Numerical Study Of The Thermo-Electro-Viscoelastic Problem With Long Memory / Zineb Allal

Public ISBD Titre : Numerical Study Of The Thermo-Electro-Viscoelastic Problem With Long Memory Type de document : document électronique Auteurs : Zineb Allal, Auteur ; Namira Lebri, Auteur Editeur : Sétif:UFA1 Année de publication : 2025 Importance : 1 vol (49 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Sub-differential Contact Elastic, Electro-elastic Electro-elasto-viscoplastic Finite elements Fixed point Evolution inequality Index. décimale : 510-Mathématique Résumé : The purpose of this work is to study a problem in contact mechanics involving thermo-electro-viscoelastic constitutive laws with long-term memory. The obtained results concern the existence and uniqueness of a weak solution. The thesis is structured in two parts: The first part recalls various contact mechanical model and presents the necessary mathematical tools. The second part focuses on the modeling and mathematical analysis of the considered contact problems. A numerical approach is also carried using a finite element scheme with implicit time discretization. Note de contenu : Contents Introduction 4 1 Modelingandmathematictools8 1.1 Modeling(thepiezoelectricproblem).......................... 9 1.1.1 Physicalframework............................... 9 1.1.2 Constitutivelaws................................. 10 1.1.2.1 Constitutivelawofelectroelasticmaterials.............. 11 1.1.2.2 Constitutivelawofthermo-electro-viscoelasticmaterialswithlong memory ................................. 11 1.1.3 Boundaryconditions............................... 12 1.1.3.1 Thedisplacementandtractionboundaryconditions......... 12 1.1.3.2 Theelectricalboundaryconditions.................. 12 1.1.3.3 SubdifferentialContactCondition................... 12 1.2 Mathematictools..................................... 14 1.2.1 Sobolevspace................................... 14 1.2.2 Spacesofvector-valuedfunctions........................ 17 1.2.3 ReviewofnonlinearanalysisinHilbertspaces................. 18 1.2.3.1 Stronglymonotoneoperator...................... 18 1.2.3.2 Ellipticandevolutionaryquasi-variationalinequalities....... 19 1.2.3.3 Evolutionarypartialdifferentialequation............... 20 1.2.3.4 Evolutionaryvariationalinequality.................. 21 1.2.4 Gronwall-typelemmas.............................. 21 1.2.5 DiscretizationandContactElements...................... 23 1.2.5.1 ApproximateVariationalApproximation............... 24 2 Thermo-electro-viscoelasticproblemwithlongmemory25 2.1 Mechanicalformulationoftheproblem......................... 26 2.2 Variationalformulation.................................. 30 2.3 Existenceanduniquenessofthesolution........................ 33 3 Numericalapproximationoftheproblem41 3.1 Approximatevariationalformulation.......................... 42 3.2 ErrorEstimateoftheApproximatedProblem..................... 43 General conclusion 49 Côte titre : MAM/0780 Numerical Study Of The Thermo-Electro-Viscoelastic Problem With Long Memory [document électronique] / Zineb Allal, Auteur ; Namira Lebri, Auteur . - [S.l.] : Sétif:UFA1, 2025 . - 1 vol (49 f.) ; 29 cm. Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Sub-differential Contact Elastic, Electro-elastic Electro-elasto-viscoplastic Finite elements Fixed point Evolution inequality Index. décimale : 510-Mathématique Résumé : The purpose of this work is to study a problem in contact mechanics involving thermo-electro-viscoelastic constitutive laws with long-term memory. The obtained results concern the existence and uniqueness of a weak solution. The thesis is structured in two parts: The first part recalls various contact mechanical model and presents the necessary mathematical tools. The second part focuses on the modeling and mathematical analysis of the considered contact problems. A numerical approach is also carried using a finite element scheme with implicit time discretization. Note de contenu : Contents Introduction 4 1 Modelingandmathematictools8 1.1 Modeling(thepiezoelectricproblem).......................... 9 1.1.1 Physicalframework............................... 9 1.1.2 Constitutivelaws................................. 10 1.1.2.1 Constitutivelawofelectroelasticmaterials.............. 11 1.1.2.2 Constitutivelawofthermo-electro-viscoelasticmaterialswithlong memory ................................. 11 1.1.3 Boundaryconditions............................... 12 1.1.3.1 Thedisplacementandtractionboundaryconditions......... 12 1.1.3.2 Theelectricalboundaryconditions.................. 12 1.1.3.3 SubdifferentialContactCondition................... 12 1.2 Mathematictools..................................... 14 1.2.1 Sobolevspace................................... 14 1.2.2 Spacesofvector-valuedfunctions........................ 17 1.2.3 ReviewofnonlinearanalysisinHilbertspaces................. 18 1.2.3.1 Stronglymonotoneoperator...................... 18 1.2.3.2 Ellipticandevolutionaryquasi-variationalinequalities....... 19 1.2.3.3 Evolutionarypartialdifferentialequation............... 20 1.2.3.4 Evolutionaryvariationalinequality.................. 21 1.2.4 Gronwall-typelemmas.............................. 21 1.2.5 DiscretizationandContactElements...................... 23 1.2.5.1 ApproximateVariationalApproximation............... 24 2 Thermo-electro-viscoelasticproblemwithlongmemory25 2.1 Mechanicalformulationoftheproblem......................... 26 2.2 Variationalformulation.................................. 30 2.3 Existenceanduniquenessofthesolution........................ 33 3 Numericalapproximationoftheproblem41 3.1 Approximatevariationalformulation.......................... 42 3.2 ErrorEstimateoftheApproximatedProblem..................... 43 General conclusion 49 Côte titre : MAM/0780

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
MAM/0780	MAM/0780	Mémoire	Bibliothèque des sciences	Anglais	Disponible Disponible

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