| Libellé du cours : | Continuum Mechanics |
|---|---|
| Département d'enseignement : | MSO / Mécanismes Structures Ouvrages |
| Responsable d'enseignement : | Monsieur TIEN TUAN DAO |
| Langue d'enseignement : | |
| Ects potentiels : | 0 |
| Grille des résultats : | |
| Code et libellé (hp) : | MR_STRAINS_CME - Continuum Mechanics |
Equipe pédagogique
Enseignants : Monsieur TIEN TUAN DAO
Intervenants extérieurs (entreprise, recherche, enseignement secondaire) : divers enseignants vacataires
Résumé
The purpose of this introductory course of continuum mechanics is to develop the generalization of rational mechanics to continuum media, to present the basic concepts for modeling continuous classical media, and to deduce conservation laws and to provide simple constitutive laws for fluid and for solid. Chapter 1: The Cartesian tensor algebra and tensor analysis: calculation of tensor fields scalar, vector and higher-order tensor invariance relationship and basic operations: scalar, vector, dyadic products… differential operators: gradient, divergence, curl and Laplacian. Stokes, Gauss and Green theorems; Reynolds transport theorem. Chapter 2: Kinematics of continuum media: body configuration and motion, description of motion through 2 approaches : material or Lagrangian and spatial or Eulerian), material derivative, velocity, acceleration, trajectory, streamline. Deformation gradient tensor and strain deformation homogeneous equation of the movement kinematics of the rigid body, and the velocity gradient tensor associated. Chapter 3: The dynamics of continuous media: conservation of mass, volume forces, contact forces, and Cauchy postulate, conservation of momentum and angular momentum, equation of motion of a continuous medium, the properties of the stress tensor Cauchy, and simple stress state examples Chapter 4: Energy: energy conservation, entropy and the first and second principle laws of thermodynamics. Chapter 5: The laws of classical behavior for simple fluids and solid : viscous Newtonian (compressible and incompressible), and applications to Fluid Mechanics: Navier-Stokes equations; linear elastic solid with small deformation, Navier equations. Examples of simple applications like fluid solid possible to obtain analytical solutions that illustrate the power of modeling and proposed.
Objectifs pédagogiques
On successful completion of the course students will be able to: ● Demonstrate a practical foundation in calculus and its applications; ● Demonstrate an understanding of matrices and eigenvectors; Demonstrate an awareness of common mathematical themes underlying different areas of mathematics (such as that of linearity).
Objectifs de développement durable
Modalités de contrôle de connaissance
Contrôle Continu
Commentaires:
Ressources en ligne
Pédagogie
Séquencement / modalités d'apprentissage
| Nombre d'heures en CM (Cours Magistraux) : | 18 |
|---|---|
| Nombre d'heures en TD (Travaux Dirigés) : | 32 |
| Nombre d'heures en TP (Travaux Pratiques) : | 0 |
| Nombre d'heures en Séminaire : | 0 |
| Nombre d'heures en Demi-séminaire : | 0 |
| Nombre d'heures élèves en TEA (Travail En Autonomie) : | 0 |
| Nombre d'heures élèves en TNE (Travail Non Encadré) : | 0 |
| Nombre d'heures en CB (Contrôle Bloqué) : | 0 |
| Nombre d'heures élèves en PER (Travail PERsonnel) : | 0 |
| Nombre d'heures en Heures Projets : | 0 |