Disponibilité aucun exemplaire
Titre : Mathematical Analysis Of A Quasistatic Frictionless Antiplane Contact Problem For Piezoelectric Materials Type de document : document électronique Auteurs : Hana Benarour, Auteur ; Laldja Benziane, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2026 Importance : 1 vol (33 f.) Format : 29 cm Note générale : Langues : Anglais (eng) Catégories : Mathématique Mots-clés : Anti-plan shear
Electro-elastic material
Frictionless contact
Weak solution
Banach space
Lax-MilgramRésumé :
In this thesis ,we consider a mathematical model describing the antiplane shear deformation of a piezoelectric cylinder in frictionless contact with a conductive foundation. The material is assumed to be electro-elastic, and homogeneous properties, and the process is modeled as quasistatic.
This work is divided into three chapters. First, we present preliminary results from functional analysis and partial differential equations, which lay the mathematical foundation for the subsequent analysis. Next, the second chapter focuses on the mathematical modeling of the antiplane shear deformation problem, electro-elastic homogeneity under quasistatic assumptions. Finally, the third chapter establishes derive a variational formulation of the models which ares given by a system coupling two variational equations for the displacement and the electric potential fields . By using the Banach space,Lax-Milgram theorem, we prove the existence and uniqueness of a weak solution to the problem.Note de contenu : Contents
Acknowledgements i
Notation iii
Introduction 1
1 MathematicalTools 4
1.1 FunctionSpaces . ...................................... 4
1.1.1 TheSpaces Cm(Ω) and Lp(Ω) . .......................... 5
1.1.2 Equivalentnormsonthespace H1(Ω) . ...................... 7
1.2 BilinearForminHilbertSpaces . ............................. 8
1.3 DiverseAdditions . ..................................... 8
1.4 Someinequalities . ..................................... 9
1.5 VariationalInequalitiesandEqualities . .......................... 10
1.5.1 EllipticVariationalInequalities . .......................... 10
1.5.2 LinearVariationalEqualities . ........................... 11
2 MathematicalModelingofAntiplaneShearDeformation 12
2.1 MathematicalModel . ................................... 12
2.2 AFunctionSpaceforAntiplaneProblems . ........................ 18
3 VariationalAnalysisoftheContactProblem 21
3.1 MechanicalFormulationoftheProblemandHypotheses . ................ 21
3.1.1 MechanicalFormulation . ............................. 22
3.1.2 Hypotheses . .................................... 22
3.1.3 Variationalformulation . .............................. 25
3.1.4 AnExistenceandUniquenessResult . ...................... 27
3.1.5 ProofofTheorem 3.3 . ............................... 28
Côte titre : MAM/0837 Mathematical Analysis Of A Quasistatic Frictionless Antiplane Contact Problem For Piezoelectric Materials [document électronique] / Hana Benarour, Auteur ; Laldja Benziane, Directeur de thèse . - [S.l.] : Sétif:UFS, 2026 . - 1 vol (33 f.) ; 29 cm.
Langues : Anglais (eng)
Catégories : Mathématique Mots-clés : Anti-plan shear
Electro-elastic material
Frictionless contact
Weak solution
Banach space
Lax-MilgramRésumé :
In this thesis ,we consider a mathematical model describing the antiplane shear deformation of a piezoelectric cylinder in frictionless contact with a conductive foundation. The material is assumed to be electro-elastic, and homogeneous properties, and the process is modeled as quasistatic.
This work is divided into three chapters. First, we present preliminary results from functional analysis and partial differential equations, which lay the mathematical foundation for the subsequent analysis. Next, the second chapter focuses on the mathematical modeling of the antiplane shear deformation problem, electro-elastic homogeneity under quasistatic assumptions. Finally, the third chapter establishes derive a variational formulation of the models which ares given by a system coupling two variational equations for the displacement and the electric potential fields . By using the Banach space,Lax-Milgram theorem, we prove the existence and uniqueness of a weak solution to the problem.Note de contenu : Contents
Acknowledgements i
Notation iii
Introduction 1
1 MathematicalTools 4
1.1 FunctionSpaces . ...................................... 4
1.1.1 TheSpaces Cm(Ω) and Lp(Ω) . .......................... 5
1.1.2 Equivalentnormsonthespace H1(Ω) . ...................... 7
1.2 BilinearForminHilbertSpaces . ............................. 8
1.3 DiverseAdditions . ..................................... 8
1.4 Someinequalities . ..................................... 9
1.5 VariationalInequalitiesandEqualities . .......................... 10
1.5.1 EllipticVariationalInequalities . .......................... 10
1.5.2 LinearVariationalEqualities . ........................... 11
2 MathematicalModelingofAntiplaneShearDeformation 12
2.1 MathematicalModel . ................................... 12
2.2 AFunctionSpaceforAntiplaneProblems . ........................ 18
3 VariationalAnalysisoftheContactProblem 21
3.1 MechanicalFormulationoftheProblemandHypotheses . ................ 21
3.1.1 MechanicalFormulation . ............................. 22
3.1.2 Hypotheses . .................................... 22
3.1.3 Variationalformulation . .............................. 25
3.1.4 AnExistenceandUniquenessResult . ...................... 27
3.1.5 ProofofTheorem 3.3 . ............................... 28
Côte titre : MAM/0837 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité MAM/0837 MAM/0837 Mémoire Bibliothèque des sciences Anglais Disponible
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