Mathematical Analysis of Thin Plate Models: (24 Mathématiques et Applications)

This book is written for teachers, researchers and students who wish to learn about different thin plate models and to master the underlying mathematical approximation problems. It contains mainly new results and original applications for the research of delamination of multilayered structures.

Table of Contents:
I — Plate models for thin structures.- I.0 — A short description of the chapter.- I.1 — The three dimensionnal elastic-model.- I.2 — The Kirchhoff-Love assumption.- I.3 — The Kirchhof f-Love plate model.- I.4 — The Naghdi model revisited using mixed variational formulation.- I.5 — About the rest of the book.- References of Chapter I.- II — Variational formulations for bending plates.- II.0 — A brief summary of the chapter.- II. 1 — Why a mixed formulation for plates.- II.2 — The primal variational formulation for Kirchhoff-Love model.- II.3 — The Reissner-Mindlin-Naghdi model for plates.- II.4 — Natural duality techniques for the bending plate model.- II.5 — A comparison between the mixed method and the one of section II.2.4.- References of Chapter II.- III — Finite element approximations for several plate models.- III.0 — A summary of the chapter.- III. 1 — Basic results in finite element approximation.- III.2 — C1 elements.- III.3 — Primal finite element methods for bending plates.- III.4 — The penalty-duality finite element method for the bending plate model.- III.5 — Numerical approximation of the mixed formulation for a bending plate.- References of Chapter III.- IV — Numerical tests for the mixed finite element schemes.- IV.0 — A brief description of the chapter.- IV. 1 — Precision tests for the mixed formulation.- IV.2 Vectorial and parallel algorithms for mixed elements.- IV.3 — Concluding remarks.- References of Chapter IV.- V — A Numerical model for delamination of composite plates.- V.O — A brief description of the chapter.- V. 1 — What is delamination of thin multilayered plates.- V.2 — The three-dimensional multilayered composite plate model with delamination.- V.3 — A plate model for largedelamination.- V.4 — The three-dimensional energy release rate.- V.5 — The mechanical example and the numerical method.- V.6 — Concluding remarks.- References of Chapter V.