Numerical Methods for the Dynamic

Analysis of Two-Scale Incompressible

Nonlinear Structures

 

Contributions of the thesis



Time integration schemes in elastodynamics


  1. Bullet  Conservation analysis for standard schemes in nonlinear incompressible elastodynamics

  2. Bullet  Energy-controlling time integration schemes for nonlinear elasticity

  3. Bullet  Extensions to viscoelasticity and impact ( extending an idea from Oscar Gonzalez )



Mortar methods and Domain Decomposition


  1. BulletTwo-field discontinuous mortar formulation ( extending the ideas from Franco Brezzi and Donatella Marini )

  2. BulletProof of convergence for linearized elastodynamics 

  3. BulletIndependance of the coercivity constant with respect to the shape and the size of the subdomains with curved interfaces ( extension of an original idea from Jayadeep Gopalakrishnan , use of Susanne Brenner's equicontinuity argument , introduction of a generalized L. Ridgway Scott and Shangyou Zhang interpolation)

  4. BulletTwo-scale Dirichlet-Neumann preconditioners for systems with geometrical refinements on the boundary

  5. BulletNeutralization of fine scale boundary conditions



Download



  1. Bulletrésumé (in French)    [postscript]

  2. Bulletabstract (in English)    [postscript]


  4. Bulletfull-version.pdf (mainly written in English, 291 pages, 12 Mo)    [pdf]


  6. BulletCouverture / Cover    [pdf]

  7. BulletRemerciements - Table des Matières    [pdf]

  8. BulletChapter 1: Introduction (in French)    [pdf]

  9. BulletChapter 2: Elements de mécanique des milieux continus (in French)    [pdf]

  10. BulletChapter 3: Time integration in nonlinear elastodynamics (in English)    [pdf]

  11. BulletChapter 4: A stabilized discontinuous mortar formulation (in English)    [pdf]

  12. BulletChapter 5: Mortiers et contributions industrielles (in French)    [pdf]

  13. BulletChapter 6: Two-scale Dirichlet-Neumann preconditionners (in English)    [pdf]

  14. BulletChapter 7: Conclusion (in French) and Bibliography    [pdf]






  1. BulletFrancois Jouve

  2. BulletTod Laursen

  3. BulletClaude Le Bris

  4. BulletPatrick Le Tallec

  5. BulletFrédéric Nataf

  6. BulletOlivier Pironneau

  7. BulletAli Rezgui


Obtained with Highest Honors & Awarded by the “Prix de Thèse de l’Ecole Polytechnique” 2005


Latest erratum corrected: September 2005

 

Méthodes numériques pour la dynamique des structures

non-linéaires incompressibles à deux échelles


Thèse de Doctorat de l’Ecole Polytechnique, 2004

Spécialité: Mathématiques Appliquées
 
Defended at Ecole Polytechnique on September 20th, 2004 before the following Jury